Backtracking.cpp

// C program for Knight Tour problem 
#include<stdio.h> 
#define N 8 

int solveKTUtil(int x, int y, int movei, int sol[N][N], 
				int xMove[], int yMove[]); 

/* A utility function to check if i,j are valid indexes 
for N*N chessboard */
bool isSafe(int x, int y, int sol[N][N]) 
{ 
	return ( x >= 0 && x < N && y >= 0 && 
			y < N && sol[x][y] == -1); 
} 

/* A utility function to print solution matrix sol[N][N] */
void printSolution(int sol[N][N]) 
{ 
	for (int x = 0; x < N; x++) 
	{ 
		for (int y = 0; y < N; y++) 
			printf(" %2d ", sol[x][y]); 
		printf("\n"); 
	} 
} 

/* This function solves the Knight Tour problem using 
Backtracking. This function mainly uses solveKTUtil() 
to solve the problem. It returns false if no complete 
tour is possible, otherwise return true and prints the 
tour. 
Please note that there may be more than one solutions, 
this function prints one of the feasible solutions. */
bool solveKT() 
{ 
	int sol[N][N]; 

	/* Initialization of solution matrix */
	for (int x = 0; x < N; x++) 
		for (int y = 0; y < N; y++) 
			sol[x][y] = -1; 

	/* xMove[] and yMove[] define next move of Knight. 
	xMove[] is for next value of x coordinate 
	yMove[] is for next value of y coordinate */
	int xMove[8] = { 2, 1, -1, -2, -2, -1, 1, 2 }; 
	int yMove[8] = { 1, 2, 2, 1, -1, -2, -2, -1 }; 

	// Since the Knight is initially at the first block 
	sol[0][0] = 0; 

	/* Start from 0,0 and explore all tours using 
	solveKTUtil() */
	if (solveKTUtil(0, 0, 1, sol, xMove, yMove) == false) 
	{ 
		printf("Solution does not exist"); 
		return false; 
	} 
	else
		printSolution(sol); 

	return true; 
} 

/* A recursive utility function to solve Knight Tour 
problem */
int solveKTUtil(int x, int y, int movei, int sol[N][N], 
				int xMove[N], int yMove[N]) 
{ 
int k, next_x, next_y; 
if (movei == N*N) 
	return true; 

/* Try all next moves from the current coordinate x, y */
for (k = 0; k < 8; k++) 
{ 
	next_x = x + xMove[k]; 
	next_y = y + yMove[k]; 
	if (isSafe(next_x, next_y, sol)) 
	{ 
		sol[next_x][next_y] = movei; 
		if (solveKTUtil(next_x, next_y, movei+1, sol, 
						xMove, yMove) == true) 
			return true; 
		else
			sol[next_x][next_y] = -1;// backtracking 
	} 
} 

return false; 
} 

/* Driver program to test above functions */
int main() 
{ 
	solveKT(); 
	return 0; 
}