# Leetcode 题解 - 树 * [Leetcode 题解 - 树](#leetcode-题解---树) * [递归](#递归) * [1. 树的高度](#1-树的高度) * [2. 平衡树](#2-平衡树) * [3. 两节点的最长路径](#3-两节点的最长路径) * [4. 翻转树](#4-翻转树) * [5. 归并两棵树](#5-归并两棵树) * [6. 判断路径和是否等于一个数](#6-判断路径和是否等于一个数) * [7. 统计路径和等于一个数的路径数量](#7-统计路径和等于一个数的路径数量) * [8. 子树](#8-子树) * [9. 树的对称](#9-树的对称) * [10. 最小路径](#10-最小路径) * [11. 统计左叶子节点的和](#11-统计左叶子节点的和) * [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) * [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) * [前中后序遍历](#前中后序遍历) * [1. 非递归实现二叉树的前序遍历](#1-非递归实现二叉树的前序遍历) * [2. 非递归实现二叉树的后序遍历](#2-非递归实现二叉树的后序遍历) * [3. 非递归实现二叉树的中序遍历](#3-非递归实现二叉树的中序遍历) * [BST](#bst) * [1. 修剪二叉查找树](#1-修剪二叉查找树) * [2. 寻找二叉查找树的第 k 个元素](#2-寻找二叉查找树的第-k-个元素) * [3. 把二叉查找树每个节点的值都加上比它大的节点的值](#3-把二叉查找树每个节点的值都加上比它大的节点的值) * [4. 二叉查找树的最近公共祖先](#4-二叉查找树的最近公共祖先) * [5. 二叉树的最近公共祖先](#5-二叉树的最近公共祖先) * [6. 从有序数组中构造二叉查找树](#6-从有序数组中构造二叉查找树) * [7. 根据有序链表构造平衡的二叉查找树](#7-根据有序链表构造平衡的二叉查找树) * [8. 在二叉查找树中寻找两个节点，使它们的和为一个给定值](#8-在二叉查找树中寻找两个节点，使它们的和为一个给定值) * [9. 在二叉查找树中查找两个节点之差的最小绝对值](#9-在二叉查找树中查找两个节点之差的最小绝对值) * [10. 寻找二叉查找树中出现次数最多的值](#10-寻找二叉查找树中出现次数最多的值) * [Trie](#trie) * [1. 实现一个 Trie](#1-实现一个-trie) * [2. 实现一个 Trie，用来求前缀和](#2-实现一个-trie，用来求前缀和) ## 递归 一棵树要么是空树，要么有两个指针，每个指针指向一棵树。树是一种递归结构，很多树的问题可以使用递归来处理。 ### 1. 树的高度 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/) ```java public int maxDepth(TreeNode root) { if (root == null) return 0; return Math.max(maxDepth(root.left), maxDepth(root.right)) + 1; } ``` ### 2. 平衡树 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/) ```html 3 / \ 9 20 / \ 15 7 ``` 平衡树左右子树高度差都小于等于 1 ```java private boolean result = true; public boolean isBalanced(TreeNode root) { maxDepth(root); return result; } public int maxDepth(TreeNode root) { if (root == null) return 0; int l = maxDepth(root.left); int r = maxDepth(root.right); if (Math.abs(l - r) > 1) result = false; return 1 + Math.max(l, r); } ``` ### 3. 两节点的最长路径 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/) ```html Input: 1 / \ 2 3 / \ 4 5 Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3]. ``` ```java private int max = 0; public int diameterOfBinaryTree(TreeNode root) { depth(root); return max; } private int depth(TreeNode root) { if (root == null) return 0; int leftDepth = depth(root.left); int rightDepth = depth(root.right); max = Math.max(max, leftDepth + rightDepth); return Math.max(leftDepth, rightDepth) + 1; } ``` ### 4. 翻转树 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/) ```java public TreeNode invertTree(TreeNode root) { if (root == null) return null; TreeNode left = root.left; // 后面的操作会改变 left 指针，因此先保存下来 root.left = invertTree(root.right); root.right = invertTree(left); return root; } ``` ### 5. 归并两棵树 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/) ```html Input: Tree 1 Tree 2 1 2 / \ / \ 3 2 1 3 / \ \ 5 4 7 Output: 3 / \ 4 5 / \ \ 5 4 7 ``` ```java public TreeNode mergeTrees(TreeNode t1, TreeNode t2) { if (t1 == null && t2 == null) return null; if (t1 == null) return t2; if (t2 == null) return t1; TreeNode root = new TreeNode(t1.val + t2.val); root.left = mergeTrees(t1.left, t2.left); root.right = mergeTrees(t1.right, t2.right); return root; } ``` ### 6. 判断路径和是否等于一个数 Leetcdoe : 112. Path Sum (Easy) [Leetcode](https://leetcode.com/problems/path-sum/description/) / [力扣](https://leetcode-cn.com/problems/path-sum/description/) ```html Given the below binary tree and sum = 22, 5 / \ 4 8 / / \ 11 13 4 / \ \ 7 2 1 return true, as there exist a root-to-leaf path 5->4->11->2 which sum is 22. ``` 路径和定义为从 root 到 leaf 的所有节点的和。 ```java public boolean hasPathSum(TreeNode root, int sum) { if (root == null) return false; if (root.left == null && root.right == null && root.val == sum) return true; return hasPathSum(root.left, sum - root.val) || hasPathSum(root.right, sum - root.val); } ``` ### 7. 统计路径和等于一个数的路径数量 437\. Path Sum III (Easy) [Leetcode](https://leetcode.com/problems/path-sum-iii/description/) / [力扣](https://leetcode-cn.com/problems/path-sum-iii/description/) ```html root = [10,5,-3,3,2,null,11,3,-2,null,1], sum = 8 10 / \ 5 -3 / \ \ 3 2 11 / \ \ 3 -2 1 Return 3. The paths that sum to 8 are: 1. 5 -> 3 2. 5 -> 2 -> 1 3. -3 -> 11 ``` 路径不一定以 root 开头，也不一定以 leaf 结尾，但是必须连续。 ```java public int pathSum(TreeNode root, int sum) { if (root == null) return 0; int ret = pathSumStartWithRoot(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum); return ret; } private int pathSumStartWithRoot(TreeNode root, int sum) { if (root == null) return 0; int ret = 0; if (root.val == sum) ret++; ret += pathSumStartWithRoot(root.left, sum - root.val) + pathSumStartWithRoot(root.right, sum - root.val); return ret; } ``` ### 8. 子树 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/) ```html Given tree s: 3 / \ 4 5 / \ 1 2 Given tree t: 4 / \ 1 2 Return true, because t has the same structure and node values with a subtree of s. Given tree s: 3 / \ 4 5 / \ 1 2 / 0 Given tree t: 4 / \ 1 2 Return false. ``` ```java public boolean isSubtree(TreeNode s, TreeNode t) { if (s == null) return false; return isSubtreeWithRoot(s, t) || isSubtree(s.left, t) || isSubtree(s.right, t); } private boolean isSubtreeWithRoot(TreeNode s, TreeNode t) { if (t == null && s == null) return true; if (t == null || s == null) return false; if (t.val != s.val) return false; return isSubtreeWithRoot(s.left, t.left) && isSubtreeWithRoot(s.right, t.right); } ``` ### 9. 树的对称 101\. Symmetric Tree (Easy) [Leetcode](https://leetcode.com/problems/symmetric-tree/description/) / [力扣](https://leetcode-cn.com/problems/symmetric-tree/description/) ```html 1 / \ 2 2 / \ / \ 3 4 4 3 ``` ```java public boolean isSymmetric(TreeNode root) { if (root == null) return true; return isSymmetric(root.left, root.right); } private boolean isSymmetric(TreeNode t1, TreeNode t2) { if (t1 == null && t2 == null) return true; if (t1 == null || t2 == null) return false; if (t1.val != t2.val) return false; return isSymmetric(t1.left, t2.right) && isSymmetric(t1.right, t2.left); } ``` ### 10. 最小路径 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/) 树的根节点到叶子节点的最小路径长度 ```java public int minDepth(TreeNode root) { if (root == null) return 0; int left = minDepth(root.left); int right = minDepth(root.right); if (left == 0 || right == 0) return left + right + 1; return Math.min(left, right) + 1; } ``` ### 11. 统计左叶子节点的和 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/) ```html 3 / \ 9 20 / \ 15 7 There are two left leaves in the binary tree, with values 9 and 15 respectively. Return 24. ``` ```java public int sumOfLeftLeaves(TreeNode root) { if (root == null) return 0; if (isLeaf(root.left)) return root.left.val + sumOfLeftLeaves(root.right); return sumOfLeftLeaves(root.left) + sumOfLeftLeaves(root.right); } private boolean isLeaf(TreeNode node){ if (node == null) return false; return node.left == null && node.right == null; } ``` ### 12. 