LeetCode 62: Unique Paths

机器人寻路算法：从起始点到终点的独特路径计数

最新推荐文章于 2025-04-02 22:31:45 发布

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本文详细介绍了如何利用动态规划解决机器人在网格上寻找从起始点到终点的独特路径数量的问题。通过构建状态转移矩阵，我们可以高效地计算出在特定网格大小下可能的路径总数。

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?
Example
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

class Solution {
public:
    int uniquePaths(int m, int n) {
        if (m == 0 || n == 0) return 0;

        vector<vector<int>> dp(m+1, vector<int>(n+1, 0));
        dp[1][1] = 1;
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (i != 1 || j != 1)
                    dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        }

        return dp[m][n];
    }
};