2.4.41 Finished

ikesnowy · ikesnowy · commit d41f04d56024 · 2018-12-30T22:17:13.000+08:00
diff --git a/2 Sorting/2.4/2.4.41/2.4.41.csproj b/2 Sorting/2.4/2.4.41/2.4.41.csproj
@@ -0,0 +1,59 @@
+﻿<?xml version="1.0" encoding="utf-8"?>
+<Project ToolsVersion="15.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <Import Project="$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props" Condition="Exists('$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props')" />
+  <PropertyGroup>
+    <Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
+    <Platform Condition=" '$(Platform)' == '' ">AnyCPU</Platform>
+    <ProjectGuid>{39888A7A-52A1-4AB5-BCC9-599725C78D15}</ProjectGuid>
+    <OutputType>Exe</OutputType>
+    <RootNamespace>_2._4._41</RootNamespace>
+    <AssemblyName>2.4.41</AssemblyName>
+    <TargetFrameworkVersion>v4.7</TargetFrameworkVersion>
+    <FileAlignment>512</FileAlignment>
+    <AutoGenerateBindingRedirects>true</AutoGenerateBindingRedirects>
+    <Deterministic>true</Deterministic>
+  </PropertyGroup>
+  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">
+    <PlatformTarget>AnyCPU</PlatformTarget>
+    <DebugSymbols>true</DebugSymbols>
+    <DebugType>full</DebugType>
+    <Optimize>false</Optimize>
+    <OutputPath>bin\Debug\</OutputPath>
+    <DefineConstants>DEBUG;TRACE</DefineConstants>
+    <ErrorReport>prompt</ErrorReport>
+    <WarningLevel>4</WarningLevel>
+  </PropertyGroup>
+  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|AnyCPU' ">
+    <PlatformTarget>AnyCPU</PlatformTarget>
+    <DebugType>pdbonly</DebugType>
+    <Optimize>true</Optimize>
+    <OutputPath>bin\Release\</OutputPath>
+    <DefineConstants>TRACE</DefineConstants>
+    <ErrorReport>prompt</ErrorReport>
+    <WarningLevel>4</WarningLevel>
+  </PropertyGroup>
+  <ItemGroup>
+    <Reference Include="System" />
+    <Reference Include="System.Core" />
+    <Reference Include="System.Xml.Linq" />
+    <Reference Include="System.Data.DataSetExtensions" />
+    <Reference Include="Microsoft.CSharp" />
+    <Reference Include="System.Data" />
+    <Reference Include="System.Net.Http" />
+    <Reference Include="System.Xml" />
+  </ItemGroup>
+  <ItemGroup>
+    <Compile Include="Program.cs" />
+    <Compile Include="Properties\AssemblyInfo.cs" />
+  </ItemGroup>
+  <ItemGroup>
+    <None Include="App.config" />
+  </ItemGroup>
+  <ItemGroup>
+    <ProjectReference Include="..\PriorityQueue\PriorityQueue.csproj">
+      <Project>{e040340e-ebb2-4650-8e19-ee46eb684e14}</Project>
+      <Name>PriorityQueue</Name>
+    </ProjectReference>
+  </ItemGroup>
+  <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
+</Project>
diff --git a/2 Sorting/2.4/2.4.41/App.config b/2 Sorting/2.4/2.4.41/App.config
@@ -0,0 +1,6 @@
+﻿<?xml version="1.0" encoding="utf-8" ?>
+<configuration>
+    <startup> 
+        <supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.7" />
+    </startup>
+</configuration>
diff --git a/2 Sorting/2.4/2.4.41/Program.cs b/2 Sorting/2.4/2.4.41/Program.cs
@@ -0,0 +1,85 @@
+﻿using System;
+using System.IO;
+using PriorityQueue;
+
+namespace _2._4._41
+{
+    /*
+     * 2.4.41
+     * 
+     * Multiway 堆。
+     * 根据正文中的描述实现基于完全堆有序的三叉树和四叉树的堆排序。
+     * 对于 N=10^3、10^6 和 10^9 大小的随机不重复数组，
+     * 记录你的程序所使用的比较次数和标准实现所使用的比较次数。
+     * 
+     */
+    class Program
+    {
+        static Random random = new Random();
+
+        static void Main(string[] args)
+        {
+            Console.WriteLine("n\t2-way\t3-way\tRatio\t4-way\tRatio");
+
+            int n = 1000;     // 当数据量到达 10^9 时会需要 2G 左右的内存
+            int multiTen = 7;
+            for (int i = 0; i < multiTen; i++)
+            {
+                Console.Write("10^" + (i + 3) + "\t");
+                short[] data = GetRandomArray(n);
+                BackupArray(data, i);       // 暂存数组
+                long originCount = HeapAnalysis.Sort(data);
+                Console.Write(originCount + "\t");
+
+                RestoreArray(data, i);      // 恢复数组
+                long threeWayCount = HeapMultiwayAnalysis.Sort(data, 3);
+                Console.Write(threeWayCount + "\t" + (float)threeWayCount / originCount + "\t");
+
+                RestoreArray(data, i);      // 恢复数组
+                long fourWayCount = HeapMultiwayAnalysis.Sort(data, 4);
