Minimum Path Sum

最新推荐文章于 2019-03-28 21:33:42 发布

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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。通过构建状态转移方程，逐层计算最优路径，最终找到整个矩阵中的最小路径和。

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;
    }
}