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?

当前状态与前一状态相关，而且只需要求出路径数，而不需要具体的路径信息，那当然是动态规划大法。

动态规划方程：dp[i][j] = dp[i-1][j] + dp[i][j-1]

代码如下：

class Solution {public:    int uniquePaths(int m, int n) {        int dp[m][n];        memset(dp,0,sizeof(int)*m*n);                dp[0][0] = 1;                for(int i=0;i<m;i++)        {            for(int j=0;j<n;j++)            {                if(i-1 >= 0)                    dp[i][j] += dp[i-1][j];                if(j-1 >= 0)                    dp[i][j] += dp[i][j-1];            }        }        return dp[m-1][n-1];    }};