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?

思路： 典型的DP，递推公式dp[i][j] = dp[i-1][j] + dp[i][j-1], 注意初始化第一行和第一列，全部为1.

public class Solution {     public int uniquePaths(int m, int n) {         if(m <=0 || n<=0) return 0;         int[][] dp = new int[m][n];         //init rows;         for(int i=0; i<m; i++){             dp[i][0] = 1;         }                  // init col;         for(int j=0; j<n; j++){             dp[0][j] = 1;         }                  // calculate;         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];     } }