[Глава 8] Сбалансированные деревья: АВЛ-дерево

2025-07-29 15:49:55 +03:00
parent 08b37fe0e1
commit 618427c2e8
5 changed files with 267 additions and 14 deletions
--- a/Chapter5_BreadthFirstSearch/Program.cs
+++ b/Chapter5_BreadthFirstSearch/Program.cs
@@ -1,5 +1,8 @@
 using GrokAlgorithms.Chapter5_BreadthFirstSearch;

+// Тут используется реализация алгоритма поиска в ширину на графе, BFS. 
+// Поиск в глубину (DFS) точно такой же, но вместо очереди использует стек
+
 int count = 0;

 // Команда для построения дерева
--- a/Chapter8_BalancedTree/AvlTree.cs
+++ b/Chapter8_BalancedTree/AvlTree.cs
@@ -0,0 +1,205 @@
+using System.Collections;
+
+class AvlTree<T> : IEnumerable<T> where T : notnull
+{
+    private IComparer<T> _comparer;
+    private TreeNode? _root;
+
+    public AvlTree(IComparer<T> comparer)
+    {
+        _comparer = comparer;
+    }
+
+    public void Insert(T value)
+    {
+        _root = Insert(_root, value, _comparer);
+    }
+
+    public void Remove(T value)
+    {
+        _root = Remove(_root, value, _comparer);
+    }
+
+    public int Count(T value)
+    {
+        var curNode = _root;
+
+        while (curNode != null)
+        {
+            var cmpResult = _comparer.Compare(value, curNode.Value);
+            if (cmpResult == 0)
+                return curNode.Count;
+            else if (cmpResult > 0)
+                curNode = curNode.Right;
+            else if (cmpResult < 0)
+                curNode = curNode.Left;
+        }
+        return 0;
+    }
+
+    public override string ToString()
+    {
+        return PrintTree(_root, "", true);
+
+        string PrintTree(TreeNode? node, string indent, bool last)
+        {
+            if (node == null)
+                return "";
+
+            var result = indent;
+            result += last ? "└─" : "├─";
+            result += $"{node.Value} (h={node.Height}, c={node.Count})\n";
+
+            indent += last ? "  " : "│ ";
+
+            var children = new List<TreeNode>();
+            if (node.Right != null) children.Add(node.Right);
+            if (node.Left != null) children.Add(node.Left);
+
+            for (int i = 0; i < children.Count; i++)
+            {
+                result += PrintTree(children[i], indent, i == children.Count - 1);
+            }
+            return result;
+        }
+    }
+
+    private static TreeNode Insert(TreeNode? node, T value, IComparer<T> comparer)
+    {
+        if (node == null)
+            return new TreeNode() { Value = value };
+        var cmpResult = comparer.Compare(value, node.Value);
+        if (cmpResult < 0)
+            node.Left = Insert(node.Left, value, comparer);
+        else if (cmpResult > 0)
+            node.Right = Insert(node.Right, value, comparer);
+        else
+            node.Count++;
+        return Balance(node);
+    }
+
+    private static TreeNode? Remove(TreeNode? node, T value, IComparer<T> comparer)
+    {
+        if (node == null)
+            return null;
+
+        var cmpResult = comparer.Compare(value, node.Value);
+        if (cmpResult != 0)
+        {
+            if (cmpResult > 0)
+                node.Right = Remove(node.Right, value, comparer);
+            else if (cmpResult < 0)
+                node.Left = Remove(node.Left, value, comparer);
+            return Balance(node);
+        }
+
+        node.Count--;
+        if (node.Count > 0) // Если после уменьшения счётчика ещё есть элементы
+            return node;
+
+
+        if (node.Right == null) // Простой случай, когда нет правого узла - возвращаем левый
+            return node.Left;
+
+        TreeNode minRight;
+        var newRight = RemoveMin(node.Right, out minRight);
+        minRight.Left = node.Left;
+        minRight.Right = newRight;
+        return Balance(minRight);
+    }
+
+    private static TreeNode? RemoveMin(TreeNode node, out TreeNode minNode)
+    {
+        if (node.Left == null)
