rat_and_maze.cpp

#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;
}