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‎1 Fundamental/1.2/1.2.18/1.2.18.csproj‎

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<?xml version="1.0" encoding="utf-8"?>
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<Project ToolsVersion="15.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
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<Import Project="$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props" Condition="Exists('$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props')" />
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<PropertyGroup>
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<Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
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<Platform Condition=" '$(Platform)' == '' ">AnyCPU</Platform>
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<ProjectGuid>{3BBA4BF1-2037-4DC2-8CC5-11F5B7165C8D}</ProjectGuid>
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<OutputType>Exe</OutputType>
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<RootNamespace>_1._2._18</RootNamespace>
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<AssemblyName>1.2.18</AssemblyName>
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<TargetFrameworkVersion>v4.7</TargetFrameworkVersion>
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<FileAlignment>512</FileAlignment>
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<AutoGenerateBindingRedirects>true</AutoGenerateBindingRedirects>
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</PropertyGroup>
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<PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">
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<PlatformTarget>AnyCPU</PlatformTarget>
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<DebugSymbols>true</DebugSymbols>
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<DebugType>full</DebugType>
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<Optimize>false</Optimize>
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<OutputPath>bin\Debug\</OutputPath>
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<DefineConstants>DEBUG;TRACE</DefineConstants>
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<ErrorReport>prompt</ErrorReport>
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<WarningLevel>4</WarningLevel>
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</PropertyGroup>
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<PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|AnyCPU' ">
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<PlatformTarget>AnyCPU</PlatformTarget>
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<DebugType>pdbonly</DebugType>
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<Optimize>true</Optimize>
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<OutputPath>bin\Release\</OutputPath>
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<DefineConstants>TRACE</DefineConstants>
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<ErrorReport>prompt</ErrorReport>
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<WarningLevel>4</WarningLevel>
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</PropertyGroup>
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<ItemGroup>
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<Reference Include="System" />
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<Reference Include="System.Core" />
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<Reference Include="System.Xml.Linq" />
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<Reference Include="System.Data.DataSetExtensions" />
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<Reference Include="Microsoft.CSharp" />
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<Reference Include="System.Data" />
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<Reference Include="System.Net.Http" />
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<Reference Include="System.Xml" />
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</ItemGroup>
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<ItemGroup>
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<Compile Include="Accumulator.cs" />
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<Compile Include="Program.cs" />
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<Compile Include="Properties\AssemblyInfo.cs" />
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</ItemGroup>
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<ItemGroup>
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<None Include="App.config" />
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</ItemGroup>
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<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
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</Project>

‎1 Fundamental/1.2/1.2.18/Accumulator.cs‎

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using System;
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using System.Collections.Generic;
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using System.Linq;
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using System.Text;
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using System.Threading.Tasks;
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namespace _1._2._18
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{
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public class Accumulator
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{
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private double m;
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private double s;
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private int N;
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public void AddDataValue(double x)
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{
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N++;
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s = s + 1.0 * (N - 1) / N * (x - m) * (x - m);
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m = m + (x - m) / N;
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}
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public double Mean()
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{
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return m;
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}
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public double Var()
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{
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return s / (N - 1);
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}
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public double Stddev()
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{
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return Math.Sqrt(this.Var());
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}
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public override string ToString()
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{
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return "Mean (" + N + " values): " + string.Format("{0, 7:F5}", Mean());
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}
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}
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}

‎1 Fundamental/1.2/1.2.18/App.config‎

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<?xml version="1.0" encoding="utf-8" ?>
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<configuration>
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<startup>
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<supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.7" />
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</startup>
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</configuration>

‎1 Fundamental/1.2/1.2.18/Program.cs‎

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using System;
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using System.Collections.Generic;
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using System.Linq;
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using System.Text;
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using System.Threading.Tasks;
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namespace _1._2._18
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{
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/*
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* 1.2.18
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*
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* 累加器的方法。
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* 以下代码为 Accumulator 类添加了 var() 和 stddev() 方法，
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* 它们计算了 addDataValue() 方法的参数的方差和标准差，验证这段代码：
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* 与直接对所有数据的平方求和的方法相比较，
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* 这种实现能够更好的避免四舍五入产生的误差。
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*
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*/
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class Program
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{
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//当数据比较大时—— 例如 10^9 加上随机小数组成的数列，这时 double 的小数精度将受限。
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//求和之后整数部分更大，小数部分将自动四舍五入，出现误差
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//这时再计算平均值时将会带来较大的误差。
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//因此采用另一个递推公式：
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//k 为下标。
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//Mk = Mk-1+ (xk – Mk-1)/k
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//Sk = Sk-1 + (xk – Mk-1)*(xk – Mk).
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//方差 s^2 = Sk/(k – 1).
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//这种情况下并没有直接对所有输入值求和，小数精度不受到整数部分长度的影响。
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static void Main(string[] args)
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{
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int T = 100000;
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Random random = new Random();
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Accumulator a = new Accumulator();
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for (int t = 0; t < T; ++t)
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{
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a.AddDataValue(random.NextDouble() + 1000000000);
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}
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Console.WriteLine(a.Stddev());
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Console.WriteLine(a);
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}
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}
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}

