Leetcode 62：Unique Paths

原创于 2019-08-10 11:44:08 发布 · 104 阅读

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本文探讨了一个机器人在限定的网格中从左上角到右下角的唯一路径数量问题。通过动态规划方法，我们实现了高效的路径计数算法。输入网格大小m和n，输出可能的不同路径数量。

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?

在这里插入图片描述
Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:

Right -> Right -> Down
Right -> Down -> Right
Down -> Right -> Right
Example 2:

Input: m = 7, n = 3
Output: 28

C++
int uniquePaths(int m, int n) {
        vector<vector<int>> map(n,vector<int>(m,1));
        for(int i = 1;i < n;++i)
        {
            for(int j = 1;j < m;++j)
            {
                map[i][j] = map[i - 1][j] + map[i][j - 1];
            }
        }
        return map[n-1][m-1];
    }