From 5b0b1d239ebc5b340b9cae69e2656bc4ea89bc84 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Sat, 31 Oct 2026 14:03:47 +0800 Subject: [PATCH] =?UTF-8?q?Update=20Leetcode=20=E9=A2=98=E8=A7=A3=20-=20?= =?UTF-8?q?=E6=A0=91.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 新增二叉树中的最大路径和（124）；题目链接统一为 leetcode.cn。 --- notes/Leetcode 题解 - 树.md | 107 +++++++++++++++++++++++++----------- 1 file changed, 76 insertions(+), 31 deletions(-) diff --git a/notes/Leetcode 题解 - 树.md b/notes/Leetcode 题解 - 树.md index 8c7a6733..0adea088 100644 --- a/notes/Leetcode 题解 - 树.md +++ b/notes/Leetcode 题解 - 树.md @@ -16,6 +16,7 @@ * [12. 相同节点值的最大路径长度](#12-相同节点值的最大路径长度) * [13. 间隔遍历](#13-间隔遍历) * [14. 找出二叉树中第二小的节点](#14-找出二叉树中第二小的节点) + * [15. 二叉树中的最大路径和](#15-二叉树中的最大路径和) * [层次遍历](#层次遍历) * [1. 一棵树每层节点的平均数](#1-一棵树每层节点的平均数) * [2. 得到左下角的节点](#2-得到左下角的节点) @@ -49,7 +50,7 @@ 104\. Maximum Depth of Binary Tree (Easy) -[Leetcode](https://leetcode.com/problems/maximum-depth-of-binary-tree/description/) / [力扣](https://leetcode-cn.com/problems/maximum-depth-of-binary-tree/description/) +[Leetcode](https://leetcode.com/problems/maximum-depth-of-binary-tree/description/) / [力扣](https://leetcode.cn/problems/maximum-depth-of-binary-tree/description/) ```java public int maxDepth(TreeNode root) { @@ -62,7 +63,7 @@ public int maxDepth(TreeNode root) { 110\. Balanced Binary Tree (Easy) -[Leetcode](https://leetcode.com/problems/balanced-binary-tree/description/) / [力扣](https://leetcode-cn.com/problems/balanced-binary-tree/description/) +[Leetcode](https://leetcode.com/problems/balanced-binary-tree/description/) / [力扣](https://leetcode.cn/problems/balanced-binary-tree/description/) ```text 3 @@ -95,7 +96,7 @@ public int maxDepth(TreeNode root) { 543\. Diameter of Binary Tree (Easy) -[Leetcode](https://leetcode.com/problems/diameter-of-binary-tree/description/) / [力扣](https://leetcode-cn.com/problems/diameter-of-binary-tree/description/) +[Leetcode](https://leetcode.com/problems/diameter-of-binary-tree/description/) / [力扣](https://leetcode.cn/problems/diameter-of-binary-tree/description/) ```text Input: @@ -132,7 +133,7 @@ private int depth(TreeNode root) { 226\. Invert Binary Tree (Easy) -[Leetcode](https://leetcode.com/problems/invert-binary-tree/description/) / [力扣](https://leetcode-cn.com/problems/invert-binary-tree/description/) +[Leetcode](https://leetcode.com/problems/invert-binary-tree/description/) / [力扣](https://leetcode.cn/problems/invert-binary-tree/description/) ```java public TreeNode invertTree(TreeNode root) { @@ -148,7 +149,7 @@ public TreeNode invertTree(TreeNode root) { 617\. Merge Two Binary Trees (Easy) -[Leetcode](https://leetcode.com/problems/merge-two-binary-trees/description/) / [力扣](https://leetcode-cn.com/problems/merge-two-binary-trees/description/) +[Leetcode](https://leetcode.com/problems/merge-two-binary-trees/description/) / [力扣](https://leetcode.cn/problems/merge-two-binary-trees/description/) ```text Input: @@ -183,7 +184,7 @@ public TreeNode mergeTrees(TreeNode t1, TreeNode t2) { 112\. Path Sum (Easy) -[Leetcode](https://leetcode.com/problems/path-sum/description/) / [力扣](https://leetcode-cn.com/problems/path-sum/description/) +[Leetcode](https://leetcode.com/problems/path-sum/description/) / [力扣](https://leetcode.cn/problems/path-sum/description/) ```text