rat in a maze.cpp

/* C++ program to solve Rat in  a Maze problem using backtracking */
#include <stdio.h>

// Maze size
#define N 4

bool solveMazeUtil(
	int maze[N][N], int x,
	int y, int sol[N][N]);

/* A utility function to print solution matrix sol[N][N] */
void printSolution(int sol[N][N])
{
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < N; j++)
			printf(" %d ", sol[i][j]);
		printf("\n");
	}
}

/* A utility function to check if x, y is valid index for N*N maze */
bool isSafe(int maze[N][N], int x, int y)
{
	// if (x, y outside maze) return false
	if (
		x >= 0 && x < N && y >= 0
		&& y < N && maze[x][y] == 1)
		return true;

	return false;
}

/* This function solves the Maze problem using Backtracking. It mainly uses solveMazeUtil() to solve the problem.
It returns false if no path is possible, otherwise return true and prints the path in the form of 1s. Please note that there
may be more than one solutions, this function prints one of the feasible solutions.*/

bool solveMaze(int maze[N][N])
{
	int sol[N][N] = { { 0, 0, 0, 0 },
					{ 0, 0, 0, 0 },
					{ 0, 0, 0, 0 },
					{ 0, 0, 0, 0 } };

	if (solveMazeUtil(
			maze, 0, 0, sol)
		== false) {
		printf("Solution doesn't exist");
		return false;
	}

	printSolution(sol);
	return true;
}

/* A recursive utility function to solve Maze problem */

bool solveMazeUtil(
	int maze[N][N], int x,
	int y, int sol[N][N])
{
	// if (x, y is goal) return true
	if (
		x == N - 1 && y == N - 1
		&& maze[x][y] == 1) {
		sol[x][y] = 1;
		return true;
	}

	// Check if maze[x][y] is valid
	if (isSafe(maze, x, y) == true) {
		// Check if the current block is already part of solution path.
		if (sol[x][y] == 1)
			return false;
	
		// mark x, y as part of solution path
		sol[x][y] = 1;

		/* Move forward in x direction */
		if (solveMazeUtil(
				maze, x + 1, y, sol)
			== true)
			return true;

		/* If moving in x direction doesn't give solution then Move down in y direction */
		if (solveMazeUtil(
				maze, x, y + 1, sol)
			== true)
			return true;
	
		/* If none of the above movements
		work then BACKTRACK: unmark
		x, y as part of solution path */
		sol[x][y] = 0;
		return false;
	}

	return false;
}

// driver program to test above function
int main()
{
	int maze[N][N] = { { 1, 0, 0, 0 },
					{ 1, 1, 0, 1 },
					{ 0, 1, 0, 0 },
					{ 1, 1, 1, 1 } };

	solveMaze(maze);
	return 0;
}