3.2.42 Finished

Author: ikesnowy

3 Searching/3.2/3.2.42/3.2.42.csproj

@@ -0,0 +1,13 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <OutputType>Exe</OutputType>
+    <TargetFramework>netcoreapp3.0</TargetFramework>
+    <RootNamespace>_3._2._42</RootNamespace>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <ProjectReference Include="..\BinarySearchTree\BinarySearchTree.csproj" />
+  </ItemGroup>
+
+</Project>

3 Searching/3.2/3.2.42/Program.cs

@@ -0,0 +1,68 @@
+using System;
+using BinarySearchTree;
+
+namespace _3._2._42
+{
+    class Program
+    {
+        static void Main(string[] args)
+        {
+            var random = new Random();
+            for (var n = 100; n <= 10000; n *= 10)
+            {
+                Console.WriteLine("n = " + n + " sqrt(n) = " + (int)(Math.Sqrt(n)));
+                var data = new int[n * n + n];
+                for (var i = 0; i < data.Length; i++)
+                {
+                    data[i] = i;
+                }
+
+                Shuffle(data);
+
+                var bstHibbard = new BST<int, int>();
+                var bstNonHibbard = new BSTNonHibbard<int, int>();
+
+                // build
+                for (var i = 0; i < n; i++)
+                {
+                    bstHibbard.Put(data[i], i);
+                    bstNonHibbard.Put(data[i], i);
+                }
+
+                var avePathHibbardBefore = bstHibbard.AverageInternalPathLength();
+                var avePathNonHibbardBefore = bstNonHibbard.AverageInternalPathLength();
+                Console.WriteLine("stage\tHibbard\tNonHibbard");
+                Console.WriteLine("before\t" + avePathHibbardBefore + "\t" + avePathNonHibbardBefore);
+
+                // test
+                for (var i = n; i < n * n; i++)
+                {
+                    var rank = random.Next(n);
+                    bstHibbard.Delete(bstHibbard.Select(rank));
+                    bstHibbard.Put(data[i], i);
+
+                    bstNonHibbard.Delete(bstNonHibbard.Select(rank));
+                    bstNonHibbard.Put(data[i], i);
+                }
+
+                var avePathHibbardAfter = bstHibbard.AverageInternalPathLength();
+                var avePathNonHibbardAfter = bstNonHibbard.AverageInternalPathLength();
+                Console.WriteLine("after\t" + avePathHibbardAfter + "\t" + avePathNonHibbardAfter);
+                Console.WriteLine("diff\t" + (avePathHibbardAfter - avePathHibbardBefore) + "\t" + (avePathNonHibbardAfter - avePathNonHibbardBefore));
+                Console.WriteLine();
+            }
+        }
+
+        static void Shuffle<T>(T[] a)
+        {
+            var random = new Random();
+            for (var i = 0; i < a.Length; i++)
+            {
+                var r = i + random.Next(a.Length - i);
+                var temp = a[i];
+                a[i] = a[r];
+                a[r] = temp;
+            }
+        }
+    }
+}

3 Searching/3.2/BinarySearchTree/BST.cs

@@ -553,6 +553,52 @@ protected virtual Node DeleteMax(Node x)
             return x;
         }
 
+        /// <summary>
+        /// 获取二叉树的内部平均路径长度。
+        /// </summary>
+        /// <returns>内部平均路径长度。</returns>
+        public int AverageInternalPathLength() => InternalPath() / Size() + 1;
+
+        /// <summary>
+        /// 二叉树的内部路径长度。
+        /// </summary>
+        /// <returns>二叉树的内部路径长度（所有结点深度之和）。</returns>
+        private int InternalPath()
+        {
+            var internalPath = 0;
+            var nowLayer = new Queue<Node>();
+            var nextLayer = new Queue<Node>();
+            nextLayer.Enqueue(root);
+
+            var depth = 0;
+            while (nextLayer.Count > 0)
+            {
+                var temp = nowLayer;
+                nowLayer = nextLayer;
+                nextLayer = temp;
+
+                while (nowLayer.Count > 0)
+                {
+                    var node = nowLayer.Dequeue();
+                    if (node.Left != null)
+                    {
+                        nextLayer.Enqueue(node.Left);
+                    }
+
+                    if (node.Right != null)
+                    {
+                        nextLayer.Enqueue(node.Right);
+                    }
+
+                    internalPath += depth;
+                }
+
+                depth++;
+            }
+
+            return internalPath;
+        }
+
         /// <summary>
         /// 按照层级顺序打印以 <paramref name="key"/> 为根的子树。
         /// </summary>