Given the below binary tree and sum = 22, @@ -213,7 +214,7 @@ public boolean hasPathSum(TreeNode root, int sum) { 437\. Path Sum III (Medium) -[Leetcode](https://leetcode.com/problems/path-sum-iii/description/) / [力扣](https://leetcode-cn.com/problems/path-sum-iii/description/) +[Leetcode](https://leetcode.com/problems/path-sum-iii/description/) / [力扣](https://leetcode.cn/problems/path-sum-iii/description/) ```text root = [10,5,-3,3,2,null,11,3,-2,null,1], sum = 8 @@ -259,7 +260,7 @@ private int pathSumStartWithRoot(TreeNode root, long sum) { 572\. Subtree of Another Tree (Easy) -[Leetcode](https://leetcode.com/problems/subtree-of-another-tree/description/) / [力扣](https://leetcode-cn.com/problems/subtree-of-another-tree/description/) +[Leetcode](https://leetcode.com/problems/subtree-of-another-tree/description/) / [力扣](https://leetcode.cn/problems/subtree-of-another-tree/description/) ```text Given tree s: @@ -312,7 +313,7 @@ private boolean isSubtreeWithRoot(TreeNode s, TreeNode t) { 101\. Symmetric Tree (Easy) -[Leetcode](https://leetcode.com/problems/symmetric-tree/description/) / [力扣](https://leetcode-cn.com/problems/symmetric-tree/description/) +[Leetcode](https://leetcode.com/problems/symmetric-tree/description/) / [力扣](https://leetcode.cn/problems/symmetric-tree/description/) ```text 1 @@ -340,7 +341,7 @@ private boolean isSymmetric(TreeNode t1, TreeNode t2) { 111\. Minimum Depth of Binary Tree (Easy) -[Leetcode](https://leetcode.com/problems/minimum-depth-of-binary-tree/description/) / [力扣](https://leetcode-cn.com/problems/minimum-depth-of-binary-tree/description/) +[Leetcode](https://leetcode.com/problems/minimum-depth-of-binary-tree/description/) / [力扣](https://leetcode.cn/problems/minimum-depth-of-binary-tree/description/) 树的根节点到叶子节点的最小路径长度。 @@ -360,7 +361,7 @@ public int minDepth(TreeNode root) { 404\. Sum of Left Leaves (Easy) -[Leetcode](https://leetcode.com/problems/sum-of-left-leaves/description/) / [力扣](https://leetcode-cn.com/problems/sum-of-left-leaves/description/) +[Leetcode](https://leetcode.com/problems/sum-of-left-leaves/description/) / [力扣](https://leetcode.cn/problems/sum-of-left-leaves/description/) ```text 3 @@ -389,7 +390,7 @@ private boolean isLeaf(TreeNode node){ 687\. Longest Univalue Path (Medium) -[Leetcode](https://leetcode.com/problems/longest-univalue-path/) / [力扣](https://leetcode-cn.com/problems/longest-univalue-path/) +[Leetcode](https://leetcode.com/problems/longest-univalue-path/) / [力扣](https://leetcode.cn/problems/longest-univalue-path/) ```text 1 @@ -426,7 +427,7 @@ private int dfs(TreeNode root){ 337\. House Robber III (Medium) -[Leetcode](https://leetcode.com/problems/house-robber-iii/description/) / [力扣](https://leetcode-cn.com/problems/house-robber-iii/description/) +[Leetcode](https://leetcode.com/problems/house-robber-iii/description/) / [力扣](https://leetcode.cn/problems/house-robber-iii/description/) ```text 3 @@ -459,7 +460,7 @@ public int rob(TreeNode root) { 671\. Second Minimum Node In a Binary Tree (Easy) -[Leetcode](https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/description/) / [力扣](https://leetcode-cn.com/problems/second-minimum-node-in-a-binary-tree/description/) +[Leetcode](https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/description/) / [力扣](https://leetcode.cn/problems/second-minimum-node-in-a-binary-tree/description/) ```text Input: @@ -490,6 +491,50 @@ public int findSecondMinimumValue(TreeNode root) { } ``` +### 15. 