[leetcode] Minimum Path Sum

最新推荐文章于 2024-04-22 14:00:57 发布

转载最新推荐文章于 2024-04-22 14:00:57 发布 · 62 阅读

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原文链接：http://www.cnblogs.com/jdflyfly/p/3811045.html

本文介绍了一种解决LeetCode上最小路径和问题的方法，采用二维动态规划算法，通过逐步计算每个节点上的最小路径和来找到从左上角到右下角的最短路径。

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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.

https://oj.leetcode.com/problems/minimum-path-sum/

思路：二维DP。 len[i][j] = min(len[i-1][j], len[i][j-1]) +grid[i][j];

 1 public class Solution {
 2     public int minPathSum(int[][] grid) {
 3         if (grid == null || grid.length == 0 || grid[0].length == 0)
 4             return 0;
 5         int m = grid.length;
 6         int n = grid[0].length;
 7         int[][] len = new int[m][n];
 8 
 9         int i;
10         int sum = 0;
11         for (i = 0; i < m; i++) {
12             sum += grid[i][0];
13             len[i][0] = sum;
14         }
15         sum = 0;
16         for (i = 0; i < n; i++) {
17             sum += grid[0][i];
18             len[0][i] = sum;
19         }
20         int j;
21         for (i = 1; i < m; i++) {
22             for (j = 1; j < n; j++) {
23                 if (len[i][j] == 0) {
24                     len[i][j] = (len[i - 1][j] < len[i][j - 1] ? len[i - 1][j]
25                             : len[i][j - 1]) + grid[i][j];
26                 }
27 
28             }
29 
30         }
31 
32         return len[m - 1][n - 1];
33     }
34 
35     public static void main(String[] args) {
36         int[][] grid = { { 1 } };
37         System.out.println(new Solution().minPathSum(grid));
38     }
39 }