Algorithm for finding all paths in a NxN grid

Question

Imagine a robot sitting on the upper left hand corner of an NxN grid. The robot can only move in two directions: right and down. How many possible paths are there for the ro

Answer 1

Scenario:
1. Imagine there is NxN zero indexed matrix.
2. Initial position of robot is upper-left corner i.e. (N-1, N-1)
3. Robot wants to reach lower right corner i.e. at (0,0)

Solution:
-- In any possible solution robot will move N rights steps and N down steps to reach (0,0), or we can say that initial robot has permission to move N rights steps and N down steps.
-- When ever robot moves right we reduce its remaining number of right steps by 1, same is for down movement.
-- At every position(except at boundary, where it will have only one option) robot have two options, one is it can go down or other is it can go right.
-- It will terminate when robot will have no remaining down of right steps.

**Below code also have driver method main(), you can change the value of N. N can be >=1

public class RobotPaths {

public static int robotPaths(int down, int right, String path)
{
    path = path+ down +","+ right +"  ";
    if(down==0 && right==0)
    {
        System.out.println(path);
        return 1;
    }

    int counter = 0;

    if(down==0)
        counter = robotPaths(down, right-1, path);
    else if(right==0)
        counter = robotPaths(down-1, right, path);
    else
        counter = robotPaths(down, right-1, path) + robotPaths(down-1, right, path);

    return counter;
}

public static void main(String[] args) 
{
    int N = 1;
    System.out.println("Total possible paths: "+RobotPaths.robotPaths(N-1, N-1, ""));

}

}