[Leetcode 64, Medium] Minimum Path Sum

最小路径和：C++、Java、Python解法

原创于 2015-07-21 00:25:03 发布 · 329 阅读

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本文介绍如何使用C++、Java、Python解决最小路径和问题，即在给定的m x n网格中，从左上角到右下角找到一条路径，使得所有经过的数字之和最小。分析了算法思路并提供了实现代码。

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.

Analysis:

Solutions:

C++:

    int minPathSum(vector<vector<int>>& grid) {
        if(grid.empty())
            return 0;
        
        int rows = grid.size();
        for(int row = 1; row < rows; ++row) {
            grid[row][0] += grid[row - 1][0];
        }
        
        int cols = grid[0].size();
        for(int col = 1; col < cols; ++col) {
            grid[0][col] += grid[0][col - 1];
        }
        
        for(int row = 1; row < rows; ++row) {
            for(int col = 1; col < cols; ++col)
                grid[row][col] += min(grid[row - 1][col], grid[row][col - 1]);
        }
        
        return grid[rows - 1][cols - 1];
    }

Java:

Python: