|
|
// File: avl_tree.zig
|
|
|
// Created Time: 2023-01-15
|
|
|
// Author: codingonion (coderonion@gmail.com)
|
|
|
|
|
|
const std = @import("std");
|
|
|
const inc = @import("include");
|
|
|
|
|
|
// AVL 樹
|
|
|
pub fn AVLTree(comptime T: type) type {
|
|
|
return struct {
|
|
|
const Self = @This();
|
|
|
|
|
|
root: ?*inc.TreeNode(T) = null, // 根節點
|
|
|
mem_arena: ?std.heap.ArenaAllocator = null,
|
|
|
mem_allocator: std.mem.Allocator = undefined, // 記憶體分配器
|
|
|
|
|
|
// 建構子
|
|
|
pub fn init(self: *Self, allocator: std.mem.Allocator) void {
|
|
|
if (self.mem_arena == null) {
|
|
|
self.mem_arena = std.heap.ArenaAllocator.init(allocator);
|
|
|
self.mem_allocator = self.mem_arena.?.allocator();
|
|
|
}
|
|
|
}
|
|
|
|
|
|
// 析構方法
|
|
|
pub fn deinit(self: *Self) void {
|
|
|
if (self.mem_arena == null) return;
|
|
|
self.mem_arena.?.deinit();
|
|
|
}
|
|
|
|
|
|
// 獲取節點高度
|
|
|
fn height(self: *Self, node: ?*inc.TreeNode(T)) i32 {
|
|
|
_ = self;
|
|
|
// 空節點高度為 -1 ，葉節點高度為 0
|
|
|
return if (node == null) -1 else node.?.height;
|
|
|
}
|
|
|
|
|
|
// 更新節點高度
|
|
|
fn updateHeight(self: *Self, node: ?*inc.TreeNode(T)) void {
|
|
|
// 節點高度等於最高子樹高度 + 1
|
|
|
node.?.height = @max(self.height(node.?.left), self.height(node.?.right)) + 1;
|
|
|
}
|
|
|
|
|
|
// 獲取平衡因子
|
|
|
fn balanceFactor(self: *Self, node: ?*inc.TreeNode(T)) i32 {
|
|
|
// 空節點平衡因子為 0
|
|
|
if (node == null) return 0;
|
|
|
// 節點平衡因子 = 左子樹高度 - 右子樹高度
|
|
|
return self.height(node.?.left) - self.height(node.?.right);
|
|
|
}
|
|
|
|
|
|
// 右旋操作
|
|
|
fn rightRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
|
|
|
var child = node.?.left;
|
|
|
var grandChild = child.?.right;
|
|
|
// 以 child 為原點，將 node 向右旋轉
|
|
|
child.?.right = node;
|
|
|
node.?.left = grandChild;
|
|
|
// 更新節點高度
|
|
|
self.updateHeight(node);
|
|
|
self.updateHeight(child);
|
|
|
// 返回旋轉後子樹的根節點
|
|
|
return child;
|
|
|
}
|
|
|
|
|
|
// 左旋操作
|
|
|
fn leftRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
|
|
|
var child = node.?.right;
|
|
|
var grandChild = child.?.left;
|
|
|
// 以 child 為原點，將 node 向左旋轉
|
|
|
child.?.left = node;
|
|
|
node.?.right = grandChild;
|
|
|
// 更新節點高度
|
|
|
self.updateHeight(node);
|
|
|
self.updateHeight(child);
|
|
|
// 返回旋轉後子樹的根節點
|
|
|
return child;
|
|
|
}
|
|
|
|
|
|
// 執行旋轉操作，使該子樹重新恢復平衡
|
|
|
fn rotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
|
|
|
// 獲取節點 node 的平衡因子
|
|
|
var balance_factor = self.balanceFactor(node);
|
|
|
// 左偏樹
|
|
|
if (balance_factor > 1) {
|
|
|
if (self.balanceFactor(node.?.left) >= 0) {
|
|
|
// 右旋
|
|
|
return self.rightRotate(node);
|
|
|
} else {
|
|
|
// 先左旋後右旋
|
|
|
node.?.left = self.leftRotate(node.?.left);
|
|
|
return self.rightRotate(node);
|
|
|
}
|
|
|
}
|
|
|
// 右偏樹
|
|
|
if (balance_factor < -1) {
|
|
|
if (self.balanceFactor(node.?.right) <= 0) {
|
|
|
// 左旋
|
|
|
return self.leftRotate(node);
|
|
|
} else {
|
|
|
// 先右旋後左旋
|
|
|
node.?.right = self.rightRotate(node.?.right);
|
|
|
return self.leftRotate(node);
|
|
|
}
|
|
|
}
|
|
|
// 平衡樹，無須旋轉，直接返回
|
|
|
return node;
|
|
|
}
|
|
|
|
|
|
// 插入節點
|
|
|
fn insert(self: *Self, val: T) !void {
|
|
|
self.root = (try self.insertHelper(self.root, val)).?;
|
|
|
}
|
|
|
|
|
|
// 遞迴插入節點（輔助方法）
|
|
|
fn insertHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) !?*inc.TreeNode(T) {
|
|
|
var node = node_;
|
|
|
if (node == null) {
|
|
|
var tmp_node = try self.mem_allocator.create(inc.TreeNode(T));
|
|
|
tmp_node.init(val);
|
|
|
return tmp_node;
|
|
|
}
|
|
|
// 1. 查詢插入位置並插入節點
|
|
|
if (val < node.?.val) {
|
|
|
node.?.left = try self.insertHelper(node.?.left, val);
|
|
|
