LeetCode (Minimum Path Sum)

最小路径和算法解析

最新推荐文章于 2019-05-17 20:06:05 发布

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最新推荐文章于 2019-05-17 20:06:05 发布

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分类专栏： C++

本文链接：https://blog.youkuaiyun.com/m0_37705274/article/details/71662955

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本文介绍了一个经典算法问题——寻找二维网格中从左上角到右下角的最小路径和。详细展示了如何通过动态规划的方法解决该问题，并提供了一段C++实现代码。

Problem:

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

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

Solution:

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        int i = 0, j = 0;
        for(j = 1; j < n; j++)
            grid[i][j] += grid[i][j - 1];
        j = 0;
        for(i = 1; i < m; i++)
            grid[i][j] += grid[i - 1][j];
        for(i = 1; i < m; i++)
            for(j = 1; j < n; j++){
                grid[i][j] += min(grid[i - 1][j], grid[i][j - 1]);
            }
        return grid[m - 1][n - 1];
    }
};