+        {
+            minNode = node;
+            return node.Right;
+        }
+        node.Left = RemoveMin(node.Left, out minNode);
+        return Balance(node);
+    }
+
+    private static TreeNode RotateRight(TreeNode p)
+    {
+        var q = p.Left!;
+        p.Left = q.Right;
+        q.Right = p;
+        p.UpdateHeight();
+        q.UpdateHeight();
+        return q;
+    }
+
+    private static TreeNode RotateLeft(TreeNode p)
+    {
+        var q = p.Right!;
+        p.Right = q.Left;
+        q.Left = p;
+        p.UpdateHeight();
+        q.UpdateHeight();
+        return q;
+    }
+
+    private static TreeNode Balance(TreeNode node)
+    {
+        node.UpdateHeight();
+        if (node.BFactor > 1)
+        {
+            if (node.Right?.BFactor < 0)
+                node.Right = RotateRight(node.Right);
+            return RotateLeft(node);
+        }
+        else if (node.BFactor < -1)
+        {
+            if (node.Left?.BFactor > 0)
+                node.Left = RotateLeft(node.Left);
+            return RotateRight(node);
+        }
+        return node;
+    }
+
+    private IEnumerable<T> Dfs(TreeNode? node)
+    {
+        if (node == null)
+            yield break;
+
+        foreach (var val in Dfs(node.Left))
+            yield return val;
+
+        for (int i = 0; i < node.Count; i++)
+            yield return node.Value;
+
+        foreach (var val in Dfs(node.Right))
+            yield return val;
+    }
+
+    public IEnumerable<T> TraverseDfs()
+    {
+        return Dfs(_root);
+    }
+
+    public IEnumerator<T> GetEnumerator()
+    {
+        return TraverseDfs().GetEnumerator();
+    }
+
+    IEnumerator IEnumerable.GetEnumerator()
+    {
+        return TraverseDfs().GetEnumerator();
+    }
+
+    private class TreeNode
+    {
+        public required T Value;
+        public TreeNode? Left;
+        public TreeNode? Right;
+        public int Height { get; private set; } = 1;
+        public int BFactor { get; private set; } = 0;
+        public int Count = 1;
+
+        public void UpdateHeight()
+        {
+            Height = Math.Max(Left?.Height ?? 0, Right?.Height ?? 0) + 1;
+            BFactor = (Right?.Height ?? 0) - (Left?.Height ?? 0);
+        }
+    }
+}
--- a/Chapter8_BalancedTree/Chapter8_BalancedTree.csproj
+++ b/Chapter8_BalancedTree/Chapter8_BalancedTree.csproj
@@ -0,0 +1,10 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <OutputType>Exe</OutputType>
+    <TargetFramework>net8.0</TargetFramework>
+    <ImplicitUsings>enable</ImplicitUsings>
+    <Nullable>enable</Nullable>
+  </PropertyGroup>
+
+</Project>
--- a/Chapter8_BalancedTree/Program.cs
+++ b/Chapter8_BalancedTree/Program.cs
@@ -0,0 +1,29 @@
+var avl = new AvlTree<int>(Comparer<int>.Default);
+
+avl.Insert(10);
+avl.Insert(10);
+avl.Insert(10);
+avl.Insert(10);
+avl.Insert(10);
+avl.Insert(10);
+avl.Insert(20);
+avl.Insert(5);
+avl.Insert(15);
+avl.Insert(25);
+avl.Insert(2);
+avl.Insert(8);
+avl.Insert(8);
+avl.Insert(8);
+
+System.Console.WriteLine(avl);
+
+System.Console.WriteLine("Удаление");
+avl.Remove(10);
+
+System.Console.WriteLine(avl);
+
+foreach (var v in avl)
+    System.Console.WriteLine($"{v} ");
+    
+foreach (var v in new[] { 8, 10, 100 })
+    System.Console.WriteLine($"Avl {v}: count={avl.Count(v)}");
--- a/GrokAlgorithms.sln
+++ b/GrokAlgorithms.sln
@@ -6,19 +6,25 @@ Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Chapter4_QuickSort", "Chapt
 EndProject
 Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Chapter5_BreadthFirstSearch", "Chapter5_BreadthFirstSearch\Chapter5_BreadthFirstSearch.csproj", "{F54FC00B-FB3D-4A8B-ABA8-33A43FC74DE4}"
 EndProject
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Chapter8_BalancedTree", "Chapter8_BalancedTree\Chapter8_BalancedTree.csproj", "{4344D4B1-E64B-4C4C-A137-923A210BCD20}"
+EndProject
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 EndGlobal