 Rubic-Cube main code.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import cv2\n",
    "box=np.zeros((3,3,3,3),dtype=int)\n",
    "pos_map={4:0,1:1,5:2,7:3,3:4,2:5,8:6,6:7,0:8}\n",
    "face_axis={'r':np.array([1,0,0]),'o':np.array([-1,0,0]),'g':np.array([0,1,0]),'b':np.array([0,-1,0]),'y':np.array([0,0,1]),'w':np.array([0,0,-1])}\n",
    "secondLayerMiddleEle={'r':np.array([np.array([1,1,0]),np.array([1,0,0])]),'g':np.array([np.array([-1,1,0]),np.array([0,1,0])]),'o':np.array([np.array([-1,-1,0]),np.array([-1,0,0])]),'b':np.array([np.array([1,-1,0]),np.array([0,-1,0])])}\n",
    "tot_steps=0\n",
    "steps_dir={}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mask(image,w,h):\n",
    "    kernel = np.ones((5,5),np.uint8)\n",
    "    image = cv2.erode(image,kernel,iterations = 1)\n",
    "    contour,_=cv2.findContours(image,cv2.RETR_TREE,cv2.CHAIN_APPROX_SIMPLE)\n",
    "    ans=[]\n",
    "    for cnt in contour:\n",
    "        area=cv2.contourArea(cnt)\n",
    "        if(area<1000):\n",
    "            continue\n",
    "        m=cv2.moments(cnt)    \n",
    "        x=m['m10']/m['m00']\n",
    "        y=m['m01']/m['m00']\n",
    "        ans.append(min(round((x-w)/(2*w)),2) + (min(round((y-h)/(2*h)),2)*3))\n",
    "    return ans "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def face_color(image,x,y):\n",
    "    sq = [None] * 9\n",
    "    hs=cv2.cvtColor(image,cv2.COLOR_BGR2HSV)\n",
    "    mask1 = cv2.inRange(hs,np.array([0,70,50]),np.array([10,255,255]))\n",
    "    mask2=cv2.inRange(hs,np.array([170,20,50]),np.array([180,255,255]))\n",
    "    maskred=mask1+mask2\n",
    "    l=mask(maskred,x,y)\n",
    "    for i in l:\n",
    "        sq[i]='r'\n",
    "    maskyel = cv2.inRange(hs,np.array([22,40,40]),np.array([35,255,255]))\n",
    "    l=mask(maskyel,x,y)\n",
    "    for i in l:\n",
    "        sq[i]='y'\n",
    "    maskora = cv2.inRange(hs,np.array([12,40,40]),np.array([20,255,255]))\n",
    "    l=mask(maskora,x,y)\n",
    "    for i in l:\n",
    "        sq[i]='o'\n",
    "    maskgre = cv2.inRange(hs,np.array([35,40,40]),np.array([85,255,255]))\n",
    "    l=mask(maskgre,x,y)\n",
    "    for i in l:\n",
    "        sq[i]='g'\n",
    "    maskblu = cv2.inRange(hs,np.array([90,40,40]),np.array([125,255,255]))\n",
    "    l=mask(maskblu,x,y)\n",
    "    for i in l:\n",
    "        sq[i]='b'\n",
    "    maskwhi = cv2.inRange(hs,np.array([0,0,215]),np.array([1,1,255]))\n",
    "    l=mask(maskwhi,x,y)\n",
    "    for i in l:\n",
    "        sq[i]='w'\n",
    "    return sq   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(6):\n",
    "    face=cv2.imread(\"face\"+str(i)+\".jpeg\")\n",
    "    r = cv2.selectROI(face)\n",
    "    crop = face[int(r[1]):int(r[1]+r[3]),int(r[0]):int(r[0]+r[2])]\n",
    "    x1,y1,x2,y2=r\n",
    "    x=(x2-x1)/6\n",
    "    y=(y2-y1)/6 \n",
    "    \n",
    "    ans=face_color(crop,x,y)\n",
    "    centre_color=ans[4]\n",
    "    base=face_axis[ans[4]] \n",
    "    #assinging position to faces of squre by a bit of hard coding\n",
    "    face_sq=[base.copy() for i in range(9)]\n",
    "    \n",
    "    if(centre_color in ['r','g','o','b']):\n",
    "        for i in [0,1,2]:\n",
    "            face_sq[i][2]=1\n",
    "        for i in [6,7,8]:\n",
    "            face_sq[i][2]=-1\n",
    "    if(centre_color in ['r','y','w']):\n",
    "        for i in [2,5,8]:\n",
    "            face_sq[i][1]=1\n",
    "        for i in [0,3,6]:\n",
    "            face_sq[i][1]=-1\n",
    "    if(centre_color in ['o']):\n",
    "        for i in [2,5,8]:\n",
    "            face_sq[i][1]=-1\n",
    "        for i in [0,3,6]:\n",
    "            face_sq[i][1]=1\n",
    "    if(centre_color in ['w']):\n",
    "        for i in [0,1,2]:\n",
    "            face_sq[i][0]=1\n",
    "        for i in [6,7,8]:\n",
    "            face_sq[i][0]=-1\n",
    "    if(centre_color in ['y']):\n",
    "        for i in [0,1,2]:\n",
    "            face_sq[i][0]=-1\n",
    "        for i in [6,7,8]:\n",
    "            face_sq[i][0]=1        \n",
    "    if(centre_color in ['g']):\n",
    "        for i in [0,3,6]:\n",
    "            face_sq[i][0]=1\n",
    "        for i in [2,5,8]:\n",
    "            face_sq[i][0]=-1 \n",
    "    if(centre_color in ['b']):\n",
    "        for i in [0,3,6]:\n",
    "            face_sq[i][0]=-1\n",
    "        for i in [2,5,8]:\n",
    "            face_sq[i][0]=1\n",
    "    co_to_int={'r':1,'o':2,'g':3,'b':4,'y':5,'w':6,'n':0}\n",
    "    #ek box matrix me color store kiye hai....a bit like virtal cube\n",
    "    for i in range(9):\n",
    "        vec=face_sq[i]\n",
    "        box[vec[0]+1][vec[1]+1][vec[2]+1]+=co_to_int[ans[i]]*abs(base)\n",
    "key = cv2.waitKey(0)\n",
    "if(key == 27):\n",
    "    cv2.destroyAllWindows()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Hard coded box matrix\n",
    "'''box=[[[[6,1,3],\n",
    "   [6, 4 ,0],\n",
    "   [2, 4 ,5]],\n",
    "\n",
    "  [[4 ,0, 5],\n",
    "   [2, 0 ,0],\n",
    "   [6, 0, 3]],\n",
    "\n",
    "  [[2 ,5 ,3],\n",
    "   [3 ,2 ,0],\n",
    "   [4 ,1 ,6]]],\n",
    "\n",
    "\n",
    " [[[0, 6, 2],\n",
    "   [0 ,4, 0],\n",
    "   [0 ,4, 2]],\n",
    "\n",
    "  [[0, 0 ,6],\n",
    "   [0 ,0, 0],\n",
    "   [0 ,0, 5]],\n",
    "\n",
    "  [[0 ,1, 3],\n",
    "   [0 ,3 ,0],\n",
    "   [0 ,5 ,2]]],\n",
    "\n",
    "\n",
    " [[[4, 1, 5],\n",
    "   [1 ,4, 0],\n",
    "   [5 ,3 ,1]],\n",
    "\n",
    "  [[1 ,0, 6],\n",
    "   [1 ,0, 0],\n",
    "   [5 ,0 ,3]],\n",
    "\n",
    "  [[6 ,2, 4],\n",
    "   [5 ,1 ,0],\n",
    "   [6 ,2 ,3]]]]'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "def face(vec_co,color,face_matrix):\n",
    "    for i in color:\n",
    "        x=1\n",
    "        y=1\n",
    "        if i in [1,2,3,4]:\n",
    "            if 5 in color:\n",
    "                y=0\n",
    "            if 6 in color:\n",
    "                y=2\n",
    "        if i in [1,5,6]:\n",
    "            if 3 in color:\n",
    "                x=2\n",
    "            if 4 in color:\n",
    "                x=0\n",
    "        if i in [2]:\n",
    "            if 4 in color:\n",
    "                x=2\n",
    "            if 3 in color:\n",
    "                x=0                \n",
    "        if i in [5]:\n",
    "            if 2 in color:\n",
    "                y=0\n",
    "            if 1 in color:\n",
    "                y=2\n",
    "        if i in [6]:\n",
    "            if 1 in color:\n",
    "                y=0\n",
    "            if 2 in color:\n",
    "                y=2\n",
    "        if i in [3]:\n",
    "            if 1 in color:\n",
    "                x=0\n",
    "            if 2 in color:\n",
    "                x=2\n",
    "        if i in [4]:\n",
    "            if 2 in color:\n",
    "                x=0\n",
    "            if 1 in color:\n",
    "                x=2\n",
    "        i_color=np.zeros((3,),dtype=int)\n",
    "        i_color[color.index(i)]=1\n",
    "        face_matrix[i][pos_map[x+y*3]][0]=np.array(vec_co)\n",
    "        face_matrix[i][pos_map[x+y*3]][1]=np.array(vec_co)*np.array(i_color)\n",
    "    return face_matrix    \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "face_matrix=np.zeros((7,9,2,3),dtype=int)\n",
    "for i in range(3):\n",
    "    for j in range(3):\n",
    "        for k in range(3):\n",
    "            x=i-1\n",
    "            y=j-1\n",
    "            z=k-1\n",
    "            if(x or y or z):\n",
    "                face_matrix=face([x,y,z],list(box[i][j][k]),face_matrix)       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 1  0  0]\n",
      "  [ 1  0  0]]\n",
      "\n",
      " [[ 1  1  0]\n",
      "  [ 0  1  0]]\n",
      "\n",
      " [[ 0  1 -1]\n",
      "  [ 0  1  0]]\n",
      "\n",
      " [[ 1  0 -1]\n",
      "  [ 1  0  0]]\n",
      "\n",
      " [[ 1 -1  0]\n",
      "  [ 1  0  0]]\n",
      "\n",
      " [[ 1 -1  1]\n",
      "  [ 0  0  1]]\n",
      "\n",
      " [[-1 -1 -1]\n",
      "  [ 0 -1  0]]\n",
      "\n",
      " [[-1  1  1]\n",
      "  [ 0  1  0]]\n",
      "\n",
      " [[ 1 -1 -1]\n",
      "  [ 0 -1  0]]]\n",
      "[[[-1  0  0]\n",
      "  [-1  0  0]]\n",
      "\n",
      " [[ 0  1  1]\n",
      "  [ 0  0  1]]\n",
      "\n",
      " [[ 0 -1  1]\n",
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      "\n",
      " [[ 0 -1 -1]\n",
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      "\n",
      " [[-1  1  0]\n",
      "  [ 0  1  0]]\n",
      "\n",
      " [[-1 -1  1]\n",
      "  [-1  0  0]]\n",
      "\n",
      " [[ 1  1 -1]\n",
      "  [ 0  1  0]]\n",
      "\n",
      " [[ 1  1  1]\n",
      "  [ 0  1  0]]\n",
      "\n",
      " [[-1  1 -1]\n",
      "  [-1  0  0]]]\n",
      "[[[ 0  1  0]\n",
      "  [ 0  1  0]]\n",
      "\n",
      " [[ 1  0  1]\n",
      "  [ 0  0  1]]\n",
      "\n",
      " [[-1  1  0]\n",
      "  [-1  0  0]]\n",
      "\n",
      " [[-1  0  1]\n",
      "  [ 0  0  1]]\n",
      "\n",
      " [[ 0  1 -1]\n",
      "  [ 0  0 -1]]\n",
      "\n",
      " [[-1  1 -1]\n",
      "  [ 0  0 -1]]\n",
      "\n",
      " [[ 1  1  1]\n",
      "  [ 0  0  1]]\n",
      "\n",
      " [[-1 -1 -1]\n",
      "  [ 0  0 -1]]\n",
      "\n",
      " [[ 1 -1  1]\n",
      "  [ 0 -1  0]]]\n",
      "[[[ 0 -1  0]\n",
      "  [ 0 -1  0]]\n",
      "\n",
      " [[-1  0 -1]\n",
      "  [-1  0  0]]\n",
      "\n",
      " [[ 1 -1  0]\n",
      "  [ 0 -1  0]]\n",
      "\n",
      " [[-1 -1  0]\n",
      "  [ 0 -1  0]]\n",
      "\n",
      " [[ 0 -1  1]\n",
      "  [ 0 -1  0]]\n",
      "\n",
      " [[ 1 -1 -1]\n",
      "  [ 1  0  0]]\n",
      "\n",
      " [[-1  1  1]\n",
      "  [-1  0  0]]\n",
      "\n",
      " [[ 1  1 -1]\n",
      "  [ 0  0 -1]]\n",
      "\n",
      " [[-1 -1  1]\n",
      "  [ 0 -1  0]]]\n",
      "[[[ 0  0  1]\n",
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      "\n",
      " [[ 0  1  1]\n",
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      "\n",
      " [[ 1  0  1]\n",
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      "\n",
      " [[ 1  1  0]\n",
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      "\n",
      " [[-1  0 -1]\n",
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      "\n",
      " [[-1  1 -1]\n",
      "  [ 0  1  0]]\n",
      "\n",
      " [[ 1 -1  1]\n",
      "  [ 1  0  0]]\n",
      "\n",
      " [[ 1 -1 -1]\n",
      "  [ 0  0 -1]]\n",
      "\n",
      " [[-1 -1  1]\n",
      "  [ 0  0  1]]]\n",
      "[[[ 0  0 -1]\n",
      "  [ 0  0 -1]]\n",
      "\n",
      " [[ 1  0 -1]\n",
      "  [ 0  0 -1]]\n",
      "\n",
      " [[-1  0  1]\n",
      "  [-1  0  0]]\n",
      "\n",
      " [[ 0 -1 -1]\n",
      "  [ 0 -1  0]]\n",
      "\n",
      " [[-1 -1  0]\n",
      "  [-1  0  0]]\n",
      "\n",
      " [[-1 -1 -1]\n",
      "  [-1  0  0]]\n",
      "\n",
      " [[ 1  1  1]\n",
      "  [ 1  0  0]]\n",
      "\n",
      " [[ 1  1 -1]\n",
      "  [ 1  0  0]]\n",
      "\n",
      " [[-1  1  1]\n",
      "  [ 0  0  1]]]\n"
     ]
    }
   ],
   "source": [
    "for i in range(1,7):\n",
    "    print(face_matrix[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def printallfaces(face_matrix):\n",
    "    red=np.zeros((3,3),dtype=int)\n",
    "    orange=np.zeros((3,3),dtype=int)\n",
    "    green=np.zeros((3,3),dtype=int)\n",
    "    blue=np.zeros((3,3),dtype=int)\n",
    "    white=np.zeros((3,3),dtype=int)\n",
    "    yellow=np.zeros((3,3),dtype=int)\n",
    "    for i in range(1,7):\n",
    "        for j in range(9):\n",
    "            v1=list(face_matrix[i][j][0])\n",
    "            v2=list(face_matrix[i][j][1])\n",
    "            if(v2[0]==1):\n",
    "                x=-v1[2]+1\n",
    "                y=v1[1]+1\n",
    "                red[x][y]=i\n",
    "            elif(v2[0]==-1):\n",
    "                x=-v1[2]+1\n",
    "                y=-v1[1]+1\n",
    "                orange[x][y]=i\n",
    "            elif(v2[1]==1):\n",
    "                x=-v1[2]+1\n",
    "                y=-v1[0]+1\n",
    "                green[x][y]=i\n",
    "            elif(v2[1]==-1):\n",
    "                x=-v1[2]+1\n",
    "                y=v1[0]+1\n",
    "                blue[x][y]=i\n",
    "            elif(v2[2]==1):\n",
    "                x=v1[0]+1\n",
    "                y=v1[1]+1\n",
    "                yellow[x][y]=i\n",
    "            else:\n",
    "                x=-v1[0]+1\n",
    "                y=v1[1]+1\n",
    "                white[x][y]=i\n",
    "    print(\"red\",red,sep='\\n')\n",
    "    print(\"orange\",orange,sep='\\n')\n",
    "    print(\"green\",green,sep='\\n')\n",
    "    print(\"blue\",blue,sep='\\n')\n",
    "    print(\"yellow\",yellow,sep='\\n')\n",
    "    print(\"white\",white,sep='\\n')\n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "red\n",
      "[[5 5 6]\n",
      " [1 1 5]\n",
      " [4 1 6]]\n",
      "orange\n",
      "[[4 6 2]\n",
      " [3 2 6]\n",
      " [2 4 6]]\n",
      "green\n",
      "[[2 5 1]\n",
      " [1 3 2]\n",
      " [2 1 5]]\n",
      "blue\n",
      "[[4 4 3]\n",
      " [4 4 4]\n",
      " [1 6 1]]\n",
      "yellow\n",
      "[[5 3 6]\n",
      " [2 5 2]\n",
      " [1 3 3]]\n",
      "white\n",
      "[[5 6 4]\n",
      " [2 6 3]\n",
      " [3 5 3]]\n"
     ]
    }
   ],
   "source": [
    "printallfaces(face_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "#direction => center_piece\n",
    "#clock=1=>clockwise else anticlockwise\n",
    "def rotate(direction,face_matrix,clock,*data):\n",
    "    if(not('fake' in data)):\n",
    "        print(\"rotating\",direction,\"in\",clock)\n",
    "    if clock==1:\n",
    "        areaVec=direction\n",
    "    else:\n",
    "        areaVec=-direction\n",
    "    if(direction[0]!=0):\n",
    "        pos=0\n",
    "    elif(direction[1]!=0):\n",
    "        pos=1\n",
    "    else:\n",
    "        pos=2   \n",
    "    for i in range(1,7):\n",
    "        for j in range(9):\n",
    "            if(face_matrix[i][j][0][pos]==direction[pos]):\n",
    "                face_matrix[i][j][0]=np.cross(face_matrix[i][j][0],areaVec) + direction\n",
    "                if(face_matrix[i][j][1][pos]!=direction[pos]):\n",
    "                    face_matrix[i][j][1]=clock*np.cross(face_matrix[i][j][1],direction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random Shuffling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rotating [0 1 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "direction=[[1,0,0],[-1,0,0],[0,1,0],[0,-1,0],[0,0,1],[0,0,-1]]\n",
    "clock=[1,-1]\n",
    "shuffle=50\n",
    "for i in range(shuffle):\n",
    "    rotate(np.array(random.choice(direction)),face_matrix,random.choice(clock))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "def faltu(x,y):\n",
    "    if(x[0]==1):\n",
    "        if(y[1]==1):\n",
    "            move=1\n",
    "        else:\n",
    "            move=-1\n",
    "    elif(x[0]==-1):\n",
    "        if(y[1]==1):\n",
    "            move=-1\n",
    "        else:\n",
    "            move=1\n",
    "    elif(x[1]==1):\n",
    "        if(y[0]==1):\n",
    "            move=-1\n",
    "        else:\n",
    "            move=1\n",
    "    else:\n",
    "        if(y[0]==1):\n",
    "            move=1\n",
    "        else:\n",
    "            move=-1\n",
    "    return move        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def step1(face,face_matrix):\n",
    "    face=np.array(face)\n",
    "    if(face[0]==1):\n",
    "        sq=1\n",
    "    elif(face[0]==-1):\n",
    "        sq=3\n",
    "    elif(face[1]==1):\n",
    "        sq=2\n",
    "    else:\n",
    "        sq=4\n",
    "    print(\"step0\")\n",
    "    steps=0\n",
    "    if(face_matrix[6][sq][0][2]==1):\n",
    "        if(face_matrix[6][sq][1][2]!=1):\n",
    "            if((face_matrix[6][sq][1][0]==face[0])and(face_matrix[6][sq][1][1]==face[1])):\n",
    "                rotate(face,face_matrix,1)\n",
    "                steps+=1\n",
    "            elif((face_matrix[6][sq][1][0]==-face[0])and(face_matrix[6][sq][1][1]==-face[1])):\n",
    "                dir1=(face_matrix[6][sq][1]).copy()\n",
    "                rotate(dir1,face_matrix,-1)\n",
    "                rotate(np.array([0,0,-1]),face_matrix,1)\n",
    "                dir2=np.bitwise_xor(face_matrix[6][sq][0],face_matrix[6][sq][1])\n",
    "                rotate(dir2,face_matrix,1)\n",
    "                rotate(np.array([0,0,-1]),face_matrix,-1)\n",
    "                rotate(dir1,face_matrix,1)\n",
    "                steps+=5\n",
    "                return steps\n",
    "            else:\n",
    "                move2=faltu(face_matrix[6][sq][1],face)\n",
    "                dir1=(face_matrix[6][sq][1]).copy()\n",
    "                rotate(dir1,face_matrix,move2)\n",
    "                rotate(face,face_matrix,-move2)\n",
    "                rotate(dir1,face_matrix,-move2)\n",
    "                steps+=3\n",
    "                return steps\n",
    "    print(\"step1\")\n",
    "    if(face_matrix[6][sq][0][2]==-1):\n",
    "        if(face_matrix[6][sq][1][2]==-1):\n",
    "            if((face_matrix[6][sq][0][0]==face[0]) and (face_matrix[6][sq][0][1]==face[1])):\n",
    "                return steps\n",
    "            else:\n",
    "                temp=np.bitwise_xor(face_matrix[6][sq][0],face_matrix[6][sq][1])\n",
    "                if((temp[0]==-face[0])and(temp[1]==-face[1])):\n",
    "                    rotate(temp,face_matrix,1)\n",
    "                    rotate(temp,face_matrix,1)\n",
    "                    steps+=2\n",
    "                else:\n",
    "                    move2=faltu(face,temp)\n",
    "                    rotate(temp,face_matrix,move2)\n",
    "                    rotate(np.array([0,0,-1]),face_matrix,move2)\n",
    "                    rotate(temp,face_matrix,-move2)\n",
    "                    rotate(np.array([0,0,-1]),face_matrix,-move2)\n",
    "                    steps+=4\n",
    "                    return steps      \n",
    "        else:\n",
    "            if((face_matrix[6][sq][0][0]==-face[0]) and (face_matrix[6][sq][0][1]==-face[1])):\n",
    "                rotate(face_matrix[6][sq][1],face_matrix,1)\n",
    "                rotate(np.array([0,0,-1]),face_matrix,1)\n",
    "                rotate(np.bitwise_xor(face_matrix[6][sq][0],face_matrix[6][sq][1]),face_matrix,1)\n",
    "                rotate(np.array([0,0,-1]),face_matrix,-1)\n",
    "                steps+=4\n",
    "                return steps\n",
    "            elif((face_matrix[6][sq][0][0]==face[0]) and (face_matrix[6][sq][0][1]==face[1])):\n",
    "                rotate(face_matrix[6][sq][1],face_matrix,1)\n",
    "                rotate(np.array([0,0,-1]),face_matrix,-1)\n",
    "                rotate(np.bitwise_xor(face_matrix[6][sq][0],face_matrix[6][sq][1]),face_matrix,1)\n",
    "                rotate(np.array([0,0,-1]),face_matrix,1)\n",
    "                steps+=4\n",
    "                return steps\n",
    "            else:\n",
    "                move2=faltu(face,face_matrix[6][sq][0])\n",
    "                rotate(face_matrix[6][sq][1],face_matrix,move2)  \n",
    "                steps+=1\n",
    "    print(\"step2\")\n",
    "    if(face_matrix[6][sq][0][2]==0):\n",
    "        temp=np.bitwise_xor(face_matrix[6][sq][0],face_matrix[6][sq][1])\n",
    "        if(list(temp)==list(face)):\n",
    "            move2=faltu(face_matrix[6][sq][1],face_matrix[6][sq][0])\n",
    "            rotate(face,face_matrix,-move2)\n",
    "            steps+=1\n",
    "            return steps\n",
    "        elif(list(face_matrix[6][sq][1])==list(face)):\n",
    "            move2=faltu(face_matrix[6][sq][1],temp)\n",
    "            rotate(np.array([0,0,-1]),face_matrix,move2)\n",
    "            rotate(temp,face_matrix,-move2)\n",
    "            rotate(np.array([0,0,-1]),face_matrix,-move2)\n",
    "            steps+=3\n",
    "            return steps\n",
    "        elif((face_matrix[6][sq][1][0]==-face[0])and(face_matrix[6][sq][1][1]==-face[1])):\n",