+                Console.WriteLine(fourWayCount + "\t" + (float)fourWayCount / originCount);
+
+                n *= 10;
+            }
+        }
+
+        static void BackupArray(short[] data, int index)
+        {
+            StreamWriter sw =
+                File.CreateText
+                (Environment.CurrentDirectory +
+                Path.DirectorySeparatorChar +
+                "data" + index + ".txt");
+            for (int i = 0; i < data.Length; i++)
+            {
+                sw.WriteLine(data[i]);
+            }
+            sw.Flush();
+            sw.Close();
+        }
+
+        static void RestoreArray(short[] data, int index)
+        {
+            StreamReader sr =
+                File.OpenText
+                (Environment.CurrentDirectory +
+                Path.DirectorySeparatorChar +
+                "data" + index + ".txt");
+            for (int i = 0; i < data.Length; i++)
+            {
+                data[i] = short.Parse(sr.ReadLine());
+            }
+            sr.Close();
+        }
+
+        static short[] GetRandomArray(int n)
+        {
+            short[] data = new short[n];
+            for (int i = 0; i < n; i++)
+            {
+                data[i] = (short)random.Next();
+            }
+            return data;
+        }
+    }
+}
diff --git a/2 Sorting/2.4/2.4.41/Properties/AssemblyInfo.cs b/2 Sorting/2.4/2.4.41/Properties/AssemblyInfo.cs
@@ -0,0 +1,35 @@
+﻿using System.Reflection;
+using System.Runtime.InteropServices;
+
+// 有关程序集的一般信息由以下
+// 控制。更改这些特性值可修改
+// 与程序集关联的信息。
+[assembly: AssemblyTitle("2.4.41")]
+[assembly: AssemblyDescription("")]
+[assembly: AssemblyConfiguration("")]
+[assembly: AssemblyCompany("")]
+[assembly: AssemblyProduct("2.4.41")]
+[assembly: AssemblyCopyright("Copyright ©  2018")]
+[assembly: AssemblyTrademark("")]
+[assembly: AssemblyCulture("")]
+
+// 将 ComVisible 设置为 false 会使此程序集中的类型
+//对 COM 组件不可见。如果需要从 COM 访问此程序集中的类型
+//请将此类型的 ComVisible 特性设置为 true。
+[assembly: ComVisible(false)]
+
+// 如果此项目向 COM 公开，则下列 GUID 用于类型库的 ID
+[assembly: Guid("39888a7a-52a1-4ab5-bcc9-599725c78d15")]
+
+// 程序集的版本信息由下列四个值组成: 
+//
+//      主版本
+//      次版本
+//      生成号
+//      修订号
+//
+// 可以指定所有值，也可以使用以下所示的 "*" 预置版本号和修订号
+// 方法是按如下所示使用“*”: :
+// [assembly: AssemblyVersion("1.0.*")]
+[assembly: AssemblyVersion("1.0.0.0")]
+[assembly: AssemblyFileVersion("1.0.0.0")]
diff --git a/2 Sorting/2.4/PriorityQueue/HeapMultiway.cs b/2 Sorting/2.4/PriorityQueue/HeapMultiway.cs
@@ -0,0 +1,79 @@
+﻿using System;
+
+namespace PriorityQueue
+{
+    /// <summary>
+    /// d 叉堆排序类，提供堆排序的静态方法。
+    /// </summary>
+    /// <typeparam name="T">需要排序的元素类型。</typeparam>
+    public static class HeapMultiway
+    {
+        /// <summary>
+        /// 利用堆排序对数组进行排序。
+        /// </summary>
+        /// <param name="pq">需要排序的数组。</param>
+        /// <param name="d">堆的分叉数。</param>
+        public static void Sort<T>(T[] pq, int d) where T : IComparable<T>
+        {
+            int n = pq.Length;
+            // 建堆
+            for (int k = (n - 2) / d + 1; k >= 1; k--)
+            {
+                Sink(pq, k, n, d);
+            }
+            // 排序
+            while (n > 1)
+            {
+                Exch(pq, 1, n--);
+                Sink(pq, 1, n, d);
+            }
+        }
+
+        /// <summary>
+        /// 令堆中的元素下沉。
+        /// </summary>
+        /// <param name="pq">需要执行操作的堆。</param>
+        /// <param name="k">需要执行下沉的结点下标。</param>
+        /// <param name="n">堆中元素的数目。</param>
+        /// <param name="d">堆的分叉数。</param>
+        private static void Sink<T>(T[] pq, int k, int n, int d) where T : IComparable<T>
+        {
+            while ((k - 1) * d + 2 <= n)
+            {
+                int j = d * (k - 1) + 2;
+                // 在 d 个子结点中找到最大的那个
+                for (int i = 0, q = j; i < d; i++)
+                {
+                    if (q + i <= n && Less(pq, j, q + i))
+                        j = q + i;
+                }
+                if (!Less(pq, k, j))
+                    break;
+                Exch(pq, k, j);
+                k = j;
+            }
+        }
+
+        /// <summary>
+        /// 比较堆中下标为 <paramref name="a"/> 的元素是否小于下标为 <paramref name="b"/> 的元素。
+        /// </summary>
+        /// <param name="pq">元素所在的数组。</param>
