LeetCode 64. Minimum Path Sum

最新推荐文章于 2024-04-22 14:00:57 发布

原创最新推荐文章于 2024-04-22 14:00:57 发布 · 243 阅读

0 ·

CC 4.0 BY-SA版权

LeetCode 题解同时被 2 个专栏收录

288 篇文章

订阅专栏

Dynamic Programming

13 篇文章

订阅专栏

本文介绍了一种寻找矩阵中从左上角到右下角路径的算法，该路径上的数值之和最小。通过动态规划的方法初始化边界并逐步计算每个位置上的最小路径和，最终返回右下角位置的值即为所求。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right whichminimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

This is very similar with LeetCode 62. Unique Paths

int minPathSum(vector< vector<int> >& grid) {
    int m = grid.size();
    int n = grid[0].size();
    for(int i = 1; i < m; ++i) {
        grid[i][0] += grid[i-1][0];  // initialize
    }

    for(int j = 1; j < n; ++j) {
        grid[0][j] += grid[0][j-1];  // initialize
    }

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