Recursive backtracking knights tour in c ++ - recursion

Question

So, in short I'm working on a knight's tour program. If you don't know what that is, the knight gets put on the chess board and you have to move it to every spot on the board exactly once. I'm using a recursive function but am having trouble getting my backtracking to work. I can get to 22 steps in a 5x5 board but the program won't back up and try a different path. I'm posting just the recursive part of my code (sorry it's a little long) Any insight would be extremely helpful. Thanks a lot!
`bool findPath ( int board[][boardSize + 4], int &currRow, int &currCol, int &currMove,int boardSize )
{
int i, j;
bool foundSpot;
board[currRow][currCol] = currMove;
if ( currMove == boardSize * boardSize )
return true;
for ( i = 0; i < boardSize + 4; i++ )
{
for ( j = 0; j < boardSize + 4; j++ )
cout << setw (3) << board[i][j];
cout<<endl;
}
cout << endl;
if ( board[currRow - 2][currCol - 1] == 0 )
{
currMove += 1;
board[currRow - 2][currCol - 1] = currMove;
currRow -= 2;
currCol -= 1;
if ( findPath( board, currRow, currCol, currMove, boardSize ) )
return true;
}
if ( board[currRow - 2][currCol + 1] == 0 )
{
currMove += 1;
board[currRow - 2][currCol + 1] = currMove ;
currRow -= 2;
currCol += 1;
if ( findPath( board, currRow, currCol, currMove, boardSize ) )
return true;
}
if ( board[currRow - 1][currCol + 2] == 0 )
{
currMove += 1;
board[currRow - 1][currCol + 2] = currMove ;
currRow -= 1;
currCol += 2;
if ( findPath( board, currRow, currCol, currMove, boardSize ) )
return true;
}
if ( board[currRow + 1][currCol + 2] == 0 )
{
currMove += 1;
board[currRow + 1][currCol + 2] = currMove ;
currRow += 1;
currCol += 2;
if ( findPath( board, currRow, currCol, currMove, boardSize ) )
return true;
}
if ( board[currRow + 2][currCol + 1] == 0 )
{
currMove += 1;
board[currRow + 2][currCol + 1] = currMove ;
currRow += 2;
currCol += 1;
if ( findPath( board, currRow, currCol, currMove, boardSize ) )
return true;
}
if ( board[currRow + 2][currCol - 1] == 0 )
{
currMove += 1;
board[currRow + 2][currCol - 1] = currMove ;
currRow += 2;
currCol -= 1;
if ( findPath( board, currRow, currCol, currMove, boardSize ) )
return true;
}
if ( board[currRow + 1][currCol - 2] == 0 )
{
currMove += 1;
board[currRow + 1][currCol - 2] = currMove ;
currRow += 1;
currCol -= 2;
if ( findPath( board, currRow, currCol, currMove, boardSize ) )
return true;
}
if ( board[currRow - 1][currCol - 2] == 0 )
{
currMove += 1;
board[currRow - 1][currCol - 2] = currMove ;
currRow -= 1;
currCol -= 2;
if ( findPath( board, currRow, currCol, currMove, boardSize ) )
return true;
}
board[currRow][currCol] = 0;
currMove -= 2;
return false;
}`

Answer 1

I worked out the following implementation of the Knights tour in c++ :
#include<cstdio>
#include<iostream>
#define MAX 10
using namespace std;
int tour=1;
int board[MAX][MAX];
bool is_travelled(int,int);
bool knights_tour(int,int,int,int);
void initialize(int);
void display(int);
int main(int argc,char** argv){
int n;
scanf("%d",&n);
for(int i=0;i<10;i++){
for(int j=0;j<10;j++){
board[i][j]=-1;
}
}
initialize(n);
display(n);
return 0;
}
bool is_travelled(int x,int y){
if(x<0 || y<0)return true;
if(board[x][y]==-1)return false;
return true;
}
bool knights_tour(int i,int j,int n,int k){ // k=number of places remained , n=side of chess_board;
int x,y;
if(k==0)return true;
// hard-coded cases;
// reordering of the cases have significant effect on the execution time
x=i+2;y=j+1;
if((!is_travelled(x,y))&&x<n&&y<n){
board[x][y]=tour;
tour+=1;
if(knights_tour(x,y,n,k-1))return true;
board[x][y]=-1;
tour-=1;
}
x=i+1;y=j+2;
if((!is_travelled(x,y))&&x<n&&y<n){
board[x][y]=tour;
tour+=1;
if(knights_tour(x,y,n,k-1))return true;
board[x][y]=-1;
tour-=1;
}
x=i-1;y=j+2;
if((!is_travelled(x,y))&&x<n&&y<n){
board[x][y]=tour;
tour+=1;
if(knights_tour(x,y,n,k-1))return true;
board[x][y]=-1;
tour-=1;
}
x=i-2;y=j+1;
if((!is_travelled(x,y))&&x<n&&y<n){
board[x][y]=tour;
tour+=1;
if(knights_tour(x,y,n,k-1))return true;
board[x][y]=-1;
tour-=1;
}
x=i-2;y=j-1;
if((!is_travelled(x,y))&&x<n&&y<n){
board[x][y]=tour;
tour+=1;
if(knights_tour(x,y,n,k-1))return true;
board[x][y]=-1;
tour-=1;
}
x=i-1;y=j-2;
if((!is_travelled(x,y))&&x<n&&y<n){
board[x][y]=tour;
tour+=1;
if(knights_tour(x,y,n,k-1))return true;
board[x][y]=-1;
tour-=1;
}
x=i+1;y=j-2;
if((!is_travelled(x,y))&&x+y<n&&x<n&&y<n){
board[x][y]=tour;
tour+=1;
if(knights_tour(x,y,n,k-1))return true;
board[x][y]=-1;
tour-=1;
}
x=i+2;y=j-1;
if((!is_travelled(x,y))&&x<n&&y<n){
board[x][y]=tour;
tour+=1;
if(knights_tour(x,y,n,k-1))return true;
board[x][y]=-1;
tour-=1;
}
return false;
}
void initialize(int n){
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
board[i][j]=0;
int r=knights_tour(i,j,n,n*n-1);
if(r==1)return;
board[i][j]=-1;
}
}
}
void display(int n){
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
printf("%2d ",board[i][j]);
}
printf("\n");
}
cout<<endl;
}
Hope this helps .
Happy Coding !