Minimum Path Sum

最新推荐文章于 2019-10-26 15:10:44 发布

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本文介绍了一个算法问题：在一个填充了非负数的网格中找到从左上角到右下角的路径，使得路径上的数字之和最小。路径只能向下或向右移动。文章通过动态规划的方法解决了这个问题，并提供了一个Java实现。

Question:

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.

Code:

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