mirror of
https://github.com/krahets/hello-algo.git
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260 lines
9.6 KiB
Zig
260 lines
9.6 KiB
Zig
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// File: avl_tree.zig
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// Created Time: 2023-01-15
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// Author: sjinzh (sjinzh@gmail.com)
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const std = @import("std");
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const inc = @import("include");
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// 平衡二叉树
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pub fn AVLTree(comptime T: type) type {
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return struct {
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const Self = @This();
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root: ?*inc.TreeNode(T) = null, // 根节点
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mem_arena: ?std.heap.ArenaAllocator = null,
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mem_allocator: std.mem.Allocator = undefined, // 内存分配器
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// 构造函数
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pub fn init(self: *Self, allocator: std.mem.Allocator) void {
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if (self.mem_arena == null) {
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self.mem_arena = std.heap.ArenaAllocator.init(allocator);
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self.mem_allocator = self.mem_arena.?.allocator();
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}
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}
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// 析构函数
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pub fn deinit(self: *Self) void {
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if (self.mem_arena == null) return;
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self.mem_arena.?.deinit();
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}
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// 获取结点高度
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fn height(self: *Self, node: ?*inc.TreeNode(T)) i32 {
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_ = self;
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// 空结点高度为 -1 ，叶结点高度为 0
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return if (node == null) -1 else node.?.height;
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}
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// 更新结点高度
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fn updateHeight(self: *Self, node: ?*inc.TreeNode(T)) void {
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// 结点高度等于最高子树高度 + 1
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node.?.height = std.math.max(self.height(node.?.left), self.height(node.?.right)) + 1;
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}
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// 获取平衡因子
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fn balanceFactor(self: *Self, node: ?*inc.TreeNode(T)) i32 {
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// 空结点平衡因子为 0
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if (node == null) return 0;
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// 结点平衡因子 = 左子树高度 - 右子树高度
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return self.height(node.?.left) - self.height(node.?.right);
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}
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// 右旋操作
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fn rightRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
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var child = node.?.left;
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var grandChild = child.?.right;
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// 以 child 为原点，将 node 向右旋转
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child.?.right = node;
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node.?.left = grandChild;
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// 更新结点高度
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self.updateHeight(node);
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self.updateHeight(child);
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// 返回旋转后子树的根节点
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return child;
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}
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// 左旋操作
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fn leftRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
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var child = node.?.right;
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var grandChild = child.?.left;
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// 以 child 为原点，将 node 向左旋转
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child.?.left = node;
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node.?.right = grandChild;
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// 更新结点高度
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self.updateHeight(node);
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self.updateHeight(child);
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// 返回旋转后子树的根节点
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return child;
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}
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// 执行旋转操作，使该子树重新恢复平衡
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fn rotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
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// 获取结点 node 的平衡因子
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var balance_factor = self.balanceFactor(node);
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// 左偏树
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if (balance_factor > 1) {
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if (self.balanceFactor(node.?.left) >= 0) {
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// 右旋
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return self.rightRotate(node);
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} else {
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// 先左旋后右旋
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node.?.left = self.leftRotate(node.?.left);
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return self.rightRotate(node);
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}
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}
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// 右偏树
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if (balance_factor < -1) {
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if (self.balanceFactor(node.?.right) <= 0) {
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// 左旋
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return self.leftRotate(node);
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} else {
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// 先右旋后左旋
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node.?.right = self.rightRotate(node.?.right);
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return self.leftRotate(node);
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}
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}
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// 平衡树，无需旋转，直接返回
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return node;
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}
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// 插入结点
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fn insert(self: *Self, val: T) !?*inc.TreeNode(T) {
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self.root = try self.insertHelper(self.root, val);
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return self.root;
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}
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// 递归插入结点（辅助函数）
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fn insertHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) !?*inc.TreeNode(T) {
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var node = node_;
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if (node == null) {
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var tmp_node = try self.mem_allocator.create(inc.TreeNode(T));
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tmp_node.init(val);
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return tmp_node;
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}
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// 1. 查找插入位置，并插入结点
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if (val < node.?.val) {
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node.?.left = try self.insertHelper(node.?.left, val);
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} else if (val > node.?.val) {
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node.?.right = try self.insertHelper(node.?.right, val);
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} else {
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return node; // 重复结点不插入，直接返回