+        /// <param name="a">需要比较是否较小的结点序号。</param>
+        /// <param name="b">需要比较是否较大的结点序号。</param>
+        /// <returns></returns>
+        private static bool Less<T>(T[] pq, int a, int b) where T : IComparable<T> => pq[a - 1].CompareTo(pq[b - 1]) < 0;
+
+        /// <summary>
+        /// 交换堆中的两个元素。
+        /// </summary>
+        /// <param name="pq">要交换的元素所在堆。</param>
+        /// <param name="a">要交换的结点序号。</param>
+        /// <param name="b">要交换的结点序号。</param>
+        private static void Exch<T>(T[] pq, int a, int b)
+        {
+            T temp = pq[a - 1];
+            pq[a - 1] = pq[b - 1];
+            pq[b - 1] = temp;
+        }
+    }
+}
diff --git a/2 Sorting/2.4/PriorityQueue/HeapMultiwayAnalysis.cs b/2 Sorting/2.4/PriorityQueue/HeapMultiwayAnalysis.cs
@@ -0,0 +1,107 @@
+﻿using System;
+
+namespace PriorityQueue
+{
+    /// <summary>
+    /// d 叉堆排序类，提供堆排序的静态方法。
+    /// </summary>
+    /// <typeparam name="T">需要排序的元素类型。</typeparam>
+    public static class HeapMultiwayAnalysis
+    {
+        /// <summary>
+        /// 堆排序的比较次数。
+        /// </summary>
+        private static long compareTimes;
+
+        /// <summary>
+        /// 利用堆排序对数组进行排序，返回比较次数。
+        /// </summary>
+        /// <param name="pq">需要排序的数组。</param>
+        /// <param name="d">堆的分叉数。</param>
+        public static long Sort<T>(T[] pq, long d) where T : IComparable<T>
+        {
+            compareTimes = 0;
+            long n = pq.Length;
+            // 建堆
+            for (long k = (n - 2) / d + 1; k >= 1; k--)
+            {
+                Sink(pq, k, n, d);
+            }
+            // 排序
+            while (n > 1)
+            {
+                Exch(pq, 1, n--);
+                Sink(pq, 1, n, d);
+            }
+            return compareTimes;
+        }
+
+        /// <summary>
+        /// 令堆中的元素下沉。
+        /// </summary>
+        /// <param name="pq">需要执行操作的堆。</param>
+        /// <param name="k">需要执行下沉的结点下标。</param>
+        /// <param name="n">堆中元素的数目。</param>
+        /// <param name="d">堆的分叉数。</param>
+        private static void Sink<T>(T[] pq, long k, long n, long d) where T : IComparable<T>
+        {
+            while ((k - 1) * d + 2 <= n)
+            {
+                long j = d * (k - 1) + 2;
+                try
+                {
+                    // 在 d 个子结点中找到最大的那个
+                    for (long i = 1, q = j; i < d; i++)
+                    {
+                        if (q + i <= n && Less(pq, j, q + i))
+                            j = q + i;
+                    }
+                    if (!Less(pq, k, j))
+                        break;
+                }
+                catch (Exception e)
+                {
+                    Console.WriteLine("j=" + j);
+                    throw e;
+                }
+
+                Exch(pq, k, j);
+                k = j;
+            }
+        }
+
+        /// <summary>
+        /// 比较堆中下标为 <paramref name="a"/> 的元素是否小于下标为 <paramref name="b"/> 的元素。
+        /// </summary>
+        /// <param name="pq">元素所在的数组。</param>
+        /// <param name="a">需要比较是否较小的结点序号。</param>
+        /// <param name="b">需要比较是否较大的结点序号。</param>
+        /// <returns></returns>
+        private static bool Less<T>(T[] pq, long a, long b) where T : IComparable<T>
+        {
+            compareTimes++;
+            try
+            {
+                return pq[a - 1].CompareTo(pq[b - 1]) < 0;
+            }
+            catch (Exception e)
+            {
+                Console.WriteLine("a=" + a + "b=" + b);
+                throw e;
+            }
+        }
+
+        /// <summary>
+        /// 交换堆中的两个元素。
+        /// </summary>
+        /// <param name="pq">要交换的元素所在堆。</param>
+        /// <param name="a">要交换的结点序号。</param>
+        /// <param name="b">要交换的结点序号。</param>
+        private static void Exch<T>(T[] pq, long a, long b)
+        {
+            T temp = pq[a - 1];
+            pq[a - 1] = pq[b - 1];
+            pq[b - 1] = temp;
+        }
+    }
+}
diff --git a/2 Sorting/2.4/PriorityQueue/MaxPQMultiway.cs b/2 Sorting/2.4/PriorityQueue/MaxPQMultiway.cs
diff --git a/2 Sorting/2.4/PriorityQueue/PriorityQueue.csproj b/2 Sorting/2.4/PriorityQueue/PriorityQueue.csproj
diff --git a/Algorithms 4th Edition.sln b/Algorithms 4th Edition.sln
