Unique Paths

最新推荐文章于 2025-08-19 00:15:00 发布

原创最新推荐文章于 2025-08-19 00:15:00 发布 · 531 阅读

0 ·

CC 4.0 BY-SA版权

算法专栏收录该内容

636 篇文章

订阅专栏

本文介绍了一个算法问题：机器人从网格左上角出发，只能向下或向右移动，到达右下角的不同路径数量。通过动态规划的方法，使用二维数组记录中间状态，避免重复计算，高效求解。

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?

class Solution {
public:
    int uniquePaths(int m, int n) {
        int buf[m][n];
        for (int i = 0; i < m; i++)
        {
            buf[i][0] = 1;
        }
        for (int i = 0; i < n; i++)
        {
            buf[0][i] = 1;
        }

        for (int i = 1; i < m; i++)
        {
            for (int j = 1; j < n; j++)
            {
                buf[i][j] = buf[i-1][j] + buf[i][j-1];
            }
        }
        return buf[m-1][n-1];
    }
};