62. Unique Paths 解题记录

题目描述：

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?

Note: m and n will be at most 100.

解题思路：

这题最先想到的是递归，但递归耗时太久了无法通过。于是改用动态规划的方法，思路与递归类似。不同的是：递归是从终点开始寻找路径，然后往前叠加；而动态规划是从起点开始寻找，往后叠加。

我的代码：

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

 

他人代码：

class Solution {
public:
    int uniquePaths(int m, int n) {
    //参考了LeetCode上的优质解答，思路也是动态规划，把无用的数组去掉了
        vector<int> ret(n, 1);
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                ret[j] += ret[j-1];
            }
        }
        return ret[n-1];
    }
};