LeetCode 64: Minimum Path Sum

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本文介绍了一个经典算法问题——最小路径和问题，并提供了一种有效的解决方案。该问题要求在一个填充了非负数的矩阵中找到从左上角到右下角路径上的最小数值总和，仅允许向下或向右移动。

Minimum Path Sum

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.

解题思路

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        if (grid.size() == 0 || grid[0].size() == 0) return 0;

        int m = grid.size(), n = grid[0].size();
        vector<vector<int>> dp(m+1, vector<int>(n+1, INT_MAX));
        dp[0][1] = dp[1][0] = 0;
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i-1][j-1];
            }
        }

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