    "            move2=faltu(face_matrix[6][sq][1],temp)\n",
    "            rotate(np.array([0,0,-1]),face_matrix,-move2)\n",
    "            rotate(temp,face_matrix,-move2)\n",
    "            rotate(np.array([0,0,-1]),face_matrix,move2)\n",
    "            steps+=3\n",
    "            return steps\n",
    "        else:\n",
    "            temp2=face_matrix[6][sq][1].copy()\n",
    "            rotate(temp2,face_matrix,1)\n",
    "            rotate(temp2,face_matrix,1)\n",
    "            move2=faltu(face_matrix[6][sq][1],face_matrix[6][sq][0])\n",
    "            rotate(face,face_matrix,-move2)\n",
    "            rotate(temp2,face_matrix,1)\n",
    "            rotate(temp2,face_matrix,1)\n",
    "            steps+=5\n",
    "            return steps\n",
    "    print(\"step3\")\n",
    "    if(face_matrix[6][sq][0][2]==1):\n",
    "        if((face_matrix[6][sq][0][0]==face[0])and(face_matrix[6][sq][0][1]==face[1])):\n",
    "            pass\n",
    "        elif((face_matrix[6][sq][0][0]==-face[0])and(face_matrix[6][sq][0][1]==-face[1])):\n",
    "            rotate(np.array([0,0,1]),face_matrix,1)\n",
    "            rotate(np.array([0,0,1]),face_matrix,1)\n",
    "            steps+=2\n",
    "        else:\n",
    "            move2=faltu(np.bitwise_xor(face_matrix[6][sq][0],face_matrix[6][sq][1]),face)\n",
    "            rotate(np.array([0,0,1]),face_matrix,-move2)\n",
    "            steps+=1      \n",
    "        rotate(face,face_matrix,1)\n",
    "        rotate(face,face_matrix,1)\n",
    "        steps+=2\n",
    "    return steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimizestep1(face_matrix):\n",
    "    itr=[[1,0,0], [0,1,0], [-1,0,0],[0,-1,0]]\n",
    "    steps=1000\n",
    "    for i in itr:\n",
    "        now1=0\n",
    "        face_matrix1=face_matrix.copy()\n",
    "        now1+=step1(i,face_matrix1)\n",
    "        for j in itr:\n",
    "            if j not in [i]:\n",
    "                now2=now1\n",
    "                face_matrix2=face_matrix1.copy()\n",
    "                now2+=step1(j,face_matrix2)\n",
    "                for k in itr:\n",
    "                    if k not in [i,j]:\n",
    "                        now3=now2\n",
    "                        face_matrix3=face_matrix2.copy()\n",
    "                        now3+=step1(k,face_matrix3)\n",
    "                        for l in itr:\n",
    "                            if l not in [i,j,k]:\n",
    "                                now4=now3\n",
    "                                now4+=step1(l,face_matrix3)\n",
    "                                if(now4<steps):\n",
    "                                    steps=now4\n",
    "                                    ans=[i,j,k,l]\n",
    "    return ans                                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0 -1  0] in -1\n",
      "step0\n",
      "step1\n",
      "rotating [-1  0  0] in -1\n",
      "step2\n",
      "rotating [ 0 -1  0] in -1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [-1  0  0] in -1\n",
      "step2\n",
      "rotating [ 0 -1  0] in -1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "step1\n",
      "rotating [-1  0  0] in -1\n",
      "step2\n",
      "rotating [ 0 -1  0] in -1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [-1  0  0] in -1\n",
      "step2\n",
      "rotating [ 0 -1  0] in -1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [1 0 0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [-1  0  0] in -1\n",
      "step2\n",
      "rotating [ 0 -1  0] in -1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0  0 -1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [ 0  0 -1] in -1\n",
      "step0\n",
      "step1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0  0 -1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [ 0  0 -1] in -1\n",
      "step0\n",
      "step1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n",
      "step2\n",
      "step3\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0 -1  0] in 1\n"
     ]
    }
   ],
   "source": [
    "ans=optimizestep1(face_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, -1, 0], [0, 1, 0], [1, 0, 0], [-1, 0, 0]]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "setting  1  piece\n",
      "step0\n",
      "step1\n",
      "rotating [-1  0  0] in -1\n",
      "step2\n",
      "rotating [ 0 -1  0] in -1\n",
      "\n",
      "setting  2  piece\n",
      "step0\n",
      "step1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "\n",
      "setting  3  piece\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0  0 -1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [ 0  0 -1] in 1\n",
      "\n",
      "setting  4  piece\n",
      "step0\n",
      "step1\n",
      "step2\n",
      "rotating [ 0  0 -1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [ 0  0 -1] in -1\n"
     ]
    }
   ],
   "source": [
    "steps=0\n",
    "for i in range(4):\n",
    "    print(\"\\nsetting \",i+1,\" piece\")\n",
    "    steps+=step1(ans[i],face_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total steps taken:-  12\n",
      "red\n",
      "[[6 1 2]\n",
      " [3 1 2]\n",
      " [2 1 4]]\n",
      "orange\n",
      "[[6 4 1]\n",
      " [1 2 5]\n",
      " [5 2 2]]\n",
      "green\n",
      "[[6 2 1]\n",
      " [5 3 4]\n",
      " [2 3 1]]\n",
      "blue\n",
      "[[5 1 4]\n",
      " [3 4 2]\n",
      " [3 4 3]]\n",
      "yellow\n",
      "[[4 5 3]\n",
      " [5 5 4]\n",
      " [1 3 4]]\n",
      "white\n",
      "[[6 6 5]\n",
      " [6 6 6]\n",
      " [5 6 3]]\n"
     ]
    }
   ],
   "source": [
    "print(\"total steps taken:- \",steps)\n",
    "printallfaces(face_matrix)\n",
    "tot_steps+=steps\n",
    "steps_dir[\"White cross\"]=steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimisingRotaion(face_matrix,p):\n",
    "    steps=[0,0]\n",
    "    a=[-1,1]\n",
    "    for i in a:\n",
    "        face_matrix3=face_matrix.copy()\n",
    "        if p==5:\n",
    "            while sum(face_matrix3[6][p][0]-np.array([0,0,1]))!=2:\n",
    "                rotate(np.array([0,0,1]),face_matrix3,i,\"fake\")\n",
    "                \n",
    "                steps[int((i+1)/2)]+=1\n",
    "        elif p==6:\n",
    "            while np.array_equal(face_matrix3[6][p][0],np.array([-1,1,1]))!=1:\n",
    "                rotate(np.array([0,0,1]),face_matrix3,i,\"fake\")\n",
    "                \n",
    "                steps[int((i+1)/2)]+=1\n",
    "        elif p==8:\n",
    "            while np.array_equal(face_matrix3[6][p][0],np.array([1,-1,1]))!=1:\n",
    "                rotate(np.array([0,0,1]),face_matrix3,i,\"fake\")\n",
    "                \n",
    "                steps[int((i+1)/2)]+=1\n",
    "        elif p==7:\n",
    "            while sum(face_matrix3[6][p][0]-np.array([0,0,1]))!=-2:\n",
    "                rotate(np.array([0,0,1]),face_matrix3,i,\"fake\")\n",
    "                \n",
    "                steps[int((i+1)/2)]+=1\n",
    "    return a[steps.index(min(steps))] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "def specificRotations(face_matrix,face,j):\n",
    "    rotate(face,face_matrix,j)\n",
    "    rotate(np.array([0,0,1]),face_matrix,j)\n",
    "    rotate(face,face_matrix,-j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "wCorners=[5,6,7,8]\n",
    "def initialRotation(face_matrix,p,nor):\n",
    "    if p==5:\n",
    "        pk=optimisingRotaion(face_matrix,p)\n",
    "        while sum(face_matrix[6][p][0]-np.array([0,0,1]))!=2:\n",
    "            rotate(np.array([0,0,1]),face_matrix,pk)\n",
    "            nor[0]+=1\n",
    "    elif p==6:\n",
    "        pk=optimisingRotaion(face_matrix,p)\n",
    "        while np.array_equal(face_matrix[6][p][0],np.array([-1,1,1]))!=1:\n",
    "            rotate(np.array([0,0,1]),face_matrix,pk)\n",
    "            nor[0]+=1\n",
    "    elif p==8:\n",
    "        pk=optimisingRotaion(face_matrix,p)\n",
    "        while np.array_equal(face_matrix[6][p][0],np.array([1,-1,1]))!=1:\n",
    "            rotate(np.array([0,0,1]),face_matrix,pk)\n",
    "            nor[0]+=1\n",
    "    elif p==7:\n",
    "        pk=optimisingRotaion(face_matrix,p)\n",
    "        while sum(face_matrix[6][p][0]-np.array([0,0,1]))!=-2:\n",
    "            rotate(np.array([0,0,1]),face_matrix,pk)\n",
    "            nor[0]+=1\n",
    " \n",
    "    \n",
    "def settingCorners(face_matrix,p,nor):\n",
    "    b=0\n",
    "    map1={5:np.array([1,1,-1]),6:np.array([-1,1,-1]),7:np.array([-1,-1,-1]),8:np.array([1,-1,-1])}\n",
    "    map2={1:np.array([1,0,0]),2:np.array([-1,0,0]),3:np.array([0,1,0]),4:np.array([0,-1,0])}\n",
    "    map3={5:np.array([1,0,0]),6:np.array([0,1,0]),7:np.array([-1,0,0]),8:np.array([0,-1,0])}\n",
    "    if(face_matrix[6][p][0][2]==-1):\n",
    "        print(p,'S3')\n",
    "        if(np.array_equal(face_matrix[6][p][0],map1[p])==1):\n",
    "            if(np.array_equal(face_matrix[6][p][1],np.array([0,0,-1]))!=1):\n",
    "                ux=face_matrix[6][p][0]-face_matrix[6][p][1]-np.array([0,0,-1])\n",
    "                vx=np.cross(face_matrix[6][p][1],ux)\n",
    "                copy=face_matrix[6][p][1].copy()\n",
    "                if(sum(vx)<0):\n",
    "                    specificRotations(face_matrix,copy,1)\n",
    "                    nor[0]+=3\n",
    "                else:\n",
    "                    specificRotations(face_matrix,copy,-1)\n",
    "                    nor[0]+=3 \n",
    "        else:\n",
    "            t=0\n",
    "            wc=wCorners.copy() \n",
    "            wc.remove(p)\n",
    "            for i in wc:\n",
    "                   if(np.array_equal(face_matrix[6][p][0],map1[i])==1):\n",
    "                        bbl=face_matrix[6][p][1].copy()\n",
    "                        t=1\n",
    "                        print(bbl)\n",
    "                        break\n",
    "            if(t==1):            \n",
    "                if(np.array_equal(bbl,np.array([0,0,-1]))==1):\n",
