(LeetCode) 62. Unique Paths

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本文介绍了一个机器人从网格左上角到右下角的不同路径数量计算问题。通过算法优化，使用了动态规划的思想来减少计算复杂度。对于m×n的网格，通过一个一维数组cur实现了高效计算。

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?
这里写图片描述

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

Note: m and n will be at most 100.

代码

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

        return cur[m-1];
    }
};