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?

状态转移方程
dp[i][j] = dp[i-1][j] + dp[i][j-1]

边界条件
dp[i][0] = 1
dp[0][j] = 1

代码

class Solution {
public:int uniquePaths(int m, int n) {int dp[105][105] = {0};for(int i = 0; i < m; i++)dp[i][0] = 1;for(int j = 0; j < n; j++)dp[0][j] = 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];}
};