leetcode 931. Minimum Falling Path Sum（最小的下降路径和）

下降的路径就是从第一行任一个元素出发，只能直着或斜着走到下一行，直到到达最后一行，返回形成的路径中最小的路径和。

思路：

DP
从下往上推，
在最后一行选一个元素，那么它是从哪里过来的？是从上一行的j-1, j, j+1 3个位置过来的。
设dp[ i ] [ j ]是从第一行任一元素到[ i][ j ]所在元素的所有路径的最小路径和。
那么dp[ i ][ j ] = min(dp[ i - 1][j - 1], dp[i - 1] [ j ], dp[i-1][j+1]) + matrix[ i ][ j ],

然后取dp[n-1]这一行的最小值即可。

    public int minFallingPathSum(int[][] matrix) {int n = matrix.length;int res = 10000000;int[][] dp = new int[n][n];for(int j = 0; j < n; j++) dp[0][j] = matrix[0][j];for(int i = 1; i < n; i++) {for(int j = 0; j < n; j++) {if(j == 0) {dp[i][j] = Math.min(dp[i-1][j], dp[i-1][j+1]) + matrix[i][j];} else if(j == n-1) {dp[i][j] = Math.min(dp[i-1][j-1], dp[i-1][j]) + matrix[i][j];} else {dp[i][j] = Math.min(Math.min(dp[i-1][j-1], dp[i-1][j]), dp[i-1][j+1]) + matrix[i][j];}}}for(int j = 0; j < n; j++) {res = Math.min(res, dp[n-1][j]);}return res;}

上面的方法好理解，但不是最快的，最快的参考

class Solution {int ans = Integer.MAX_VALUE;public int minFallingPathSum(int[][] matrix) {helper(matrix, matrix.length-2);return ans;}void helper(int[][] matrix, int r) {if(r<0) {for(int i=0; i<matrix.length; i++) {ans = Math.min(ans, matrix[0][i]);}return;}for(int i=0; i<matrix.length; i++) {int minNextVal = matrix[r+1][i];if(i>0) {minNextVal = Math.min(minNextVal, matrix[r+1][i-1]);}if(i<matrix.length-1) {minNextVal = Math.min(minNextVal, matrix[r+1][i+1]);}matrix[r][i] += minNextVal;}helper(matrix, r-1);}
}

leetcode 931. Minimum Falling Path Sum（最小的下降路径和）相关推荐

【leetcode】931. Minimum Falling Path Sum
题目如下: Given a square array of integers A, we want the minimum sum of a falling path through A. A fal ...
Leetcode | Binary Tree Maximum Path Sum
Given a binary tree, find the maximum path sum. The path may start and end at any node in the tree. ...
[Leetcode] Binary Tree Maximum Path Sum
这是LeetCode上的一道题目,需要求二叉树中两点路径的最大和.原题是 https://oj.leetcode.com/problems/binary-tree-maximum-path-sum/ ...
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 712. Minimum ASCII Delete Sum for Two Strings
712.Minimum ASCII Delete Sum for Two Strings(两个字符串的最小ASCII删除和) 题目: 给定两个字符串s1, s2,找到使两个字符串相等所需删除字符的AS ...
Leetcode: Binary Tree Maximum Path Sum
Given a binary tree, find the maximum path sum.The path may start and end at any node in the tree.Fo ...
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 ...
leetcode 712. Minimum ASCII Delete Sum for Two Strings | 712. 两个字符串的最小ASCII删除和（暴力递归-＞傻缓存-＞DP）
题目 https://leetcode.com/problems/minimum-ascii-delete-sum-for-two-strings/ 题解经典的暴力递归 -> 傻缓存 -&g ...
leetcode 209. Minimum Size Subarray Sum | 209. 长度最小的子数组（Java）
题目 https://leetcode.com/problems/minimum-size-subarray-sum/ 题解双指针解法,左指针和右指针在合适的时候向右走,并维护一个sum 版本1 思 ...

leetcode 931. Minimum Falling Path Sum（最小的下降路径和）

思路：

leetcode 931. Minimum Falling Path Sum（最小的下降路径和）相关推荐

最新文章

热门文章