} else if (val > node.?.val) {
|
|
|
node.?.right = try self.insertHelper(node.?.right, val);
|
|
|
} else {
|
|
|
return node; // 重複節點不插入，直接返回
|
|
|
}
|
|
|
self.updateHeight(node); // 更新節點高度
|
|
|
// 2. 執行旋轉操作，使該子樹重新恢復平衡
|
|
|
node = self.rotate(node);
|
|
|
// 返回子樹的根節點
|
|
|
return node;
|
|
|
}
|
|
|
|
|
|
// 刪除節點
|
|
|
fn remove(self: *Self, val: T) void {
|
|
|
self.root = self.removeHelper(self.root, val).?;
|
|
|
}
|
|
|
|
|
|
// 遞迴刪除節點（輔助方法）
|
|
|
fn removeHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) ?*inc.TreeNode(T) {
|
|
|
var node = node_;
|
|
|
if (node == null) return null;
|
|
|
// 1. 查詢節點並刪除
|
|
|
if (val < node.?.val) {
|
|
|
node.?.left = self.removeHelper(node.?.left, val);
|
|
|
} else if (val > node.?.val) {
|
|
|
node.?.right = self.removeHelper(node.?.right, val);
|
|
|
} else {
|
|
|
if (node.?.left == null or node.?.right == null) {
|
|
|
var child = if (node.?.left != null) node.?.left else node.?.right;
|
|
|
// 子節點數量 = 0 ，直接刪除 node 並返回
|
|
|
if (child == null) {
|
|
|
return null;
|
|
|
// 子節點數量 = 1 ，直接刪除 node
|
|
|
} else {
|
|
|
node = child;
|
|
|
}
|
|
|
} else {
|
|
|
// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點
|
|
|
var temp = node.?.right;
|
|
|
while (temp.?.left != null) {
|
|
|
temp = temp.?.left;
|
|
|
}
|
|
|
node.?.right = self.removeHelper(node.?.right, temp.?.val);
|
|
|
node.?.val = temp.?.val;
|
|
|
}
|
|
|
}
|
|
|
self.updateHeight(node); // 更新節點高度
|
|
|
// 2. 執行旋轉操作，使該子樹重新恢復平衡
|
|
|
node = self.rotate(node);
|
|
|
// 返回子樹的根節點
|
|
|
return node;
|
|
|
}
|
|
|
|
|
|
// 查詢節點
|
|
|
fn search(self: *Self, val: T) ?*inc.TreeNode(T) {
|
|
|
var cur = self.root;
|
|
|
// 迴圈查詢，越過葉節點後跳出
|
|
|
while (cur != null) {
|
|
|
// 目標節點在 cur 的右子樹中
|
|
|
if (cur.?.val < val) {
|
|
|
cur = cur.?.right;
|
|
|
// 目標節點在 cur 的左子樹中
|
|
|
} else if (cur.?.val > val) {
|
|
|
cur = cur.?.left;
|
|
|
// 找到目標節點，跳出迴圈
|
|
|
} else {
|
|
|
break;
|
|
|
}
|
|
|
}
|
|
|
// 返回目標節點
|
|
|
return cur;
|
|
|
}
|
|
|
};
|
|
|
}
|
|
|
|
|
|
pub fn testInsert(comptime T: type, tree_: *AVLTree(T), val: T) !void {
|
|
|
var tree = tree_;
|
|
|
try tree.insert(val);
|
|
|
std.debug.print("\n插入節點 {} 後，AVL 樹為\n", .{val});
|
|
|
try inc.PrintUtil.printTree(tree.root, null, false);
|
|
|
}
|
|
|
|
|
|
pub fn testRemove(comptime T: type, tree_: *AVLTree(T), val: T) void {
|
|
|
var tree = tree_;
|
|
|
tree.remove(val);
|
|
|
std.debug.print("\n刪除節點 {} 後，AVL 樹為\n", .{val});
|
|
|
try inc.PrintUtil.printTree(tree.root, null, false);
|
|
|
}
|
|
|
|
|
|
// Driver Code
|
|
|
pub fn main() !void {
|
|
|
// 初始化空 AVL 樹
|
|
|
var avl_tree = AVLTree(i32){};
|
|
|
avl_tree.init(std.heap.page_allocator);
|
|
|
defer avl_tree.deinit();
|
|
|
|
|
|
// 插入節點
|
|
|
// 請關注插入節點後，AVL 樹是如何保持平衡的
|
|
|
try testInsert(i32, &avl_tree, 1);
|
|
|
try testInsert(i32, &avl_tree, 2);
|
|
|
try testInsert(i32, &avl_tree, 3);
|
|
|
try testInsert(i32, &avl_tree, 4);
|
|
|
try testInsert(i32, &avl_tree, 5);
|
|
|
try testInsert(i32, &avl_tree, 8);
|
|
|
try testInsert(i32, &avl_tree, 7);
|
|
|
try testInsert(i32, &avl_tree, 9);
|
|
|
try testInsert(i32, &avl_tree, 10);
|
|
|
try testInsert(i32, &avl_tree, 6);
|
|
|
|
|
|
// 插入重複節點
|
|
|
try testInsert(i32, &avl_tree, 7);
|
|
|
|
|
|
// 刪除節點
|
|
|
// 請關注刪除節點後，AVL 樹是如何保持平衡的
|
|
|
testRemove(i32, &avl_tree, 8); // 刪除度為 0 的節點
|
|
|
testRemove(i32, &avl_tree, 5); // 刪除度為 1 的節點
|
|
|
testRemove(i32, &avl_tree, 4); // 刪除度為 2 的節點
|
|
|
|
|
|
// 查詢節點
|
|
|
var node = avl_tree.search(7).?;
|
|
|
std.debug.print("\n查詢到的節點物件為 {any}，節點值 = {}\n", .{node, node.val});
|
|
|
|
|
|
_ = try std.io.getStdIn().reader().readByte();
|
|
|
} |