    "                    specificRotations(face_matrix,map3[p],-1)\n",
    "                    nor[0]+=3\n",
    "                else:\n",
    "                    v1=face_matrix[6][p][0]-bbl-np.array([0,0,-1])\n",
    "                    v2=np.cross(bbl,v1)\n",
    "                    if(sum(v2)<0):\n",
    "                        specificRotations(face_matrix,bbl,1)\n",
    "                        nor[0]+=3\n",
    "                    else:\n",
    "                        specificRotations(face_matrix,bbl,-1)\n",
    "                        nor[0]+=3            \n",
    "    z=[]\n",
    "    if face_matrix[6][p][0][2]==1 and face_matrix[6][p][1][2]==1:\n",
    "        print(p,'S2')\n",
    "        initialRotation(face_matrix,p,nor) \n",
    "        for i in range(3):\n",
    "            e=[]\n",
    "            for j in range(3):\n",
    "                if(i==j):\n",
    "                    e.append(face_matrix[6][p][0][i])\n",
    "                else:\n",
    "                    e.append(0)\n",
    "            if(e!=list(face_matrix[6][p][1])):\n",
    "                z.append(np.array(e))             \n",
    "        v5=np.cross(z[0],z[1])\n",
    "        if(sum(v5)>0):\n",
    "            rotate(z[0],face_matrix,-1)\n",
    "            rotate(np.array([0,0,1]),face_matrix,1)\n",
    "            rotate(np.array([0,0,1]),face_matrix,1)\n",
    "            rotate(z[0],face_matrix,1)\n",
    "            nor[0]+=4\n",
    "        else:\n",
    "            rotate(z[0],face_matrix,1)\n",
    "            rotate(np.array([0,0,1]),face_matrix,1)\n",
    "            rotate(np.array([0,0,1]),face_matrix,1)\n",
    "            rotate(z[0],face_matrix,-1)\n",
    "            nor[0]+=4\n",
    "    k=np.array([0,0,0])\n",
    "    if face_matrix[6][p][0][2]==1 and face_matrix[6][p][1][2]!=1 and face_matrix[6][p][1][2]!=-1:\n",
    "        print(p,\"S1\")\n",
    "        initialRotation(face_matrix,p,nor)\n",
    "        print(face_matrix[6][p][1])\n",
    "        k=face_matrix[6][p][1].copy()          \n",
    "        v3=face_matrix[6][p][0]-k-np.array([0,0,1])\n",
    "        v4=np.cross(k,v3)\n",
    "        if(sum(v4)<0):   \n",
    "            specificRotations(face_matrix,k,1)\n",
    "            nor[0]+=3\n",
    "        if(sum(v4)>0): \n",
    "            specificRotations(face_matrix,k,-1)\n",
    "            nor[0]+=3\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "def optimisingSolvingWhiteCorners(face_matrix):\n",
    "    combinations=list(itertools.permutations(wCorners))\n",
    "    print(combinations)\n",
    "    cmp=[]\n",
    "    for i in combinations:\n",
    "        nor=[0]\n",
    "        kg=face_matrix.copy()\n",
    "        for m in range(3):\n",
    "            for j in i:\n",
    "                settingCorners(kg,j,nor)    \n",
    "        cmp.append(nor) \n",
    "    print(cmp)\n",
    "    return combinations[cmp.index(min(cmp))]\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(5, 6, 7, 8), (5, 6, 8, 7), (5, 7, 6, 8), (5, 7, 8, 6), (5, 8, 6, 7), (5, 8, 7, 6), (6, 5, 7, 8), (6, 5, 8, 7), (6, 7, 5, 8), (6, 7, 8, 5), (6, 8, 5, 7), (6, 8, 7, 5), (7, 5, 6, 8), (7, 5, 8, 6), (7, 6, 5, 8), (7, 6, 8, 5), (7, 8, 5, 6), (7, 8, 6, 5), (8, 5, 6, 7), (8, 5, 7, 6), (8, 6, 5, 7), (8, 6, 7, 5), (8, 7, 5, 6), (8, 7, 6, 5)]\n",
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "6 S3\n",
      "[ 0  0 -1]\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "7 S1\n",
      "rotating [0 0 1] in 1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "8 S2\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "8 S1\n",
      "rotating [0 0 1] in -1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "5 S3\n",
      "6 S1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "7 S3\n",
      "8 S3\n",
      "5 S3\n",
      "6 S3\n",
      "7 S3\n",
      "8 S3\n",
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "6 S3\n",
      "[ 0  0 -1]\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "8 S2\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "8 S1\n",
      "rotating [0 0 1] in -1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "7 S2\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "7 S1\n",
      "rotating [0 0 1] in 1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "5 S3\n",
      "6 S2\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "6 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "8 S3\n",
      "7 S3\n",
      "5 S3\n",
      "6 S3\n",
      "8 S3\n",
      "7 S3\n",
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "7 S1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "6 S3\n",
      "[ 0  0 -1]\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "8 S1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "5 S3\n",
      "7 S3\n",
      "6 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "8 S3\n",
      "5 S3\n",
      "7 S3\n",
      "6 S3\n",
      "8 S3\n",
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "7 S1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "8 S1\n",
      "rotating [0 0 1] in -1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "6 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
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      "rotating [-1  0  0] in -1\n",
      "5 S3\n",
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      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
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      "rotating [0 1 0] in -1\n",
      "8 S2\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
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      "rotating [1 0 0] in -1\n",
      "8 S1\n",
      "rotating [0 0 1] in -1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
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      "6 S1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in -1\n",
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      "rotating [0 1 0] in 1\n",
      "7 S1\n",
      "rotating [0 0 1] in 1\n",
      "[ 0 -1  0]\n",
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      "5 S3\n",
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      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
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      "8 S2\n",
      "rotating [0 0 1] in 1\n",
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      "rotating [1 0 0] in -1\n",
      "8 S1\n",
      "rotating [0 0 1] in -1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
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      "7 S1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
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      "6 S1\n",
      "rotating [0 0 1] in -1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in -1\n",
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      "5 S3\n",
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      "[ 0  0 -1]\n",
      "rotating [0 1 0] in -1\n",
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      "rotating [0 1 0] in 1\n",
      "5 S3\n",
      "[-1  0  0]\n",
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      "5 S1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
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      "rotating [0 1 0] in -1\n",
      "7 S1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
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      "8 S3\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in -1\n",
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      "rotating [0 1 0] in 1\n",
      "8 S1\n",
      "rotating [0 0 1] in -1\n",
      "[ 0 -1  0]\n",
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      "6 S1\n",
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      "[-1  0  0]\n",
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      "5 S3\n",
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      "[ 0  0 -1]\n",
      "rotating [0 1 0] in -1\n",
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      "5 S3\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
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      "5 S1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
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      "8 S3\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in -1\n",
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      "8 S1\n",
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      "[ 0 -1  0]\n",
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      "7 S1\n",
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      "[ 0 -1  0]\n",
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      "6 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
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      "5 S3\n",
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      "[ 0  0 -1]\n",
      "rotating [0 1 0] in -1\n",
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      "7 S1\n",
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      "rotating [0 0 1] in -1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
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      "5 S3\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
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      "5 S1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
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      "8 S1\n",
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      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
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      "6 S1\n",
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      "[0 1 0]\n",
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      "7 S3\n",
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      "[ 0  0 -1]\n",
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      "7 S1\n",
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      "[ 0 -1  0]\n",
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      "8 S1\n",
      "[ 0 -1  0]\n",
