Leetcode: Minimum Path Sum

最新推荐文章于 2025-08-11 00:49:14 发布

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最新推荐文章于 2025-08-11 00:49:14 发布

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分类专栏： Leetcode 文章标签： leetcode

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本文介绍了如何使用动态规划算法解决多维数组中从左上角到右下角的最小路径和问题。通过构建状态转移矩阵并逐步计算最优路径，实现了高效求解。

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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.

Dynamic programming.

public class Solution {
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0) {
            return 0;
        }
        
        int[][] minSum = new int[grid.length][grid[0].length];
        minSum[0][0] = grid[0][0];
        for (int i = 1; i < grid[0].length; i++) {
            minSum[0][i] = grid[0][i] + minSum[0][i - 1];
        }
        for (int i = 1; i < grid.length; i++) {
            minSum[i][0] = grid[i][0] + minSum[i - 1][0];
        }
        
        for (int i = 1; i < grid.length; i++) {
            for (int j = 1; j < grid[0].length; j++) {
                minSum[i][j] = grid[i][j] + Math.min(minSum[i - 1][j], minSum[i][j - 1]);
            }
        }
        
        return minSum[grid.length - 1][grid[0].length - 1];
    }
}