Paper--Andrea Palacios

lib/max_subarray.py

@@ -1,12 +1,26 @@
+#Time Complexity: O(n)
+#Space Complexity: O(n)
+
 
 def max_sub_array(nums):
-    """ Returns the max subarray of the given list of numbers.
-        Returns 0 if  nums is None or an empty list.
-        Time Complexity: ?
-        Space Complexity: ?
-    """
+    '''
+    Time Complexity: O(n)
+    Space Complexity: O(n)
+
+    '''
     if nums == None:
         return 0
-    if len(nums) == 0:
+    if len(nums)==0:
         return 0
-    pass
+
+    max_so_far = nums[0]
+    max_ending_here = nums[0]
+
+    for i in range(1,len(nums)):
+        max_ending_here = max_ending_here + nums[i]
+        if(max_ending_here < 0):
+            max_ending_here = max(max_ending_here,nums[i])
+        if(max_so_far < max_ending_here):
+                max_so_far = max_ending_here
+
+    return max_so_far

lib/newman_conway.py

@@ -1,10 +1,18 @@
 
 
-# Time complexity: ?
-# Space Complexity: ?
 def newman_conway(num):
-    """ Returns a list of the Newman Conway numbers for the given value.
-        Time Complexity: ?
-        Space Complexity: ?
-    """
-    pass
+    '''
+    Time Complexity: O(n)
+    Space Complexity: O(n)
+
+    '''
+    if num < 1:
+        raise ValueError
+    elif num == 1:
+        return "1"
+
+    sequence = [0,1,1]
+
+    for i in range(3, num+1):
+        sequence.append(sequence[sequence[i - 1]] + sequence[i - sequence[i - 1]])
+    return (" ".join(map(str, sequence[1:])))