相同节点值的最大路径长度 687\. Longest Univalue Path (Easy) [Leetcode](https://leetcode.com/problems/longest-univalue-path/) / [力扣](https://leetcode-cn.com/problems/longest-univalue-path/) ```html 1 / \ 4 5 / \ \ 4 4 5 Output : 2 ``` ```java private int path = 0; public int longestUnivaluePath(TreeNode root) { dfs(root); return path; } private int dfs(TreeNode root){ if (root == null) return 0; int left = dfs(root.left); int right = dfs(root.right); int leftPath = root.left != null && root.left.val == root.val ? left + 1 : 0; int rightPath = root.right != null && root.right.val == root.val ? right + 1 : 0; path = Math.max(path, leftPath + rightPath); return Math.max(leftPath, rightPath); } ``` ### 13. 间隔遍历 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/) ```html 3 / \ 2 3 \ \ 3 1 Maximum amount of money the thief can rob = 3 + 3 + 1 = 7. ``` ```java public int rob(TreeNode root) { if (root == null) return 0; int val1 = root.val; if (root.left != null) val1 += rob(root.left.left) + rob(root.left.right); if (root.right != null) val1 += rob(root.right.left) + rob(root.right.right); int val2 = rob(root.left) + rob(root.right); return Math.max(val1, val2); } ``` ### 14. 找出二叉树中第二小的节点 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/) ```html Input: 2 / \ 2 5 / \ 5 7 Output: 5 ``` 一个节点要么具有 0 个或 2 个子节点，如果有子节点，那么根节点是最小的节点。 ```java public int findSecondMinimumValue(TreeNode root) { if (root == null) return -1; if (root.left == null && root.right == null) return -1; int leftVal = root.left.val; int rightVal = root.right.val; if (leftVal == root.val) leftVal = findSecondMinimumValue(root.left); if (rightVal == root.val) rightVal = findSecondMinimumValue(root.right); if (leftVal != -1 && rightVal != -1) return Math.min(leftVal, rightVal); if (leftVal != -1) return leftVal; return rightVal; } ``` ## 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。 ### 1. 一棵树每层节点的平均数 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/) ```java public List averageOfLevels(TreeNode root) { List ret = new ArrayList<>(); if (root == null) return ret; Queue queue = new LinkedList<>(); queue.add(root); while (!queue.isEmpty()) { int cnt = queue.size(); double sum = 0; for (int i = 0; i < cnt; i++) { TreeNode node = queue.poll(); sum += node.val; if (node.left != null) queue.add(node.left); if (node.right != null) queue.add(node.right); } ret.add(sum / cnt); } return ret; } ``` ### 2. 得到左下角的节点 513\. Find Bottom Left Tree Value (Easy) [Leetcode](https://leetcode.com/problems/find-bottom-left-tree-value/description/) / [力扣](https://leetcode-cn.com/problems/find-bottom-left-tree-value/description/) ```html Input: 1 / \ 2 3 / / \ 4 5 6 / 7 Output: 7 ``` ```java public int findBottomLeftValue(TreeNode root) { Queue queue = new LinkedList<>(); queue.add(root); while (!queue.isEmpty()) { root = queue.poll(); if (root.right != null) queue.add(root.right); if (root.left != null) queue.add(root.left); } return root.val; } ``` ## 前中后序遍历 ```html 1 / \ 2 3 / \ \ 4 5 6 ``` - 层次遍历顺序：[1 2 3 4 5 6] - 前序遍历顺序：[1 2 4 5 3 6] - 中序遍历顺序：[4 2 5 1 3 6] - 后序遍历顺序：[4 5 2 6 3 1] 层次遍历使用 BFS 实现，利用的就是 BFS 一层一层遍历的特性；而前序、中序、后序遍历利用了 DFS 实现。 前序、中序、后序遍只是在对节点访问的顺序有一点不同，其它都相同。 ① 前序 ```java void dfs(TreeNode root) { visit(root); dfs(root.left); dfs(root.right); } ``` ② 中序 ```java void dfs(TreeNode root) { dfs(root.left); visit(root); dfs(root.right); } ``` ③ 后序 ```java void dfs(TreeNode root) { dfs(root.left); dfs(root.right); visit(root); } ``` ### 1. 