Unique Paths (Medium)

Description

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?

Analysis

简单的dp

My Solution

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//C++
class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int> > ans(m,vector<int>(n));
        for(int i = 0;i<n;i++)
            ans[0][i]=1;
        for(int i = 0;i<m;i++)
            ans[i][0]=1;
        for(int i = 1;i<m;i++)
            for(int j = 1;j<n;j++){
                ans[i][j] = ans[i-1][j]+ans[i][j-1];
            }
        return ans[m-1][n-1];
    }
};