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      "5 S3\n",
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      "5 S1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
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      "6 S1\n",
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      "7 S3\n",
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      "8 S1\n",
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      "[ 0 -1  0]\n",
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      "5 S3\n",
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      "5 S1\n",
      "[0 1 0]\n",
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      "7 S2\n",
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      "7 S1\n",
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      "6 S1\n",
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      "8 S1\n",
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      "[ 0 -1  0]\n",
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      "7 S1\n",
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      "5 S3\n",
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      "5 S1\n",
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      "6 S1\n",
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      "[0 1 0]\n",
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      "[ 0 -1  0]\n",
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      "5 S1\n",
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      "[0 1 0]\n",
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      "6 S3\n",
      "[ 0  0 -1]\n",
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      "8 S3\n",
      "[-1  0  0]\n",
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      "rotating [0 0 1] in 1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rotating [-1  0  0] in -1\n",
      "8 S1\n",
      "rotating [0 0 1] in 1\n",
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      "5 S1\n",
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      "6 S1\n",
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      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "6 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "7 S1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "8 S3\n",
      "5 S3\n",
      "6 S3\n",
      "7 S3\n",
      "8 S3\n",
      "5 S3\n",
      "6 S3\n",
      "7 S3\n",
      "8 S1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "5 S2\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "7 S1\n",
      "rotating [0 0 1] in 1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "6 S2\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "6 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "8 S3\n",
      "5 S3\n",
      "7 S3\n",
      "6 S3\n",
      "8 S3\n",
      "5 S3\n",
      "7 S3\n",
      "6 S3\n",
      "8 S1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "6 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "5 S2\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "7 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "8 S3\n",
      "6 S3\n",
      "5 S3\n",
      "7 S3\n",
      "8 S3\n",
      "6 S3\n",
      "5 S3\n",
      "7 S3\n",
      "8 S1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "6 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "7 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "5 S1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 0 1] in -1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "8 S3\n",
      "6 S3\n",
      "7 S3\n",
      "5 S3\n",
      "8 S3\n",
      "6 S3\n",
      "7 S3\n",
      "5 S3\n",
      "8 S1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "7 S1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 0 1] in -1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "5 S2\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "6 S1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "8 S3\n",
      "7 S3\n",
      "5 S3\n",
      "6 S3\n",
      "8 S3\n",
      "7 S3\n",
      "5 S3\n",
      "6 S3\n",
      "8 S1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "7 S1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 0 1] in -1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "6 S1\n",
      "rotating [0 0 1] in 1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[1 0 0]\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "8 S3\n",
      "7 S3\n",
      "6 S3\n",
      "5 S3\n",
      "8 S3\n",
      "7 S3\n",
      "6 S3\n",
      "5 S3\n",
      "[[22], [34], [17], [15], [20], [20], [23], [24], [23], [21], [29], [21], [23], [18], [19], [24], [16], [16], [24], [25], [20], [16], [19], [16]]\n",
      "(5, 7, 8, 6)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "ans=optimisingSolvingWhiteCorners(face_matrix)\n",
    "print(ans)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 S1\n",
      "rotating [0 0 1] in 1\n",
      "[0 1 0]\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "7 S1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "8 S1\n",
      "rotating [0 0 1] in -1\n",
      "[ 0 -1  0]\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "6 S1\n",
      "rotating [0 0 1] in -1\n",
      "[-1  0  0]\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "5 S3\n",
      "7 S3\n",
      "8 S3\n",
      "6 S3\n",
      "5 S3\n",
      "7 S3\n",
      "8 S3\n",
      "6 S3\n",
      "steps[15]\n"
     ]
    }
   ],
   "source": [
    "def solvingWhiteCorners(face_matrix):\n",
    "    nor=[0]\n",
    "    for j in range(3):\n",
    "        for i in ans:\n",
    "            settingCorners(face_matrix,i,nor)\n",
    "    print(\"steps\"+str(nor)) \n",
    "    return nor[0]\n",
    "step=solvingWhiteCorners(face_matrix) \n",
    "tot_steps+=step\n",
    "steps_dir[\"White corner\"]=step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "red\n",
      "[[4 2 3]\n",
      " [3 1 5]\n",
      " [1 1 1]]\n",
      "orange\n",
      "[[5 2 5]\n",
      " [4 2 2]\n",
      " [2 2 2]]\n",
      "green\n",
      "[[5 1 2]\n",
      " [1 3 5]\n",
      " [3 3 3]]\n",
      "blue\n",
      "[[2 3 5]\n",
      " [5 4 1]\n",
      " [4 4 4]]\n",
      "yellow\n",
      "[[4 4 3]\n",
      " [5 5 4]\n",
      " [1 3 1]]\n",
      "white\n",
      "[[6 6 6]\n",
      " [6 6 6]\n",
      " [6 6 6]]\n"
     ]
    }
   ],
   "source": [
    "printallfaces(face_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Second Layer\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we have tried to solve the second layer of the cube"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ansIsSame(ans1,ans2):\n",
    "    if list(ans1[0])==list(ans2[0]) and ans1[1]==ans2[1]:\n",
    "        return True\n",
    "    else:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "def secondLayerEle(face_matrix):\n",
    "    elem_req=[]\n",
    "    index=[]\n",
    "    red_green=[face_matrix[1,2],face_matrix[3,4]]\n",
    "    green_orange=[face_matrix[3,2],face_matrix[2,4]]\n",
    "    orange_blue=[face_matrix[2,2],face_matrix[4,4]]\n",
    "    blue_red=[face_matrix[4,2],face_matrix[1,4]]\n",
    "    \n",
    "    order=['rg','go','ob','br']\n",
    "    \n",
    "    elem_req.append(red_green)\n",
    "    elem_req.append(green_orange)\n",
    "    elem_req.append(orange_blue)\n",
    "    elem_req.append(blue_red)\n",
    "    \n",
    "    index.append([[1,2],[3,4]])\n",
    "    index.append([[3,2],[2,4]])\n",
    "    index.append([[2,2],[4,4]])\n",
    "    index.append([[4,2],[1,4]])\n",
    "    \n",
    "    return elem_req,order,index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rightTriger(face,face_matrix):\n",
    "    ans=[]\n",
    "    right_face=np.cross(np.array([0,0,1]),face)\n",
    "    \n",
    "    rotate(right_face,face_matrix,1)\n",
    "    ans.append((right_face,1))\n",
    "    \n",
    "    rotate(np.array([0,0,1]),face_matrix,1)\n",
    "    ans.append(([0,0,1],1))\n",
    "    \n",
    "    rotate(right_face,face_matrix,-1)\n",
    "    ans.append((right_face,-1))\n",
    "   \n",
    "    return ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "def leftTriger(face,face_matrix):\n",
    "    left_face=np.cross(face,np.array([0,0,1]))\n",
    "    ans=[]\n",
    "    \n",
    "    rotate(left_face,face_matrix,-1)\n",
    "    ans.append((left_face,-1))\n",
    "    \n",
    "    rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "    ans.append(([0,0,1],-1))\n",
    "    \n",
    "    rotate(left_face,face_matrix,1)\n",
    "    ans.append((left_face,1))\n",
    "    \n",
    "    return ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "def firstCaseSecondLayer(face_matrix,side_ele,side_color,top_ele,top_color):\n",
    "    final_dir=face_axis[side_color]\n",
    "    curr_dir=np.copy(side_ele[1])\n",
    "    ans=[]\n",
    "    while(list(curr_dir)!=list(final_dir)):\n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "        curr_dir=np.cross(curr_dir,np.array([0,0,1]))\n",
    "        ans.append(([0,0,1],1))\n",
    "    #Now the side color matches the center piece\n",
    "    top_color_dir=face_axis[top_color]\n",
    "    cross_prd=np.cross(final_dir,top_color_dir)\n",
    "    if list(cross_prd)==[0,0,1]:\n",
    "        # the top color centre_piece is in right\n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "        ans.append(([0,0,1],1))\n",
    "        ans=ans+rightTriger(final_dir,face_matrix)\n",
    "        # Now a white piece is removed so I have to get it back to the same \n",
    "                \n",
    "        rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "        ans.append(([0,0,1],-1))\n",
    "        ans=ans+leftTriger(top_color_dir,face_matrix)\n",
    "        # Now its done\n",
    "    else:\n",
    "        #the top color center_piece is in left\n",
    "        rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "        ans.append(([0,0,1],-1))\n",
    "        ans=ans+leftTriger(final_dir,face_matrix)\n",
    "        # Now a white piece is removed so I have to get it back to the same \n",
