[leetcode]62. Unique Paths

[leetcode]62. Unique Paths

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Analysis

周一鸭—— [每天刷题并不难0.0]

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?

Implement

方法一

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

方法二（space optimization）

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