[Leetcode] 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?

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

Note: m and n will be at most 100.

Solution：

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