    "                \n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "        ans.append(([0,0,1],1))\n",
    "        ans=ans+rightTriger(top_color_dir,face_matrix)\n",
    "    return ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solveSecondLayer(face_matrix,ele,order,index):\n",
    "    ans=[]\n",
    "    for i in range(len(ele)):\n",
    "        fir_cubit,sec_cubit=ele[i]\n",
    "        fir_color,sec_color=order[i]\n",
    "        fir_index,sec_index=index[i]\n",
    "        if list(secondLayerMiddleEle[fir_color][0])==list(fir_cubit[0]) and list(secondLayerMiddleEle[fir_color][1])==list(fir_cubit[1]):\n",
    "            continue\n",
    "        if list(fir_cubit[1])!=[0,0,1] and list(sec_cubit[1])!=[0,0,1]:\n",
    "            cross_prd=np.cross(fir_cubit[1],sec_cubit[1])\n",
    "            if cross_prd[2]==1:\n",
    "                #the second cubit is in left\n",
    "                ans=ans+leftTriger(sec_cubit[1],face_matrix)\n",
    "                rotate(np.array([0,0,1]),face_matrix,1)\n",
    "                ans.append([[0,0,1],1])\n",
    "                ans=ans+rightTriger(fir_cubit[1],face_matrix)\n",
    "                \n",
    "            else:\n",
    "                #the first cubit is in left\n",
    "                ans=ans+leftTriger(fir_cubit[1],face_matrix)\n",
    "                rotate(np.array([0,0,1]),face_matrix,1)\n",
    "                ans.append([[0,0,1],1])\n",
    "                ans=ans+rightTriger(sec_cubit[1],face_matrix)\n",
    "                \n",
    "            fir_cubit=face_matrix[fir_index[0],fir_index[1]]\n",
    "            sec_cubit=face_matrix[sec_index[0],sec_index[1]]\n",
    "        if list(fir_cubit[1]) == [0,0,1]:\n",
    "            ans=ans+firstCaseSecondLayer(face_matrix,sec_cubit,sec_color,fir_cubit,fir_color)\n",
    "        elif list(sec_cubit[1])==[0,0,1]:\n",
    "            ans=ans+firstCaseSecondLayer(face_matrix,fir_cubit,fir_color,sec_cubit,sec_color)\n",
    "            \n",
    "    return ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimiseAnsList(ans):\n",
    "    optimisedAns=[]\n",
    "    length=len(ans)\n",
    "    i=0\n",
    "    while(i<length):\n",
    "        if (len(optimisedAns)>=2 and list(optimisedAns[-1][0])==list(optimisedAns[-2][0]) and optimisedAns[-1][1]==-optimisedAns[-2][1]):\n",
    "            del optimisedAns[-1]\n",
    "            del optimisedAns[-1]\n",
    "        if (i<=length-3 and ansIsSame(ans[i],ans[i+1]) and ansIsSame(ans[i+1],ans[i+2])):\n",
    "            optimisedAns.append([ans[i][0],-ans[i][1]])\n",
    "            i+=3\n",
    "        elif (len(optimisedAns)!=0 and list(optimisedAns[-1][0])==list(ans[i][0]) and optimisedAns[-1][1]==-ans[i][1]):\n",
    "            del optimisedAns[-1]\n",
    "            i+=1\n",
    "        else:\n",
    "            optimisedAns.append(ans[i])\n",
    "            i+=1\n",
    "    return optimisedAns    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimisedSolveSecondLayer(face_matrix):\n",
    "    ele,order,index=secondLayerEle(face_matrix)\n",
    "    perm_ele=list(itertools.permutations(ele))\n",
    "    perm_order=list(itertools.permutations(order))\n",
    "    perm_index=list(itertools.permutations(index))\n",
    "    \n",
    "    superOptimisedAns=[]\n",
    "    \n",
    "    min_ele=[]\n",
    "    min_order=[]\n",
    "    min_index=[]\n",
    "    \n",
    "    \n",
    "    \n",
    "    for i in range(len(perm_ele)):\n",
    "        face_matrix_copy=face_matrix.copy()\n",
    "        ele_i=perm_ele[i]\n",
    "        order_i=perm_order[i]\n",
    "        index_i=perm_index[i]\n",
    "        \n",
    "        ans=solveSecondLayer(face_matrix_copy,ele_i,order_i,index_i)\n",
    "        \n",
    "        optimisedAns=optimiseAnsList(ans)\n",
    "        \n",
    "        if i==0:\n",
    "            superOptimisedAns=optimisedAns\n",
    "            min_ele=ele_i\n",
    "            min_order=order_i\n",
    "            min_index=index_i\n",
    "            \n",
    "        elif len(superOptimisedAns)>len(optimisedAns):\n",
    "            superOptimisedAns=optimisedAns\n",
    "            min_ele=ele_i\n",
    "            min_order=order_i\n",
    "            min_index=index_i\n",
    "        print(\"Got\",i)\n",
    "    \n",
    "    _=solveSecondLayer(face_matrix,min_ele,min_order,min_index)\n",
    "    return superOptimisedAns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "Got 0\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "Got 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "Got 2\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "Got 3\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "Got 4\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "Got 5\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "Got 6\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "Got 7\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "Got 8\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "Got 9\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "Got 10\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "Got 11\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "Got 12\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "Got 13\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "Got 14\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "Got 15\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "Got 16\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "Got 17\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "Got 18\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "Got 19\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "Got 20\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "Got 21\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "Got 22\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "Got 23\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [ 0 -1  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in 1\n"
     ]
    }
   ],
   "source": [
    "optimisedAns=optimisedSolveSecondLayer(face_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30\n"
     ]
    }
   ],
   "source": [
    "print(len(optimisedAns))\n",
    "tot_steps+=len(optimisedAns)\n",
    "steps_dir[\"2nd layer\"]=len(optimisedAns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "red\n",
      "[[3 5 2]\n",
      " [1 1 1]\n",
      " [1 1 1]]\n",
      "orange\n",
      "[[4 1 5]\n",
      " [2 2 2]\n",
      " [2 2 2]]\n",
      "green\n",
      "[[5 5 2]\n",
      " [3 3 3]\n",
      " [3 3 3]]\n",
      "blue\n",
      "[[4 4 1]\n",
      " [4 4 4]\n",
      " [4 4 4]]\n",
      "yellow\n",
      "[[1 5 5]\n",
      " [5 5 3]\n",
      " [5 2 3]]\n",
      "white\n",
      "[[6 6 6]\n",
      " [6 6 6]\n",
      " [6 6 6]]\n"
     ]
    }
   ],
   "source": [
    "printallfaces(face_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thirdEdgeEle(face_matrix):\n",
    "    yell_top=face_matrix[5,1]\n",
    "    yell_right=face_matrix[5,2]\n",
    "    yell_bottom=face_matrix[5,3]\n",
    "    yell_left=face_matrix[5,4]\n",
    "    \n",
    "    face_dir=[]\n",
    "    ele_pos=[]\n",
    "    pattern=''\n",
    "    front_face=np.array([1,0,0])\n",
    "    index=[]\n",
    "    \n",
    "    face_dir.append(list(yell_top[1]))\n",
    "    face_dir.append(list(yell_right[1]))\n",
    "    face_dir.append(list(yell_bottom[1]))\n",
    "    face_dir.append(list(yell_left[1]))\n",
    "    \n",
    "    ele_pos.append(yell_top[0])\n",
    "    ele_pos.append(yell_right[0])\n",
    "    ele_pos.append(yell_bottom[0])\n",
    "    ele_pos.append(yell_left[0])\n",
    "    \n",
    "    \n",
    "    if face_dir[0]!=[0,0,1] and face_dir[1]!=[0,0,1] and face_dir[2]!=[0,0,1] and face_dir[3]!=[0,0,1]:\n",
    "        pattern='dot'\n",
    "        return front_face,pattern\n",
    "    elif face_dir[0]==[0,0,1] and face_dir[1]==[0,0,1] and face_dir[2]==[0,0,1] and face_dir[3]==[0,0,1]:\n",
    "        pattern='cross'\n",
    "        return front_face,pattern\n",
    "    for i in range(4):\n",
    "        if face_dir[i]==[0,0,1]:\n",
    "            index.append(i)\n",
    "    a=ele_pos[index[0]]-np.array([0,0,1])\n",
    "    b=ele_pos[index[1]]-np.array([0,0,1])\n",
    "    \n",
    "    aCrossb=np.cross(a,b)\n",
    "    \n",
    "    if list(aCrossb)==[0,0,0]:\n",
    "        pattern='bar'\n",
    "        front_face=np.cross(np.array([0,0,1]),a)\n",
    "        \n",
    "        return front_face,pattern\n",
    "    elif list(aCrossb)==[0,0,1]:\n",
    "        pattern='L'\n",
    "        front_face=-a\n",
    "        return front_face,pattern\n",
    "    elif list(aCrossb)==[0,0,-1]:\n",
    "        pattern='L'\n",
    "        front_face=-b\n",
    "        return front_face,pattern\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0]\n",
      "L\n"
     ]
    }
   ],
   "source": [
    "front_face,pattern=thirdEdgeEle(face_matrix)\n",
    "print(front_face)\n",
    "print(pattern)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "def makeYellowCross(face_matrix):\n",
    "    front_face,pattern=thirdEdgeEle(face_matrix)\n",
    "    front_face=np.copy(front_face)\n",
    "    up_face=np.array([0,0,1])\n",
    "    right_face=np.cross(up_face,front_face)\n",
    "    back_face=-front_face\n",
    "    left_face=-right_face\n",
    "    ans=[]\n",
    "    \n",
    "    if pattern=='bar':\n",
    "        #F\n",
    "        rotate(front_face,face_matrix,1)\n",
    "        ans.append([front_face,1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #F'\n",
    "        rotate(front_face,face_matrix,-1)\n",
    "        ans.append([front_face,-1])\n",
    "    elif pattern=='L':\n",
    "        #F\n",
    "        rotate(front_face,face_matrix,1)\n",
    "        ans.append([front_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #F'\n",
    "        rotate(front_face,face_matrix,-1)\n",
    "        ans.append([front_face,-1])\n",
    "    elif pattern=='dot':\n",
    "        #F\n",
    "        rotate(front_face,face_matrix,1)\n",