3 Searching/3.2/BinarySearchTree/BSTNonHibbard.cs

@@ -0,0 +1,62 @@
+using System;
+
+namespace BinarySearchTree
+{
+    public class BSTNonHibbard<TKey, TValue> : BST<TKey, TValue> where TKey : IComparable<TKey>
+    {
+        private readonly Random _random = new Random();
+
+        /// <summary>
+        /// 从二叉查找树中删除键为 <paramref name="key"/> 的结点。
+        /// </summary>
+        /// <param name="x">要删除的结点的二叉查找树。</param>
+        /// <param name="key">要删除的键。</param>
+        /// <returns>删除结点后的二叉查找树。</returns>
+        protected override Node Delete(Node x, TKey key)
+        {
+            if (x == null)
+            {
+                return null;
+            }
+
+            var cmp = key.CompareTo(x.Key);
+            if (cmp < 0)
+            {
+                x.Left = Delete(x.Left, key);
+            }
+            else if (cmp > 0)
+            {
+                x.Right = Delete(x.Right, key);
+            }
+            else
+            {
+                if (x.Right == null)
+                {
+                    return x.Left;
+                }
+
+                if (x.Left == null)
+                {
+                    return x.Right;
+                }
+                var t = x;
+                if (_random.NextDouble() < 0.5)
+                {
+                    x = Min(t.Right);
+                    x.Right = DeleteMin(t.Right);
+                    x.Left = t.Left;
+                }
+                else
+                {
+                    x = Max(t.Left);
+                    x.Left = DeleteMax(t.Left);
+                    x.Right = t.Right;
+                }
+            }
+            x.Size = Size(x.Left) + Size(x.Right) + 1;
+            return x;
+        }
+
+
+    }
+}

Algorithms 4th Edition.sln

@@ -1035,7 +1035,9 @@ Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.39", "3 Searching\3.2\3
 EndProject
 Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.40", "3 Searching\3.2\3.2.40\3.2.40.csproj", "{28E56928-AA66-464E-B791-A72889D4C624}"
 EndProject
-Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "3.2.41", "3 Searching\3.2\3.2.41\3.2.41.csproj", "{64038379-9705-4127-A25C-BC0391298EE0}"
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.41", "3 Searching\3.2\3.2.41\3.2.41.csproj", "{64038379-9705-4127-A25C-BC0391298EE0}"
+EndProject
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "3.2.42", "3 Searching\3.2\3.2.42\3.2.42.csproj", "{BAD1523D-5DE5-4117-9D57-C7A1F4A2A29A}"
 EndProject
 Global
 	GlobalSection(SolutionConfigurationPlatforms) = preSolution
@@ -2847,6 +2849,10 @@ Global
 		{64038379-9705-4127-A25C-BC0391298EE0}.Debug|Any CPU.Build.0 = Debug|Any CPU
 		{64038379-9705-4127-A25C-BC0391298EE0}.Release|Any CPU.ActiveCfg = Release|Any CPU
 		{64038379-9705-4127-A25C-BC0391298EE0}.Release|Any CPU.Build.0 = Release|Any CPU
+		{BAD1523D-5DE5-4117-9D57-C7A1F4A2A29A}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{BAD1523D-5DE5-4117-9D57-C7A1F4A2A29A}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{BAD1523D-5DE5-4117-9D57-C7A1F4A2A29A}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{BAD1523D-5DE5-4117-9D57-C7A1F4A2A29A}.Release|Any CPU.Build.0 = Release|Any CPU
 	EndGlobalSection
 	GlobalSection(SolutionProperties) = preSolution
 		HideSolutionNode = FALSE
@@ -3361,6 +3367,7 @@ Global
 		{2428EF52-8CE9-48F9-95DD-707B1E5F8DF5} = {69512490-D514-490D-9088-D514FC5C770A}
 		{28E56928-AA66-464E-B791-A72889D4C624} = {69512490-D514-490D-9088-D514FC5C770A}
 		{64038379-9705-4127-A25C-BC0391298EE0} = {69512490-D514-490D-9088-D514FC5C770A}
+		{BAD1523D-5DE5-4117-9D57-C7A1F4A2A29A} = {69512490-D514-490D-9088-D514FC5C770A}
 	EndGlobalSection
 	GlobalSection(ExtensibilityGlobals) = postSolution
 		SolutionGuid = {EE55CF8D-6F35-464D-B95B-ED85644AE41C}