非递归实现二叉树的前序遍历 144\. Binary Tree Preorder Traversal (Medium) [Leetcode](https://leetcode.com/problems/binary-tree-preorder-traversal/description/) / [力扣](https://leetcode-cn.com/problems/binary-tree-preorder-traversal/description/) ```java public List preorderTraversal(TreeNode root) { List ret = new ArrayList<>(); Stack stack = new Stack<>(); stack.push(root); while (!stack.isEmpty()) { TreeNode node = stack.pop(); if (node == null) continue; ret.add(node.val); stack.push(node.right); // 先右后左，保证左子树先遍历 stack.push(node.left); } return ret; } ``` ### 2. 非递归实现二叉树的后序遍历 145\. Binary Tree Postorder Traversal (Medium) [Leetcode](https://leetcode.com/problems/binary-tree-postorder-traversal/description/) / [力扣](https://leetcode-cn.com/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。 ```java public List postorderTraversal(TreeNode root) { List ret = new ArrayList<>(); Stack stack = new Stack<>(); stack.push(root); while (!stack.isEmpty()) { TreeNode node = stack.pop(); if (node == null) continue; ret.add(node.val); stack.push(node.left); stack.push(node.right); } Collections.reverse(ret); return ret; } ``` ### 3. 非递归实现二叉树的中序遍历 94\. Binary Tree Inorder Traversal (Medium) [Leetcode](https://leetcode.com/problems/binary-tree-inorder-traversal/description/) / [力扣](https://leetcode-cn.com/problems/binary-tree-inorder-traversal/description/) ```java public List inorderTraversal(TreeNode root) { List ret = new ArrayList<>(); if (root == null) return ret; Stack stack = new Stack<>(); TreeNode cur = root; while (cur != null || !stack.isEmpty()) { while (cur != null) { stack.push(cur); cur = cur.left; } TreeNode node = stack.pop(); ret.add(node.val); cur = node.right; } return ret; } ``` ## BST 二叉查找树（BST）：根节点大于等于左子树所有节点，小于等于右子树所有节点。 二叉查找树中序遍历有序。 ### 1. 修剪二叉查找树 669\. Trim a Binary Search Tree (Easy) [Leetcode](https://leetcode.com/problems/trim-a-binary-search-tree/description/) / [力扣](https://leetcode-cn.com/problems/trim-a-binary-search-tree/description/) ```html Input: 3 / \ 0 4 \ 2 / 1 L = 1 R = 3 Output: 3 / 2 / 1 ``` 题目描述：只保留值在 L \~ R 之间的节点 ```java public TreeNode trimBST(TreeNode root, int L, int R) { if (root == null) return null; if (root.val > R) return trimBST(root.left, L, R); if (root.val < L) return trimBST(root.right, L, R); root.left = trimBST(root.left, L, R); root.right = trimBST(root.right, L, R); return root; } ``` ### 2. 寻找二叉查找树的第 k 个元素 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/) 中序遍历解法： ```java private int cnt = 0; private int val; public int kthSmallest(TreeNode root, int k) { inOrder(root, k); return val; } private void inOrder(TreeNode node, int k) { if (node == null) return; inOrder(node.left, k); cnt++; if (cnt == k) { val = node.val; return; } inOrder(node.right, k); } ``` 递归解法： ```java public int kthSmallest(TreeNode root, int k) { int leftCnt = count(root.left); if (leftCnt == k - 1) return root.val; if (leftCnt > k - 1) return kthSmallest(root.left, k); return kthSmallest(root.right, k - leftCnt - 1); } private int count(TreeNode node) { if (node == null) return 0; return 1 + count(node.left) + count(node.right); } ``` ### 3. 把二叉查找树每个节点的值都加上比它大的节点的值 Convert BST to Greater Tree (Easy) [Leetcode](https://leetcode.com/problems/convert-bst-to-greater-tree/description/) / [力扣](https://leetcode-cn.com/problems/convert-bst-to-greater-tree/description/) ```html Input: The root of a Binary Search Tree like this: 5 / \ 2 13 Output: The root of a Greater Tree like this: 18 / \ 20 13 ``` 先遍历右子树。 ```java private int sum = 0; public TreeNode convertBST(TreeNode root) { traver(root); return root; } private void traver(TreeNode node) { if (node == null) return; traver(node.right); sum += node.val; node.val = sum; traver(node.left); } ``` ### 4. 二叉查找树的最近公共祖先 235\. Lowest Common Ancestor of a Binary Search Tree (Easy) [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/) ```html _______6______ / \ ___2__ ___8__ / \ / \ 0 4 7 9 / \ 3 5 For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition. ``` ```java public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { if (root.val > p.val && root.val > q.val) return lowestCommonAncestor(root.left, p, q); if (root.val < p.val && root.val < q.val) return lowestCommonAncestor(root.right, p, q); return root; } ``` ### 5. 二叉树的最近公共祖先 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/) ```html _______3______ / \ ___5__ ___1__ / \ / \ 6 2 0 8 / \ 7 4 For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition. ``` ```java public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { if (root == null || root == p || root == q) return root; TreeNode left = lowestCommonAncestor(root.left, p, q); TreeNode right = lowestCommonAncestor(root.right, p, q); return left == null ? right : right == null ? left : root; } ``` ### 6. 从有序数组中构造二叉查找树 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/) ```java public TreeNode sortedArrayToBST(int[] nums) { return toBST(nums, 0, nums.length - 1); } private TreeNode toBST(int[] nums, int sIdx, int eIdx){ if (sIdx > eIdx) return null; int mIdx = (sIdx + eIdx) / 2; TreeNode root = new TreeNode(nums[mIdx]); root.left = toBST(nums, sIdx, mIdx - 1); root.right = toBST(nums, mIdx + 1, eIdx); return root; } ``` ### 7. 根据有序链表构造平衡的二叉查找树 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/) ```html Given the sorted linked list: [-10,-3,0,5,9], One possible answer is: [0,-3,9,-10,null,5], which represents the following height balanced BST: 0 / \ -3 9 / / -10 5 ``` ```java public TreeNode sortedListToBST(ListNode head) { if (head == null) return null; if (head.next == null) return new TreeNode(head.val); ListNode preMid = preMid(head); ListNode mid = preMid.next; preMid.next = null; // 断开链表 TreeNode t = new TreeNode(mid.val); t.left = sortedListToBST(head); t.right = sortedListToBST(mid.next); return t; } private ListNode preMid(ListNode head) { ListNode slow = head, fast = head.next; ListNode pre = head; while (fast != null && fast.next != null) { pre = slow; slow = slow.next; fast = fast.next.next; } return pre; } ``` ### 8. 在二叉查找树中寻找两个节点，使它们的和为一个给定值 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/) ```html Input: 5 / \ 3 6 / \ \ 2 4 7 Target = 9 Output: True ``` 使用中序遍历得到有序数组之后，再利用双指针对数组进行查找。 应该注意到，这一题不能用分别在左右子树两部分来处理这种思想，因为两个待求的节点可能分别在左右子树中。 ```java public boolean findTarget(TreeNode root, int k) { List nums = new ArrayList<>(); inOrder(root, nums); int i = 0, j = nums.size() - 1; while (i < j) { int sum = nums.get(i) + nums.get(j); if (sum == k) return true; if (sum < k) i++; else j--; } return false; } private void inOrder(TreeNode root, List nums) { if (root == null) return; inOrder(root.left, nums); nums.add(root.val); inOrder(root.right, nums); } ``` ### 9. 在二叉查找树中查找两个节点之差的最小绝对值 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/) ```html Input: 1 \ 3 / 2 Output: 1 ``` 利用二叉查找树的中序遍历为有序的性质，计算中序遍历中临近的两个节点之差的绝对值，取最小值。 ```java private int minDiff = Integer.MAX_VALUE; private TreeNode preNode = null; public int getMinimumDifference(TreeNode root) { inOrder(root); return minDiff; } private void inOrder(TreeNode node) { if (node == null) return; inOrder(node.left); if (preNode != null) minDiff = Math.min(minDiff, node.val - preNode.val); preNode = node; inOrder(node.right); } ``` ### 10. 寻找二叉查找树中出现次数最多的值 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/) ```html 1 \ 2 / 2 return [2]. ``` 答案可能不止一个，也就是有多个值出现的次数一样多。 ```java private int curCnt = 1; private int maxCnt = 1; private TreeNode preNode = null; public int[] findMode(TreeNode root) { List maxCntNums = new ArrayList<>(); inOrder(root, maxCntNums); int[] ret = new int[maxCntNums.size()]; int idx = 0; for (int num : maxCntNums) { ret[idx++] = num; } return ret; } private void inOrder(TreeNode node, List nums) { if (node == null) return; inOrder(node.left, nums); if (preNode != null) { if (preNode.val == node.val) curCnt++; else curCnt = 1; } if (curCnt > maxCnt) { maxCnt = curCnt; nums.clear(); nums.add(node.val); } else if (curCnt == maxCnt) { nums.add(node.val); } preNode = node; inOrder(node.right, nums); } ``` ## Trie

Trie，又称前缀树或字典树，用于判断字符串是否存在或者是否具有某种字符串前缀。 ### 1. 实现一个 Trie 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/) ```java class Trie { private class Node { Node[] childs = new Node[26]; boolean isLeaf; } private Node root = new Node(); public Trie() { } public void insert(String word) { insert(word, root); } private void insert(String word, Node node) { if (node == null) return; if (word.length() == 0) { node.isLeaf = true; return; } int index = indexForChar(word.charAt(0)); if (node.childs[index] == null) { node.childs[index] = new Node(); } insert(word.substring(1), node.childs[index]); } public boolean search(String word) { return search(word, root); } private boolean search(String word, Node node) { if (node == null) return false; if (word.length() == 0) return node.isLeaf; int index = indexForChar(word.charAt(0)); return search(word.substring(1), node.childs[index]); } public boolean startsWith(String prefix) { return startWith(prefix, root); } private boolean startWith(String prefix, Node node) { if (node == null) return false; if (prefix.length() == 0) return true; int index = indexForChar(prefix.charAt(0)); return startWith(prefix.substring(1), node.childs[index]); } private int indexForChar(char c) { return c - 'a'; } } ``` ### 2. 实现一个 Trie，用来求前缀和 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/) ```html Input: insert("apple", 3), Output: Null Input: sum("ap"), Output: 3 Input: insert("app", 2), Output: Null Input: sum("ap"), Output: 5 ``` ```java class MapSum { private class Node { Node[] child = new Node[26]; int value; } private Node root = new Node(); public MapSum() { } public void insert(String key, int val) { insert(key, root, val); } private void insert(String key, Node node, int val) { if (node == null) return; if (key.length() == 0) { node.value = val; return; } int index = indexForChar(key.charAt(0)); if (node.child[index] == null) { node.child[index] = new Node(); } insert(key.substring(1), node.child[index], val); } public int sum(String prefix) { return sum(prefix, root); } private int sum(String prefix, Node node) { if (node == null) return 0; if (prefix.length() != 0) { int index = indexForChar(prefix.charAt(0)); return sum(prefix.substring(1), node.child[index]); } int sum = node.value; for (Node child : node.child) { sum += sum(prefix, child); } return sum; } private int indexForChar(char c) { return c - 'a'; } } ```