Leetcode 62 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?

image.png

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

Note: m and n will be at most 100.

DP基础题，不多说了，左和上方转移

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<int> row(n+1,0);
        vector<vector<int>> dp(m+1,row);
        dp[0][1]=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][n];
    }
};