2.4 Unique Paths

Description

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?

Method

dynamic problem coordinate

Time and Space Complexity

o(mn)

Code

public class Solution {

public int uniquePaths(int m, int n) {
    if (m == 0 || n == 0){
        return 0;
    }
    int[][] paths = new int[m][n];

    for (int i = 0; i < m; i++){
         paths[i][0] = 1;
    }
    for (int j = 0; j < n; j++){
         paths[0][j] = 1;
    }

    for (int i = 1; i < m; i++){
        for (int j = 1; j < n; j++){
             paths[i][j] = paths[i - 1][j] + paths[i][j - 1];
        }
    }
    return paths[m - 1][n - 1];
}

}