‎1 Fundamental/1.2/1.2.18/Properties/AssemblyInfo.cs‎

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using System.Reflection;
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using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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// 有关程序集的一般信息由以下
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// 控制。更改这些特性值可修改
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// 与程序集关联的信息。
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[assembly: AssemblyTitle("1.2.18")]
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[assembly: AssemblyDescription("")]
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[assembly: AssemblyConfiguration("")]
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[assembly: AssemblyCompany("")]
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[assembly: AssemblyProduct("1.2.18")]
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[assembly: AssemblyCopyright("Copyright © 2017")]
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[assembly: AssemblyTrademark("")]
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[assembly: AssemblyCulture("")]
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// 将 ComVisible 设置为 false 会使此程序集中的类型
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//对 COM 组件不可见。如果需要从 COM 访问此程序集中的类型
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//请将此类型的 ComVisible 特性设置为 true。
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[assembly: ComVisible(false)]
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// 如果此项目向 COM 公开，则下列 GUID 用于类型库的 ID
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[assembly: Guid("3bba4bf1-2037-4dc2-8cc5-11f5b7165c8d")]
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// 程序集的版本信息由下列四个值组成:
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//
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// 主版本
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// 次版本
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// 生成号
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// 修订号
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//
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// 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
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// 方法是按如下所示使用“*”: :
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// [assembly: AssemblyVersion("1.0.*")]
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[assembly: AssemblyVersion("1.0.0.0")]
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[assembly: AssemblyFileVersion("1.0.0.0")]

‎Algorithms 4th Edition.sln‎

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EndProject
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Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "1.2.17", "1 Fundamental\1.2\1.2.17\1.2.17.csproj", "{45B8DC5B-4439-42DF-AD86-40548C5CD01D}"
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EndProject
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Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "1.2.18", "1 Fundamental\1.2\1.2.18\1.2.18.csproj", "{3BBA4BF1-2037-4DC2-8CC5-11F5B7165C8D}"
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EndProject
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Global
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GlobalSection(SolutionConfigurationPlatforms) = preSolution
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Debug|Any CPU = Debug|Any CPU
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{45B8DC5B-4439-42DF-AD86-40548C5CD01D}.Debug|Any CPU.Build.0 = Debug|Any CPU
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{45B8DC5B-4439-42DF-AD86-40548C5CD01D}.Release|Any CPU.ActiveCfg = Release|Any CPU
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{45B8DC5B-4439-42DF-AD86-40548C5CD01D}.Release|Any CPU.Build.0 = Release|Any CPU
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{3BBA4BF1-2037-4DC2-8CC5-11F5B7165C8D}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
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{3BBA4BF1-2037-4DC2-8CC5-11F5B7165C8D}.Debug|Any CPU.Build.0 = Debug|Any CPU
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{3BBA4BF1-2037-4DC2-8CC5-11F5B7165C8D}.Release|Any CPU.ActiveCfg = Release|Any CPU
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{3BBA4BF1-2037-4DC2-8CC5-11F5B7165C8D}.Release|Any CPU.Build.0 = Release|Any CPU
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EndGlobalSection
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GlobalSection(SolutionProperties) = preSolution
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HideSolutionNode = FALSE
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{5D194E09-4D75-4F8F-8296-B923CCEC6C0E} = {1EF9D9DA-B4CF-4467-A5F4-CDBACEAA34CD}
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{2AF0C58F-9CCB-457D-97C5-C73DB45F31BD} = {9D948552-DF2E-412F-AEA6-B59F8BB708C5}
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{45B8DC5B-4439-42DF-AD86-40548C5CD01D} = {1EF9D9DA-B4CF-4467-A5F4-CDBACEAA34CD}
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{3BBA4BF1-2037-4DC2-8CC5-11F5B7165C8D} = {1EF9D9DA-B4CF-4467-A5F4-CDBACEAA34CD}
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EndGlobalSection
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EndGlobal

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