施工阶段3：选择排序

.idea/.idea.Algorithm-FSharp/.idea/workspace.xml

@@ -8,8 +8,7 @@
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   <component name="ChangeListManager">
     <list default="true" id="32b2067c-6667-4162-834b-afaa5fbc533d" name="Changes" comment="">
-      <change afterPath="$PROJECT_DIR$/Algorithm-FSharp/MergeSort.fs" afterDir="false" />
-      <change afterPath="$PROJECT_DIR$/Algorithm-FSharp/TestList.fs" afterDir="false" />
+      <change afterPath="$PROJECT_DIR$/Algorithm-FSharp/SelectionSort.fs" afterDir="false" />
       <change beforePath="$PROJECT_DIR$/.idea/.idea.Algorithm-FSharp/.idea/workspace.xml" beforeDir="false" afterPath="$PROJECT_DIR$/.idea/.idea.Algorithm-FSharp/.idea/workspace.xml" afterDir="false" />
       <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" />
@@ -96,7 +95,9 @@
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       <workItem from="1660136010329" duration="3458000" />
       <workItem from="1660181422024" duration="2137000" />
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+      <workItem from="1660186635954" duration="1867000" />
+      <workItem from="1660231505344" duration="3491000" />
+      <workItem from="1660267756436" duration="6060000" />
     </task>
     <task id="LOCAL-00001" summary="施工阶段1 快速排序">
       <created>1660059459924</created>
@@ -119,7 +120,14 @@
       <option name="project" value="LOCAL" />
       <updated>1660059986664</updated>
     </task>
-    <option name="localTasksCounter" value="4" />
+    <task id="LOCAL-00004" summary="施工阶段2：归并排序">
+      <created>1660187524761</created>
+      <option name="number" value="00004" />
+      <option name="presentableId" value="LOCAL-00004" />
+      <option name="project" value="LOCAL" />
+      <updated>1660187524761</updated>
+    </task>
+    <option name="localTasksCounter" value="5" />
     <servers />
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   <component name="TypeScriptGeneratedFilesManager">
@@ -144,6 +152,7 @@
     <MESSAGE value="施工阶段1 快速排序" />
     <MESSAGE value="施工阶段1：快速排序" />
     <MESSAGE value="真的只是一点小问题！" />
-    <option name="LAST_COMMIT_MESSAGE" value="真的只是一点小问题！" />
+    <MESSAGE value="施工阶段2：归并排序" />
+    <option name="LAST_COMMIT_MESSAGE" value="施工阶段2：归并排序" />
   </component>
 </project>

Algorithm-FSharp/Algorithm-FSharp.fsproj

@@ -8,6 +8,7 @@
 
     <ItemGroup>
         <Compile Include="TestList.fs" />
+        <Compile Include="SelectionSort.fs" />
         <Compile Include="MergeSort.fs" />
         <Compile Include="QuickSort.fs" />
         <Compile Include="Program.fs" />

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.MergeSort
+open Algorithm_FSharp.SelectionSort
 open Algorithm_FSharp.TestList
 
 // 测试用例
 printfn $"%A{myList
-              |> mergesort}"
+              |> selection_sort}"

Algorithm-FSharp/SelectionSort.fs

@@ -0,0 +1,36 @@
+module Algorithm_FSharp.SelectionSort
+// 选择序列中的最小值
+// select_min_inner : 'a -> 'a list -> 'a
+// cur中存储有当前的最小值
+let rec select_min_inner cur = function
+ | [] -> cur // 若序列中数已经用光，则返回cur
+ | x::xs -> // 若序列中还有数，则取出第一个数
+  match x < cur with // 并将其和目前的最小值比较
+  | true -> select_min_inner x xs // 若当前数小于目前的最小值，则将最小值更新为当前数
+  | false -> select_min_inner cur xs // 若当前数大于等于目前最小值，则不更新最小值
+  // 并继续在剩余元素中寻找
+
+// select_min_inner的包装，可以方便的选择最小值
+// 会将序列的第一个元素作为目前的“最小值”传给select_min_inner
+// select_min : 'T list -> 'T
+let select_min (arr: 'T list) = select_min_inner arr.Head arr
+
+// 除去序列中不满足谓词的元素
+// remove_elem : ('a -> bool) -> 'a list -> 'a list
+// 对每一个元素调用pred，若结果为假，则将此元素从序列中去除
+let rec remove_elem pred = function
+ | [] -> [] // 递归边界：若序列中没有元素，则什么都不用做
+ | x::xs -> // 若序列中有其他元素
+  match pred x with // 取出序列中第一个元素，并对其调用pred
+  | true -> x::(remove_elem pred xs) // 若返回值为真，则扫描剩余元素
+  | false -> remove_elem pred xs // 若返回值为假，则去除此元素，并扫描剩余元素
+// 选择排序的F#实现
+// selection_sort : 'a list -> 'a list
+let rec selection_sort = function
+ | [] -> [] // 若待排序序列为空或只有一个元素，则它已经有序，直接返回
+ | [single] -> [single]
+ | xs -> // 若待排序序列含有不止一个元素
+  let min = select_min xs // 选出最小值
+  let rest = xs // 将最小值从序列中移除
+             |> remove_elem (fun x -> x <> min)
+  min::(selection_sort rest) // 对剩余部分进行递归排序，将最小值附加在排序结果的首部