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}
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self.updateHeight(node); // 更新结点高度
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// 2. 执行旋转操作，使该子树重新恢复平衡
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node = self.rotate(node);
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// 返回子树的根节点
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return node;
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}
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// 删除结点
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fn remove(self: *Self, val: T) ?*inc.TreeNode(T) {
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self.root = self.removeHelper(self.root, val);
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return self.root;
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}
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// 递归删除结点（辅助函数）
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fn removeHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) ?*inc.TreeNode(T) {
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var node = node_;
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if (node == null) return null;
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// 1. 查找结点，并删除之
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if (val < node.?.val) {
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node.?.left = self.removeHelper(node.?.left, val);
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} else if (val > node.?.val) {
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node.?.right = self.removeHelper(node.?.right, val);
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} else {
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if (node.?.left == null or node.?.right == null) {
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var child = if (node.?.left != null) node.?.left else node.?.right;
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// 子结点数量 = 0 ，直接删除 node 并返回
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if (child == null) {
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return null;
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// 子结点数量 = 1 ，直接删除 node
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} else {
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node = child;
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}
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} else {
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// 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点
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var temp = self.getInOrderNext(node.?.right);
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node.?.right = self.removeHelper(node.?.right, temp.?.val);
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node.?.val = temp.?.val;
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}
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}
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self.updateHeight(node); // 更新结点高度
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// 2. 执行旋转操作，使该子树重新恢复平衡
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node = self.rotate(node);
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// 返回子树的根节点
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return node;
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}
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// 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况）
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fn getInOrderNext(self: *Self, node_: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
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_ = self;
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var node = node_;
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if (node == null) return node;
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// 循环访问左子结点，直到叶结点时为最小结点，跳出
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while (node.?.left != null) {
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node = node.?.left;
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}
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return node;
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}
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// 查找结点
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fn search(self: *Self, val: T) ?*inc.TreeNode(T) {
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var cur = self.root;
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// 循环查找，越过叶结点后跳出
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while (cur != null) {
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// 目标结点在 cur 的右子树中
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if (cur.?.val < val) {
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cur = cur.?.right;
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// 目标结点在 cur 的左子树中
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} else if (cur.?.val > val) {
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cur = cur.?.left;
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// 找到目标结点，跳出循环
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} else {
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break;
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}
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}
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// 返回目标结点
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return cur;
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}
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};
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}
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pub fn testInsert(comptime T: type, tree_: *AVLTree(T), val: T) !void {
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var tree = tree_;
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_ = try tree.insert(val);
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std.debug.print("\n插入结点 {} 后，AVL 树为\n", .{val});
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try inc.PrintUtil.printTree(tree.root, null, false);
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}
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pub fn testRemove(comptime T: type, tree_: *AVLTree(T), val: T) void {
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var tree = tree_;
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_ = tree.remove(val);
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std.debug.print("\n删除结点 {} 后，AVL 树为\n", .{val});
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try inc.PrintUtil.printTree(tree.root, null, false);
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}
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// Driver Code
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pub fn main() !void {
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// 初始化空 AVL 树
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var avl_tree = AVLTree(i32){};
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avl_tree.init(std.heap.page_allocator);
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defer avl_tree.deinit();
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// 插入结点
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// 请关注插入结点后，AVL 树是如何保持平衡的
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try testInsert(i32, &avl_tree, 1);
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try testInsert(i32, &avl_tree, 2);
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try testInsert(i32, &avl_tree, 3);
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try testInsert(i32, &avl_tree, 4);
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try testInsert(i32, &avl_tree, 5);
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try testInsert(i32, &avl_tree, 8);
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try testInsert(i32, &avl_tree, 7);
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try testInsert(i32, &avl_tree, 9);
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try testInsert(i32, &avl_tree, 10);
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try testInsert(i32, &avl_tree, 6);
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// 插入重复结点
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try testInsert(i32, &avl_tree, 7);
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// 删除结点
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// 请关注删除结点后，AVL 树是如何保持平衡的
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testRemove(i32, &avl_tree, 8); // 删除度为 0 的结点
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testRemove(i32, &avl_tree, 5); // 删除度为 1 的结点
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testRemove(i32, &avl_tree, 4); // 删除度为 2 的结点
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// 查找结点
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var node = avl_tree.search(7).?;
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std.debug.print("\n查找到的结点对象为 {any}，结点值 = {}\n", .{node, node.val});
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_ = try std.io.getStdIn().reader().readByte();
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}
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