    "        ans.append([front_face,1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #S\n",
    "        rotate(front_face,face_matrix,-1)\n",
    "        rotate(back_face,face_matrix,1)\n",
    "        ans.append([front_face,-1])\n",
    "        ans.append([back_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #L\n",
    "        rotate(left_face,face_matrix,1)\n",
    "        ans.append([left_face,1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #L'\n",
    "        rotate(left_face,face_matrix,-1)\n",
    "        ans.append([left_face,-1])\n",
    "        #f'\n",
    "        rotate(back_face,face_matrix,-1)\n",
    "        ans.append([back_face,-1])\n",
    "    return ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [1 0 0] in -1\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "ans=makeYellowCross(face_matrix)\n",
    "print(len(ans))\n",
    "tot_steps+=len(ans)\n",
    "steps_dir[\"yellow cross\"]=len(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "red\n",
      "[[2 3 1]\n",
      " [1 1 1]\n",
      " [1 1 1]]\n",
      "orange\n",
      "[[4 2 4]\n",
      " [2 2 2]\n",
      " [2 2 2]]\n",
      "green\n",
      "[[3 1 5]\n",
      " [3 3 3]\n",
      " [3 3 3]]\n",
      "blue\n",
      "[[5 4 3]\n",
      " [4 4 4]\n",
      " [4 4 4]]\n",
      "yellow\n",
      "[[2 5 1]\n",
      " [5 5 5]\n",
      " [5 5 5]]\n",
      "white\n",
      "[[6 6 6]\n",
      " [6 6 6]\n",
      " [6 6 6]]\n"
     ]
    }
   ],
   "source": [
    "printallfaces(face_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thirdCornerPieces(face_matrix):\n",
    "    top_right=face_matrix[5,5]\n",
    "    bottom_right=face_matrix[5,6]\n",
    "    bottom_left=face_matrix[5,7]\n",
    "    top_left=face_matrix[5,8]\n",
    "    ele_pos=[[-1,1,1],[1,1,1],[1,-1,1],[-1,-1,1]]\n",
    "    \n",
    "    face_dir=[1,2,3,4]\n",
    "    \n",
    "    face_dir[ele_pos.index(list(top_right[0]))]=top_right[1]\n",
    "    face_dir[ele_pos.index(list(bottom_right[0]))]=bottom_right[1]\n",
    "    face_dir[ele_pos.index(list(bottom_left[0]))]=bottom_left[1]\n",
    "    face_dir[ele_pos.index(list(top_left[0]))]=top_left[1]\n",
    "    \n",
    "    front_face=np.array([0,0,0])\n",
    "    pattern=''\n",
    "    \n",
    "    count=0\n",
    "    face_index=[]\n",
    "    \n",
    "    for i in range(4):\n",
    "        if list(face_dir[i])==[0,0,1]:\n",
    "            count+=1\n",
    "            face_index.append(i)\n",
    "    \n",
    "    if count==0:\n",
    "        for i in range(4):\n",
    "            if list(np.cross(face_dir[i],np.array([0,0,1])))==list(face_dir[(i+1)%4]) and list(face_dir[(i+3)%4])!=list(face_dir[i]):\n",
    "                front_face=face_dir[i]\n",
    "                pattern='Pi'\n",
    "                return front_face,pattern\n",
    "        front_face=face_dir[0]\n",
    "        pattern='H'\n",
    "        return front_face,pattern\n",
    "    elif count==1:\n",
    "        index=face_index[0]\n",
    "        temp=[[-1,0,0],[0,1,0],[1,0,0],[0,-1,0]]\n",
    "        if list(face_dir[(index+3)%4])==temp[index]:\n",
    "            front_face=face_dir[(index+3)%4]\n",
    "            pattern='sune'\n",
    "            return front_face,pattern\n",
    "        front_face=face_dir[(index+2)%4]\n",
    "        pattern='antisune'\n",
    "        return front_face,pattern\n",
    "    elif count==2:\n",
    "        index1=face_index[0]\n",
    "        index2=face_index[1]\n",
    "        temp=[[-1,0,0],[0,1,0],[1,0,0],[0,-1,0]]\n",
    "        if index2-index1==2:\n",
    "            pattern='L'\n",
    "            if list(face_dir[(index1+1)%4])==temp[(index1+1)%4]:\n",
    "                front_face=face_dir[(index1+1)%4]\n",
    "                return front_face,pattern\n",
    "            front_face=face_dir[(index2+1)%4]\n",
    "            return front_face,pattern\n",
    "        else:\n",
    "            if list(face_dir[(index1+2)%4])==list(face_dir[(index2+2)%4]):\n",
    "                pattern='U'\n",
    "                front_face=face_dir[(index1+2)%4]\n",
    "                return front_face,pattern\n",
    "            pattern='T'\n",
    "            if list(face_dir[(index1+2)%4])==temp[(index1+3)%4]:\n",
    "                front_face=face_dir[(index1+2)%4]\n",
    "                return front_face,pattern\n",
    "            front_face=face_dir[(index2+2)%4]\n",
    "            return front_face,pattern\n",
    "    else:\n",
    "        pattern='completed'\n",
    "        return front_face,pattern\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T\n",
      "[0 1 0]\n"
     ]
    }
   ],
   "source": [
    "front_face,pattern=thirdCornerPieces(face_matrix)\n",
    "print(pattern)\n",
    "print(front_face)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "def oll(face_matrix):\n",
    "    front_face,pattern=thirdCornerPieces(face_matrix)\n",
    "    front_face=np.copy(front_face)\n",
    "    up_face=np.array([0,0,1])\n",
    "    right_face=np.cross(up_face,front_face)\n",
    "    left_face=-right_face\n",
    "    down_face=-up_face\n",
    "    back_face=-front_face\n",
    "    \n",
    "    ans=[]\n",
    "    \n",
    "    if pattern=='H':\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "    elif pattern=='Pi':\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "    elif pattern=='antisune':\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U'\n",
    "        rotate(up_face,face_matrix,-1)\n",
    "        ans.append([up_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "    elif pattern=='sune':\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "    elif pattern=='L':\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #F\n",
    "        rotate(front_face,face_matrix,1)\n",
    "        ans.append([front_face,1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #B'\n",
    "        rotate(back_face,face_matrix,-1)\n",
    "        ans.append([back_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #F'\n",
    "        rotate(front_face,face_matrix,-1)\n",
    "        ans.append([front_face,-1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #B\n",
    "        rotate(back_face,face_matrix,1)\n",
    "        ans.append([back_face,1])\n",
    "    elif pattern=='U':\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #D\n",
    "        rotate(down_face,face_matrix,1)\n",
    "        ans.append([down_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #D'\n",
    "        rotate(down_face,face_matrix,-1)\n",
    "        ans.append([down_face,-1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #U\n",
    "        rotate(up_face,face_matrix,1)\n",
    "        ans.append([up_face,1])\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "    elif pattern == 'T':\n",
    "        #R'\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        ans.append([right_face,-1])\n",
    "        #F'\n",
    "        rotate(front_face,face_matrix,-1)\n",
    "        ans.append([front_face,-1])\n",
    "        #L\n",
    "        rotate(left_face,face_matrix,1)\n",
    "        ans.append([left_face,1])\n",
    "        #F\n",
    "        rotate(front_face,face_matrix,1)\n",
    "        ans.append([front_face,1])\n",
    "        #R\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        ans.append([right_face,1])\n",
    "        #F'\n",
    "        rotate(front_face,face_matrix,-1)\n",
    "        ans.append([front_face,-1])\n",
    "        #L'\n",
    "        rotate(left_face,face_matrix,-1)\n",
    "        ans.append([left_face,-1])\n",
    "        #F\n",
    "        rotate(front_face,face_matrix,1)\n",
    "        ans.append([front_face,1])\n",
    "    return ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rotating [-1  0  0] in -1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 1 0] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 1 0] in 1\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "ans=oll(face_matrix)\n",
    "print(len(ans))\n",
    "tot_steps+=len(ans)\n",
    "steps_dir[\"yellow top (OLL)\"]=len(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "red\n",
      "[[1 3 1]\n",
      " [1 1 1]\n",
      " [1 1 1]]\n",
      "orange\n",
      "[[4 2 3]\n",
      " [2 2 2]\n",
      " [2 2 2]]\n",
      "green\n",
      "[[3 1 2]\n",
      " [3 3 3]\n",
      " [3 3 3]]\n",
      "blue\n",
      "[[2 4 4]\n",
      " [4 4 4]\n",
      " [4 4 4]]\n",
      "yellow\n",
      "[[5 5 5]\n",
      " [5 5 5]\n",
      " [5 5 5]]\n",
      "white\n",
      "[[6 6 6]\n",
      " [6 6 6]\n",
      " [6 6 6]]\n"
     ]
    }
   ],
   "source": [
    "printallfaces(face_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PLL Corner Pieces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "face_dict={1:np.array([1,0,0]),2:np.array([-1,0,0]),3:np.array([0,1,0]),4:np.array([0,-1,0]),5:np.array([0,0,1]),6:np.array([0,0,-1])}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 1 0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [-1  0  0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [-1  0  0] in -1\n",
      "rotating [0 1 0] in -1\n",
      "15\n"
     ]
    }
   ],
   "source": [
    "placed=[]\n",
    "for i in range(1,5):\n",
    "    if(np.array_equal(face_matrix[i][5][1],face_matrix[i][8][1])):\n",
    "        placed.append(i)\n",
    "steps=0        \n",
    "if(len(placed)==0):\n",
    "    #Diagonal Corner swap\n",
    "    f=np.array([1,0,0])\n",
    "    r=np.array([0,1,0])\n",
    "    u=np.array([0,0,1])\n",
    "    #fru'r'u'rur'f'rur'u'r'frf'\n",
    "    rotate(f,face_matrix,1)\n",
    "    rotate(r,face_matrix,1)\n",
    "    rotate(u,face_matrix,-1)\n",
    "    rotate(r,face_matrix,-1)\n",
    "    rotate(u,face_matrix,-1)\n",
    "    rotate(r,face_matrix,1)\n",
    "    rotate(u,face_matrix,1)\n",
    "    rotate(r,face_matrix,-1)\n",
    "    rotate(f,face_matrix,-1)\n",
    "    rotate(r,face_matrix,1)\n",
    "    rotate(u,face_matrix,1)\n",
    "    rotate(r,face_matrix,-1)\n",
