62. Unique Paths java solutions

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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

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 1 public class Solution {
 2     public int uniquePaths(int m, int n) {
 3         int[][] ans = new int[m][n];
 4         for(int i = 0; i< m;i++){
 5             ans[i][0] = 1;
 6         }
 7         for(int i = 0; i< n;i++){
 8             ans[0][i] = 1;
 9         }
10         for(int i = 1;i < m; i++){
11             for(int j = 1; j< n; j++){
12                 ans[i][j] = ans[i][j-1] + ans[i-1][j];
13             }
14         }
15         return ans[m-1][n-1];
16     }
17 }

本地是最最简单的DP，非常有学习和理解的价值。