LeetCode-Minimum Path Sum[dp]

Minimum Path Sum

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.

分析：

动态规划的经典题目，设dp[i][j]表示从位置[0,0]到[i,j]的最小路径和，要到达位置[i,j]只能从[i,j-1]或[i-1,j]向右或向下走一步到达，

所以状态转移方程为：

dp[i][j]=min(dp[i-1][j],dp[i][j-1])+grid[i][j];

由二维dp进一步优化为一维dp：

当j=0时，dp[j]=dp[j]+grid[i][j];

当0<j&&j<n时，dp[j]=min(dp[j],dp[j-1])+grid[i][j];

(此时的dp[j]等价于二维dp中的dp[i][j])

参考代码：

public class Solution {public int minPathSum(int[][] grid) {int nlen=grid.length;int mlen=grid[0].length;int dp[]=new int[mlen];dp[0]=grid[0][0];for(int j=1;j<mlen;j++){dp[j]=dp[j-1]+grid[0][j];}for(int i=1;i<nlen;i++){for(int j=0;j<mlen;j++){dp[j]=grid[i][j]+(j==0?(dp[j]):(Math.min(dp[j-1], dp[j])));}}return dp[mlen-1];}
}

转载于:https://www.cnblogs.com/xiaolu266/p/7151034.html

LeetCode-Minimum Path Sum[dp]相关推荐

[leetcode] Minimum Path Sum
Minimum Path Sum Given a m x n grid filled with non-negative numbers, find a path from top left to b ...
LeetCode Minimum Path Sum(动态规划)
Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right wh ...
LeetCode:Minimum Path Sum（网格最大路径和）
Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which ...
【DP】LeetCode 64. Minimum Path Sum
LeetCode 64. Minimum Path Sum Solution1:标准的动态规划题目 class Solution { public:int minPathSum(vector<v ...
【leetcode】Minimum Path Sum
Minimum Path Sum Given a m x n grid filled with non-negative numbers, find a path from top left to b ...
63. Unique Paths II and 64. Minimum Path Sum
文章目录 1 63 Unique Paths II 1.1 题目描述 1.2 动态规划解决 2 64. Minimum Path Sum 2.1 题目理解 2.2 动态规划这一遍刷dp的题目就很轻松 ...
[勇者闯LeetCode] 112. Path Sum
[勇者闯LeetCode] 112. Path Sum Description Given a binary tree and a sum, determine if the tree has a r ...
[LeetCode]113.Path Sum II
[题目] Given a binary tree and a sum, find all root-to-leaf paths where each path's sum equals the giv ...
leetcode 112. Path Sum, 113. Path Sum II | 112,113. 路径总和 I, II（Java）
题目 https://leetcode.com/problems/path-sum/ https://leetcode.com/problems/path-sum-ii/ 题解简单的遍历二叉树,不解 ...

LeetCode-Minimum Path Sum[dp]

Minimum Path Sum

LeetCode-Minimum Path Sum[dp]相关推荐

最新文章

热门文章