    "    rotate(u,face_matrix,-1)\n",
    "    rotate(r,face_matrix,-1)\n",
    "    rotate(f,face_matrix,1)\n",
    "    rotate(r,face_matrix,1)\n",
    "    rotate(f,face_matrix,-1)\n",
    "    steps+=17\n",
    "if(len(placed)==1):\n",
    "    #Adjacent corner swap\n",
    "    i=placed[0]\n",
    "    #rur'u'r'frru'r'u'rur'f'\n",
    "    u=np.array([0,0,1])\n",
    "    f=np.bitwise_xor(face_matrix[i][5][0],face_matrix[i][5][1])\n",
    "    f[2]=0\n",
    "    r=-face_matrix[i][5][1]\n",
    "    rotate(r,face_matrix,1)\n",
    "    rotate(u,face_matrix,1)\n",
    "    rotate(r,face_matrix,-1)\n",
    "    rotate(u,face_matrix,-1)\n",
    "    rotate(r,face_matrix,-1)\n",
    "    rotate(f,face_matrix,1)\n",
    "    rotate(r,face_matrix,1)\n",
    "    rotate(r,face_matrix,1)\n",
    "    rotate(u,face_matrix,-1)\n",
    "    rotate(r,face_matrix,-1)\n",
    "    rotate(u,face_matrix,-1)\n",
    "    rotate(r,face_matrix,1)\n",
    "    rotate(u,face_matrix,1)\n",
    "    rotate(r,face_matrix,-1)\n",
    "    rotate(f,face_matrix,-1)\n",
    "    steps+=15\n",
    "\n",
    "face=face_dict[1]    \n",
    "if(np.array_equal(face_matrix[1][5][1],face )):\n",
    "    pass\n",
    "elif(np.array_equal(face_matrix[1][5][1],-face)):\n",
    "    rotate(np.array([0,0,1]),face_matrix,1)\n",
    "    rotate(np.array([0,0,1]),face_matrix,1)\n",
    "    steps+=2\n",
    "else:\n",
    "    if((face_matrix[1][5][0][0]==face[0]) or(face_matrix[1][5][0][1]==face[1])):\n",
    "        rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "    else:\n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "    steps+=1\n",
    "print(steps) \n",
    "tot_steps+=steps\n",
    "steps_dir[\"yellow Corner (PLL-1)\"]=steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "red\n",
      "[[1 2 1]\n",
      " [1 1 1]\n",
      " [1 1 1]]\n",
      "orange\n",
      "[[2 3 2]\n",
      " [2 2 2]\n",
      " [2 2 2]]\n",
      "green\n",
      "[[3 1 3]\n",
      " [3 3 3]\n",
      " [3 3 3]]\n",
      "blue\n",
      "[[4 4 4]\n",
      " [4 4 4]\n",
      " [4 4 4]]\n",
      "yellow\n",
      "[[5 5 5]\n",
      " [5 5 5]\n",
      " [5 5 5]]\n",
      "white\n",
      "[[6 6 6]\n",
      " [6 6 6]\n",
      " [6 6 6]]\n"
     ]
    }
   ],
   "source": [
    "printallfaces(face_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "[-1  0  0]\n",
      "[1 0 0]\n",
      "2\n",
      "1\n",
      "[1 0 0]\n",
      "[0 1 0]\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in -1\n",
      "rotating [1 0 0] in -1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [0 0 1] in 1\n",
      "rotating [1 0 0] in 1\n",
      "rotating [1 0 0] in 1\n"
     ]
    }
   ],
   "source": [
    "#below func. is used in end...start\n",
    "def RotationForcorrectPos(face_matrix):\n",
    "    if(list(face_matrix[1][1][1])!=list(np.array([1,0,0]))):\n",
    "        vec=np.cross(face_matrix[1][1][1],np.array([1,0,0]))\n",
    "        if(sum(vec)==0):\n",
    "                     rotate(np.array([0,0,1]),face_matrix,1)\n",
    "                     rotate(np.array([0,0,1]),face_matrix,1)\n",
    "                     return 2\n",
    "        elif(sum(vec)<0):\n",
    "                     rotate(np.array([0,0,1]),face_matrix,1)\n",
    "                     return 1\n",
    "        elif(sum(vec)>0):\n",
    "                     rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "                     return 1\n",
    "#...end                   \n",
    "dic={tuple(np.array([1,0,0])):1,tuple(np.array([-1,0,0])):2,tuple(np.array([0,1,0])):3,tuple(np.array([0,-1,0])):4}\n",
    "correct_pos=[]\n",
    "noOfOpp=0\n",
    "steps=0\n",
    "for i in range(1,5):\n",
    "    if(list(face_dict[i])==list(face_matrix[i][1][1])):\n",
    "        correct_pos.append(i)\n",
    "    if(list(face_matrix[i][1][1].copy()*-1)==list(face_dict[i])):\n",
    "        noOfOpp+=1\n",
    "print(noOfOpp)\n",
    "if(len(correct_pos)==1):\n",
    "    right_face=np.cross(face_dict[correct_pos[0]],np.array([0,0,1]))\n",
    "    left_face=right_face*-1\n",
    "    print(right_face)\n",
    "    print(left_face)\n",
    "    print(dic[tuple(right_face)])\n",
    "    print(dic[tuple(left_face)])\n",
    "    print(face_matrix[dic[tuple(right_face)]][1][1])\n",
    "    print(face_matrix[dic[tuple(left_face)]][1][1])\n",
    "    if(list(face_matrix[dic[tuple(right_face)]][1][1])==list(left_face)):\n",
    "        rotate(left_face,face_matrix,-1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "        rotate(left_face,face_matrix,-1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "        rotate(left_face,face_matrix,-1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "        rotate(left_face,face_matrix,-1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "        rotate(left_face,face_matrix,1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "        rotate(left_face,face_matrix,1)\n",
    "        rotate(left_face,face_matrix,1)\n",
    "        steps+=12\n",
    "    elif(list(face_matrix[dic[tuple(left_face)]][1][1])==list(right_face)):\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,1)\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        rotate(np.array([0,0,1]),face_matrix,-1)\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        steps+=12\n",
    "        \n",
    "if(len(correct_pos)==0 and noOfOpp==4):\n",
    "    #m2 start\n",
    "    rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,1,0]),face_matrix,1)   \n",
    "    #m2 ends\n",
    "    #u'\n",
    "    rotate(np.array([0,0,-1]),face_matrix,-1)\n",
    "    #m2 start\n",
    "    rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,1,0]),face_matrix,1)   \n",
    "    #m2 ends\n",
    "    #u2 starts\n",
    "    rotate(np.array([0,0,1]),face_matrix,1)\n",
    "    rotate(np.array([0,0,1]),face_matrix,1)\n",
    "    #u2 ends\n",
    "    #m2 start\n",
    "    rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,1,0]),face_matrix,1)   \n",
    "    #m2 ends\n",
    "    #u'\n",
    "    rotate(np.array([0,0,-1]),face_matrix,-1)\n",
    "    #m2 start\n",
    "    rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,1,0]),face_matrix,1)\n",
    "    rotate(np.array([0,1,0]),face_matrix,1)   \n",
    "    #m2 ends\n",
    "    steps+=12\n",
    "if(len(correct_pos)==0 and noOfOpp==0):\n",
    "    right_face=np.array([0,-1,0])\n",
    "    left_face=right_face*-1\n",
    "    front_face=face_matrix[4][1][1].copy()\n",
    "    if(sum(front_face)<0):\n",
    "        print('1st one')\n",
    "        #m' \n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        rotate(left_face,face_matrix,1)\n",
    "        #u'\n",
    "        rotate(front_face,face_matrix,-1)\n",
    "        #m2 start\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        #m2 end\n",
    "        #u'\n",
    "        rotate(front_face*-1,face_matrix,-1)\n",
    "        #m2 start\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        #m2 end\n",
    "        #u'\n",
    "        rotate(front_face,face_matrix,-1)\n",
    "        #m' \n",
    "        rotate(right_face,face_matrix,-1)\n",
    "        rotate(left_face,face_matrix,1)\n",
    "        #u2 start\n",
    "        rotate(np.array([0,0,-1]),face_matrix,1)\n",
    "        rotate(np.array([0,0,-1]),face_matrix,1)\n",
    "        #u2 ends\n",
    "        #m2 start\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        #m2 end\n",
    "        steps+=13\n",
    "        steps+=RotationForcorrectPos(face_matrix)\n",
    "    elif(sum(front_face)>0):\n",
    "        print(\"2nd one\")\n",
    "        #m' \n",
    "        rotate(left_face,face_matrix,-1)\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        #u\n",
    "        rotate(front_face,face_matrix,1)\n",
    "        #m2 start\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        #m2 end\n",
    "        #u\n",
    "        rotate(front_face*-1,face_matrix,1)\n",
    "        #m2 start\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        #m2 end\n",
    "        #u\n",
    "        rotate(front_face,face_matrix,1)\n",
    "        #m' \n",
    "        rotate(left_face,face_matrix,-1)\n",
    "        rotate(right_face,face_matrix,1)\n",
    "        #u2 start\n",
    "        rotate(np.array([0,0,-1]),face_matrix,1)\n",
    "        rotate(np.array([0,0,-1]),face_matrix,1)\n",
    "        #u2 ends\n",
    "        #m2 start\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,-1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        rotate(np.array([0,1,0]),face_matrix,1)\n",
    "        #m2 end\n",
    "        steps+=13\n",
    "        steps+=RotationForcorrectPos(face_matrix) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no. of steps 12\n",
      "red\n",
      "[[1 1 1]\n",
      " [1 1 1]\n",
      " [1 1 1]]\n",
      "orange\n",
      "[[2 2 2]\n",
      " [2 2 2]\n",
      " [2 2 2]]\n",
      "green\n",
      "[[3 3 3]\n",
      " [3 3 3]\n",
      " [3 3 3]]\n",
      "blue\n",
      "[[4 4 4]\n",
      " [4 4 4]\n",
      " [4 4 4]]\n",
      "yellow\n",
      "[[5 5 5]\n",
      " [5 5 5]\n",
      " [5 5 5]]\n",
      "white\n",
      "[[6 6 6]\n",
      " [6 6 6]\n",
      " [6 6 6]]\n"
     ]
    }
   ],
   "source": [
    "print(\"no. of steps \" + str(steps))\n",
    "printallfaces(face_matrix)\n",
    "tot_steps+=steps\n",
    "steps_dir[\"yellow Edge (PLL-2)\"]=steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "White cross :  12\n",
      "White corner :  15\n",
      "2nd layer :  30\n",
      "yellow cross :  6\n",
      "yellow top (OLL) :  8\n",
      "yellow Corner (PLL-1) :  15\n",
      "yellow Edge (PLL-2) :  12\n"
     ]
    }
   ],
   "source": [
    "for i in steps_dir:\n",
    "    print(i,\": \",steps_dir[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total steps taken 98\n"
     ]
    }
   ],
   "source": [
    "print(\"total steps taken\",tot_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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