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Print Maze Paths With Jumps

1. You are given a number n and a number m representing number of rows and columns in a maze.

2. You are standing in the top-left corner and have to reach the bottom-right corner. 

3. In a single move you are allowed to jump 1 or more steps horizontally (as h1, h2, .. ), or 1 or more steps vertically (as v1, v2, ..) or 1 or more steps diagonally (as d1, d2, ..). 

4. Complete the body of printMazePath function - without changing signature - to print the list of all paths that can be used to move from top-left to bottom-right.

Use sample input and output to take idea about output.


Input Format

A number n

A number m

Output Format

Print paths (one path in each line) in order hinted by Sample output


Constraints

0 <= n <= 5

0 <= m <= 5

Sample Input

3

3

Sample Output

h1h1v1v1

h1h1v2

h1v1h1v1

h1v1v1h1

h1v1d1

h1v2h1

h1d1v1

h2v1v1

h2v2

v1h1h1v1

v1h1v1h1

v1h1d1

v1h2v1

v1v1h1h1

v1v1h2

v1d1h1

v2h1h1

v2h2

d1h1v1

d1v1h1

d1d1

d2


Solution:

import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(), m = sc.nextInt();
        printMazePaths(1,1,n,m,"");
    }

    // sr - source row
    // sc - source column
    // dr - destination row
    // dc - destination column
    public static void printMazePaths(int sr, int sc, int dr, int dc, String psf) {
        
        if(sr>dr || sc>dc)  return;
        if(sr==dr && sc==dc){
            System.out.println(psf);
            return;
        }
        
        for(int j=1;j<=dc-sc;j++)
            printMazePaths(sr,sc+j,dr,dc,psf+"h"+j);
        
        for(int i=1;i<=dr-sr;i++)
            printMazePaths(sr+i,sc,dr,dc,psf+"v"+i);
        
        for(int d=1;d<=(dr-sr) && d<=(dc-sc);d++){
            printMazePaths(sr+d,sc+d,dr,dc,psf+"d"+d);
        }
        
    }

}
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