二叉树中的最大路径和 + +124\. Binary Tree Maximum Path Sum (Hard) + +[Leetcode](https://leetcode.com/problems/binary-tree-maximum-path-sum/) / [力扣](https://leetcode.cn/problems/binary-tree-maximum-path-sum/) + +```text +Input: + 2 + / \ + -6 3 + / \ / \ + 3 1 4 6 + +Output: 13，路径为 4 -> 3 -> 6 +``` + +做法与 [两节点的最长路径](#3-两节点的最长路径) 相同：以每个节点为最高点算一次经过它的最大路径，取最大值。不同的有两处： + +- 子树的贡献是负数时不如不走，记为 0，例如 -6 这棵子树向上最多贡献 -6 + 3 = -3，所以根节点不接它； +- 递归返回的只能是向下走一侧的最大和，不能是两侧之和。3 这个节点两侧都接上是 4 + 3 + 6 = 13，但返回给父节点的是 3 + 6 = 9，否则路径会在 3 处分叉。 + +节点值可能全是负数，max 的初值取 Integer.MIN_VALUE，不能取 0。 + +```java +private int max = Integer.MIN_VALUE; + +public int maxPathSum(TreeNode root) { + gain(root); + return max; +} + +// 以 root 为起点向下走一侧的最大路径和 +private int gain(TreeNode root) { + if (root == null) return 0; + int left = Math.max(gain(root.left), 0); + int right = Math.max(gain(root.right), 0); + max = Math.max(max, root.val + left + right); + return root.val + Math.max(left, right); +} +``` + +每个节点访问一次，时间复杂度 O(N)；递归深度为树的高度，空间复杂度 O(H)。 + ## 层次遍历 使用 BFS 进行层次遍历。不需要使用两个队列来分别存储当前层的节点和下一层的节点，因为在开始遍历一层的节点时，当前队列中的节点数就是当前层的节点数，只要控制遍历这么多节点数，就能保证这次遍历的都是当前层的节点。按层输出（102 题）和之字形输出的写法见[剑指 Offer 32.2](32.2%20把二叉树打印成多行.md)、[32.3](32.3%20按之字形顺序打印二叉树.md)。 @@ -498,7 +543,7 @@ public int findSecondMinimumValue(TreeNode root) { 637\. Average of Levels in Binary Tree (Easy) -[Leetcode](https://leetcode.com/problems/average-of-levels-in-binary-tree/description/) / [力扣](https://leetcode-cn.com/problems/average-of-levels-in-binary-tree/description/) +[Leetcode](https://leetcode.com/problems/average-of-levels-in-binary-tree/description/) / [力扣](https://leetcode.cn/problems/average-of-levels-in-binary-tree/description/) ```java public List averageOfLevels(TreeNode root) { @@ -525,7 +570,7 @@ public List averageOfLevels(TreeNode root) { 513\. Find Bottom Left Tree Value (Medium) -[Leetcode](https://leetcode.com/problems/find-bottom-left-tree-value/description/) / [力扣](https://leetcode-cn.com/problems/find-bottom-left-tree-value/description/) +[Leetcode](https://leetcode.com/problems/find-bottom-left-tree-value/description/) / [力扣](https://leetcode.cn/problems/find-bottom-left-tree-value/description/) ```text Input: @@ -613,7 +658,7 @@ void dfs(TreeNode root) { 144\. Binary Tree Preorder Traversal (Easy) -[Leetcode](https://leetcode.com/problems/binary-tree-preorder-traversal/description/) / [力扣](https://leetcode-cn.com/problems/binary-tree-preorder-traversal/description/) +[Leetcode](https://leetcode.com/problems/binary-tree-preorder-traversal/description/) / [力扣](https://leetcode.cn/problems/binary-tree-preorder-traversal/description/) ```java public List preorderTraversal(TreeNode root) { @@ -635,7 +680,7 @@ public List preorderTraversal(TreeNode root) { 145\. Binary Tree Postorder Traversal (Easy) -[Leetcode](https://leetcode.com/problems/binary-tree-postorder-traversal/description/) / [力扣](https://leetcode-cn.com/problems/binary-tree-postorder-traversal/description/) +[Leetcode](https://leetcode.com/problems/binary-tree-postorder-traversal/description/) / [力扣](https://leetcode.cn/problems/binary-tree-postorder-traversal/description/) 前序遍历为 root -\> left -\> right，后序遍历为 left -\> right -\> root。