62 Unique Paths

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?


  public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        
        for(int i=0;i<dp[0].length;i++){
            dp[0][i] = 1;
        }
        for(int i=0;i<dp.length;i++){
            dp[i][0] = 1;
        }
        
        for(int i=1;i<dp.length;i++){
            for(int j=1;j<dp[0].length;j++){
                dp[i][j] = dp[i-1][j]+dp[i][j-1];
            }
        }
        
        return dp[m-1][n-1];
        
        
    }