施工阶段2：归并排序

2022-08-11 11:12:04 +08:00 · 2022-08-11 11:12:04 +08:00 · c9dc0930ed
parent b8308cff5d
commit c9dc0930ed
5 changed files with 172 additions and 7 deletions
--- a/.idea/.idea.Algorithm-FSharp/.idea/workspace.xml
+++ b/.idea/.idea.Algorithm-FSharp/.idea/workspace.xml
@ -7,7 +7,13 @@
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+      <change afterPath="$PROJECT_DIR$/Algorithm-FSharp/MergeSort.fs" afterDir="false" />
+      <change afterPath="$PROJECT_DIR$/Algorithm-FSharp/TestList.fs" afterDir="false" />
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+      <change beforePath="$PROJECT_DIR$/Algorithm-FSharp/Algorithm-FSharp.fsproj" beforeDir="false" afterPath="$PROJECT_DIR$/Algorithm-FSharp/Algorithm-FSharp.fsproj" afterDir="false" />
+      <change beforePath="$PROJECT_DIR$/Algorithm-FSharp/Program.fs" beforeDir="false" afterPath="$PROJECT_DIR$/Algorithm-FSharp/Program.fs" afterDir="false" />
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@ -24,6 +30,12 @@
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+    <setting file="file://$APPLICATION_CONFIG_DIR$/resharper-host/DecompilerCache/decompiler/1a6d778498705eb358dcc13260cac0712f0088/7d/a1c780dd/FSharpList`1.cs" root0="SKIP_HIGHLIGHTING" />
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@ -87,7 +105,21 @@
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+    <MESSAGE value="真的只是一点小问题！" />
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 </project>
--- a/Algorithm-FSharp/Algorithm-FSharp.fsproj
+++ b/Algorithm-FSharp/Algorithm-FSharp.fsproj
@ -7,6 +7,8 @@
    </PropertyGroup>

    <ItemGroup>
+        <Compile Include="TestList.fs" />
+        <Compile Include="MergeSort.fs" />
        <Compile Include="QuickSort.fs" />
        <Compile Include="Program.fs" />
    </ItemGroup>
--- a/Algorithm-FSharp/MergeSort.fs
+++ b/Algorithm-FSharp/MergeSort.fs
@ -0,0 +1,26 @@
+module Algorithm_FSharp.MergeSort
+
+// 合并有序数列算法
+// merge : 'a list -> 'a list -> 'a list -> 'a list
+// 待合并的有序数列存储在lhs和rhs中，每一步合并后中间结果都存放在res中
+let rec merge lhs rhs res =
+ match (lhs, rhs) with // 判断lhs和rhs是否为空
+ | [], [] -> res // 若两者均为空，直接返回res
+ | [], ys -> res @ ys // 若lhs中的数已经用光，则将rhs追加到res末尾并返回
+ | xs, [] -> res @ xs // 若rhs中的数已经用光，则将lhs追加到res末尾并返回
+ | x::xs, y::ys ->    // 若二者均不为空
+  match x < y with // 取出第一个元素，并判断二者的大小关系
+  | true -> merge xs (y::ys) (res @ [x])  // 若lhs的第一个元素小于rhs的第一个元素，则将其取出并放置在res的末尾，递归合并剩余的元素
+  | false -> merge (x::xs) ys (res @ [y]) // 若rhs的第一个元素小于lhs的第一个元素，则将其取出并放置在res的末尾，递归合并剩余的元素
+
+// 归并排序算法的F#实现
+// mergesort : 'a list -> 'a list
+let rec mergesort arr =
+ match arr with // 模式匹配
+ | [] -> []     // 若arr为空或只有一个元素，则它已经有序，直接返回
+ | [single] -> [single]
+ | _ ->         // 若arr的元素多于一个
+         let mid = arr.Length / 2 // 计算序列中点的索引
+         let left, right = arr // 从中点切分序列为两部分
+                           |> List.splitAt mid
+         merge (mergesort left) (mergesort right) [] // 将两部分分别归并排序，然后合并为有序数列
--- a/Algorithm-FSharp/Program.fs
+++ b/Algorithm-FSharp/Program.fs
@ -1,8 +1,8 @@
 // For more information see https://aka.ms/fsharp-console-apps
 module Algorithm_FSharp.Program
-open Algorithm_FSharp.QuickSort
+open Algorithm_FSharp.MergeSort
+open Algorithm_FSharp.TestList

 // 测试用例
-let myList = [1; 1; 4; 5; 1; 4; 1; 9; 1; 9; 8; 1; 0] // 你是一个一个一个快速排序算法啊啊啊啊啊啊
 printfn $"%A{myList
-              |> quicksort}"
+              |> mergesort}"
--- a/Algorithm-FSharp/TestList.fs
+++ b/Algorithm-FSharp/TestList.fs
@ -0,0 +1,104 @@
+module Algorithm_FSharp.TestList
+// 测试用数据集
+let myList = [
+    371
+    42
+    583
+    67
+    201
+    740
+    468
+    424
+    853
+    539
+    158
+    982
+    178
+    644
+    585
+    152
+    820
+    719
+    994
+    43
+    368
+    378
+    95
+    685
+    609
+    153
+    841
+    466
+    214
+    432 
+    809
+    499
+    66
+    512
+    652
+    111
+    851
+    98
+    277
+    223
+    922
+    533
+    969
+    407
+    694
+    32
+    36
+    242
+    491
+    99
+    987
+    519
+    336
+    1000
+    359
+    930
+    892
+    833
+    417
+    981
+    827
+    945
+    195
+    389
+    664
+    601 
+    864
+    607
+    911
+    445
+    252
+    681
+    413
+    228
+    77
+    758
+    799
+    620
+    898 
+    545
+    110
+    560
+    883
+    107
+    703
+    263
+    148
+    617
+    137
+    628
+    155
+    908
+    598
+    220
+    318
+    877
+    315
+    978
+    645
+    75
+]