可以修改前序遍历成为 root -\> right -\> left，那么这个顺序就和后序遍历正好相反。 @@ -687,7 +732,7 @@ public List postorderTraversal(TreeNode root) { 94\. Binary Tree Inorder Traversal (Easy) -[Leetcode](https://leetcode.com/problems/binary-tree-inorder-traversal/description/) / [力扣](https://leetcode-cn.com/problems/binary-tree-inorder-traversal/description/) +[Leetcode](https://leetcode.com/problems/binary-tree-inorder-traversal/description/) / [力扣](https://leetcode.cn/problems/binary-tree-inorder-traversal/description/) 从 cur 一路向左压栈直到为空，弹出栈顶访问后转向它的右子树。以上面的树为例： @@ -722,7 +767,7 @@ public List inorderTraversal(TreeNode root) { 669\. Trim a Binary Search Tree (Medium) -[Leetcode](https://leetcode.com/problems/trim-a-binary-search-tree/description/) / [力扣](https://leetcode-cn.com/problems/trim-a-binary-search-tree/description/) +[Leetcode](https://leetcode.com/problems/trim-a-binary-search-tree/description/) / [力扣](https://leetcode.cn/problems/trim-a-binary-search-tree/description/) ```text Input: @@ -766,7 +811,7 @@ public TreeNode trimBST(TreeNode root, int L, int R) { 230\. Kth Smallest Element in a BST (Medium) -[Leetcode](https://leetcode.com/problems/kth-smallest-element-in-a-bst/description/) / [力扣](https://leetcode-cn.com/problems/kth-smallest-element-in-a-bst/description/) +[Leetcode](https://leetcode.com/problems/kth-smallest-element-in-a-bst/description/) / [力扣](https://leetcode.cn/problems/kth-smallest-element-in-a-bst/description/) 中序遍历解法： @@ -812,7 +857,7 @@ private int count(TreeNode node) { 538\. Convert BST to Greater Tree (Medium) -[Leetcode](https://leetcode.com/problems/convert-bst-to-greater-tree/description/) / [力扣](https://leetcode-cn.com/problems/convert-bst-to-greater-tree/description/) +[Leetcode](https://leetcode.com/problems/convert-bst-to-greater-tree/description/) / [力扣](https://leetcode.cn/problems/convert-bst-to-greater-tree/description/) ```text Input: The root of a Binary Search Tree like this: @@ -851,7 +896,7 @@ private void traver(TreeNode node) { 235\. Lowest Common Ancestor of a Binary Search Tree (Medium) -[Leetcode](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/description/) / [力扣](https://leetcode-cn.com/problems/lowest-common-ancestor-of-a-binary-search-tree/description/) +[Leetcode](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/description/) / [力扣](https://leetcode.cn/problems/lowest-common-ancestor-of-a-binary-search-tree/description/) ```text _______6______ @@ -879,7 +924,7 @@ public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { 236\. Lowest Common Ancestor of a Binary Tree (Medium) -[Leetcode](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/description/) / [力扣](https://leetcode-cn.com/problems/lowest-common-ancestor-of-a-binary-tree/description/) +[Leetcode](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/description/) / [力扣](https://leetcode.cn/problems/lowest-common-ancestor-of-a-binary-tree/description/) ```text _______3______ @@ -912,7 +957,7 @@ public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { 108\. Convert Sorted Array to Binary Search Tree (Easy) -[Leetcode](https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/description/) / [力扣](https://leetcode-cn.com/problems/convert-sorted-array-to-binary-search-tree/description/) +[Leetcode](https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/description/) / [力扣](https://leetcode.cn/problems/convert-sorted-array-to-binary-search-tree/description/) 取中间的元素作为根，两侧的元素个数最多相差 1，因此树是平衡的。 @@ -935,7 +980,7 @@ private TreeNode toBST(int[] nums, int sIdx, int eIdx){ 109\. Convert Sorted List to Binary Search Tree (Medium) -[Leetcode](https://leetcode.com/problems/convert-sorted-list-to-binary-search-tree/description/) / [力扣](https://leetcode-cn.com/problems/convert-sorted-list-to-binary-search-tree/description/) +[Leetcode](https://leetcode.com/problems/convert-sorted-list-to-binary-search-tree/description/) / [力扣](https://leetcode.cn/problems/convert-sorted-list-to-binary-search-tree/description/) ```text Given the sorted linked list: [-10,-3,0,5,9], @@ -980,7 +1025,7 @@ private ListNode preMid(ListNode head) { 653\. Two Sum IV - Input is a BST (Easy) -[Leetcode](https://leetcode.com/problems/two-sum-iv-input-is-a-bst/description/) / [力扣](https://leetcode-cn.com/problems/two-sum-iv-input-is-a-bst/description/) +[Leetcode](https://leetcode.com/problems/two-sum-iv-input-is-a-bst/description/) / [力扣](https://leetcode.cn/problems/two-sum-iv-input-is-a-bst/description/) ```text Input: @@ -1026,7 +1071,7 @@ private void inOrder(TreeNode root, List nums) { 530\. Minimum Absolute Difference in BST (Easy) -[Leetcode](https://leetcode.com/problems/minimum-absolute-difference-in-bst/description/) / [力扣](https://leetcode-cn.com/problems/minimum-absolute-difference-in-bst/description/) +[Leetcode](https://leetcode.com/problems/minimum-absolute-difference-in-bst/description/) / [力扣](https://leetcode.cn/problems/minimum-absolute-difference-in-bst/description/) ```text Input: @@ -1066,7 +1111,7 @@ private void inOrder(TreeNode node) { 501\. Find Mode in Binary Search Tree (Easy) -[Leetcode](https://leetcode.com/problems/find-mode-in-binary-search-tree/description/) / [力扣](https://leetcode-cn.com/problems/find-mode-in-binary-search-tree/description/) +[Leetcode](https://leetcode.com/problems/find-mode-in-binary-search-tree/description/) / [力扣](https://leetcode.cn/problems/find-mode-in-binary-search-tree/description/) ```text 1 @@ -1127,7 +1172,7 @@ Trie，又称前缀树或字典树，用于判断字符串是否存在或者是 208\. Implement Trie (Prefix Tree) (Medium) -[Leetcode](https://leetcode.com/problems/implement-trie-prefix-tree/description/) / [力扣](https://leetcode-cn.com/problems/implement-trie-prefix-tree/description/) +[Leetcode](https://leetcode.com/problems/implement-trie-prefix-tree/description/) / [力扣](https://leetcode.cn/problems/implement-trie-prefix-tree/description/) ```java class Trie { @@ -1193,7 +1238,7 @@ class Trie { 677\. Map Sum Pairs (Medium) -[Leetcode](https://leetcode.com/problems/map-sum-pairs/description/) / [力扣](https://leetcode-cn.com/problems/map-sum-pairs/description/) +[Leetcode](https://leetcode.com/problems/map-sum-pairs/description/) / [力扣](https://leetcode.cn/problems/map-sum-pairs/description/) ```text Input: insert("apple", 3), Output: Null