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‎3 Searching/3.2/3.2.35/3.2.35.csproj‎

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<Project Sdk="Microsoft.NET.Sdk">
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<PropertyGroup>
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<OutputType>Exe</OutputType>
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<TargetFramework>netcoreapp3.0</TargetFramework>
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<RootNamespace>_3._2._35</RootNamespace>
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</PropertyGroup>
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</Project>

‎3 Searching/3.2/3.2.35/Program.cs‎

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namespace _3._2._35
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{
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class Program
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{
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static void Main(string[] args)
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{
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// 根据书中已经给出的归纳关系式（中文版P255 / 英文版P403）：
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//
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// CN = N - 1 + (C0 + C(N - 1)) / N + (C1 + C(N - 2)) / N + ... + (C(N - 1) + C0) / N
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//
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// 整理得：
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//
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// CN = N - 1 + (C0 + C1 + ... + C(N - 1))/ N + (C(N - 1) + ... + C1 + C0) / N
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//
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// 这和快速排序的式子基本一致，只是 N + 1 变成了 N - 1。
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// 遵循相同的推导过程，我们可以获得类似的结果，两边同乘以 N：
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//
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// NCN = N(N - 1) + 2(C0 + C1 + ... + C(N - 1))
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//
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// 用 N + 1 时的等式减去该式得：
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//
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// (N + 1)C(N + 1) - NCN = 2N + 2CN
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// (N + 1)C(N + 1) = 2N + (N + 2)CN
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// C(N + 1) / (N + 2) = 2N / [(N + 1)(N + 2)] + CN / (N + 1)
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//
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// 令 TN = CN / (N + 1)，得到：
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//
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// T(N + 1) = 2N / [(N + 1)(N + 2)]+TN
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// T(N + 1)-T(N) = 2N / [(N + 1)(N + 2)]
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//
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// 归纳得：
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//
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// TN = 2Σ[(i - 1) / i(i + 1)]
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// CN = 2(N + 1)Σ[(i - 1) / i(i + 1))]
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// CN = 2(N + 1)Σ{(i - 1)[(1 / i) - 1 / (i + 1)]}
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// CN = 2(N + 1)(HN - 1) - 2(N - 1)
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// CN ~ 2(N + 1)(lnN + γ) - 4N
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//
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// 于是根据书中的公式，平均成本为 1 + CN / N ~ 2lnN + 2γ - 3 。
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}
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}
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}

‎Algorithms 4th Edition.sln‎

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EndProject
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Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.27", "3 Searching\3.2\3.2.27\3.2.27.csproj", "{30EAE388-2751-4E2A-8FA3-DE3DFF0429E9}"
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Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.28", "3 Searching\3.2\3.2.28\3.2.28.csproj", "{B72FC2E0-9428-414E-8582-AFF39E461C02}"
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Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "3.2.29", "3 Searching\3.2\3.2.29\3.2.29.csproj", "{0AF0A0B5-10F0-4B14-858C-9F88F5BEF13A}"
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Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.29", "3 Searching\3.2\3.2.29\3.2.29.csproj", "{0AF0A0B5-10F0-4B14-858C-9F88F5BEF13A}"
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Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "3.2.30", "3 Searching\3.2\3.2.30\3.2.30.csproj", "{41058D4A-FF6D-4197-AE28-4B82FDE23FC9}"
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Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.30", "3 Searching\3.2\3.2.30\3.2.30.csproj", "{41058D4A-FF6D-4197-AE28-4B82FDE23FC9}"
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Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.31", "3 Searching\3.2\3.2.31\3.2.31.csproj", "{72A97447-5CBE-43D0-A719-A31F96F978B7}"
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Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.32", "3 Searching\3.2\3.2.32\3.2.32.csproj", "{E74C74C3-8847-4EA5-97E5-80BCB43CC58E}"
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EndProject
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Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "3.2.33", "3 Searching\3.2\3.2.33\3.2.33.csproj", "{C44A238D-56F4-4316-954E-33D3FD73093C}"
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Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.33", "3 Searching\3.2\3.2.33\3.2.33.csproj", "{C44A238D-56F4-4316-954E-33D3FD73093C}"
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EndProject
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Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "3.2.34", "3 Searching\3.2\3.2.34\3.2.34.csproj", "{E2CFD797-005D-41F2-AFCF-212FB5352432}"
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Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "3.2.34", "3 Searching\3.2\3.2.34\3.2.34.csproj", "{E2CFD797-005D-41F2-AFCF-212FB5352432}"
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EndProject
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Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "3.2.35", "3 Searching\3.2\3.2.35\3.2.35.csproj", "{97B6B0DD-EB46-45C3-A917-47D05783243C}"
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EndProject
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Global
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GlobalSection(SolutionConfigurationPlatforms) = preSolution
@@ -2805,6 +2807,10 @@ Global
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{E2CFD797-005D-41F2-AFCF-212FB5352432}.Debug|Any CPU.Build.0 = Debug|Any CPU
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{E2CFD797-005D-41F2-AFCF-212FB5352432}.Release|Any CPU.ActiveCfg = Release|Any CPU
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{E2CFD797-005D-41F2-AFCF-212FB5352432}.Release|Any CPU.Build.0 = Release|Any CPU
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{97B6B0DD-EB46-45C3-A917-47D05783243C}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
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{97B6B0DD-EB46-45C3-A917-47D05783243C}.Debug|Any CPU.Build.0 = Debug|Any CPU
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{97B6B0DD-EB46-45C3-A917-47D05783243C}.Release|Any CPU.ActiveCfg = Release|Any CPU
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{97B6B0DD-EB46-45C3-A917-47D05783243C}.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
@@ -3312,6 +3318,7 @@ Global
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{E74C74C3-8847-4EA5-97E5-80BCB43CC58E} = {136F3860-08E9-4C37-BC04-679085D442B4}
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{C44A238D-56F4-4316-954E-33D3FD73093C} = {136F3860-08E9-4C37-BC04-679085D442B4}
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{E2CFD797-005D-41F2-AFCF-212FB5352432} = {136F3860-08E9-4C37-BC04-679085D442B4}
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{97B6B0DD-EB46-45C3-A917-47D05783243C} = {136F3860-08E9-4C37-BC04-679085D442B4}
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EndGlobalSection
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GlobalSection(ExtensibilityGlobals) = postSolution
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SolutionGuid = {EE55CF8D-6F35-464D-B95B-ED85644AE41C}

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