Lintcode: Unique paths

Problem description:

A robot is located at the top-left corner ofMXNGrid (marked 'start' in the dimo-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 dimo-below ).

How many possible unique paths are there?

Code:

public class Solution {    /**     * @param n, m: positive integer (1 <= n ,m <= 100)     * @return an integer     */    public int uniquePaths(int m, int n) {        // write your code here        if (m == 0 || n == 0) {            return 0;        }        int[][] sum = new int[m][n];        for (int i = 0; i < m; i++) {            sum[i][0] = 1;        }        for (int j = 0; j < n; j++) {            sum[0][j] = 1;        }        for (int i = 1; i < m; i++) {            for (int j = 1; j < n; j++) {                sum[i][j] = sum[i - 1][j] + sum[i][j - 1];            }        }        return sum[m - 1][n - 1];    }}

Hint:

Here we use dynamic programming, the most important thing is know that sum [I] [J] = sum [I-1] [J] + sum [I] [J-1], because you can go right from position (I, j-1) or go down from position (I-1, J) to get to position (I, j ).

Lintcode: Unique paths