[leetcode]64. Minimum Path Sum(Java)

最新推荐文章于 2025-08-20 09:37:41 发布

JacobGo

最新推荐文章于 2025-08-20 09:37:41 发布

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分类专栏： leetcode 文章标签： Minimum Path Sum leetcode Java

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本文介绍了一个算法问题：在一个非负数构成的网格中寻找从左上角到右下角的路径，使得路径上的数值之和最小。文章提供了一种有效的解决方案，并详细解释了其背后的逻辑，包括如何通过动态规划来更新每个网格单元的最小路径和。

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https://leetcode.com/problems/minimum-path-sum/#/description

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.

package go.jacob.day628;

public class Demo2 {
	/*
	 * 除去第一行第一列，每一格的最短路径为左一格最短路径加上当前值，或者上一格最短路径加上当前值
	 * Runtime: 3 ms.Your runtime beats 86.66 % of java submissions
	 */
	public int minPathSum(int[][] grid) {
		if (grid == null || grid.length == 0 || grid[0].length == 0)
			return 0;
		int m = grid.length;
		int n = grid[0].length;
		for (int i = 1; i < m; i++) {
			grid[i][0] = grid[i - 1][0] + grid[i][0];
		}
		for (int i = 1; i < n; i++) {
			grid[0][i] = grid[0][i] + grid[0][i - 1];
		}

		for (int i = 1; i < m; i++) {
			for (int j = 1; j < n; j++) {
				grid[i][j] = (grid[i - 1][j] < grid[i][j - 1] ? grid[i - 1][j] : grid[i][j - 1]) + grid[i][j];
			}
		}

		return grid[m - 1][n - 1];
	}
}