修正了数值比例分摊算法的一些原先不太合理的地方

guogangj · Nov 29, 2024 · ee77276 · ee77276
1 parent 8bd2793
commit ee77276
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Showing 4 changed files with 56 additions and 16 deletions.
diff --git a/AlgorithmLib/AlgorithmLib.csproj b/AlgorithmLib/AlgorithmLib.csproj
@@ -2,13 +2,13 @@
 
   <PropertyGroup>
     <TargetFramework>netstandard2.0</TargetFramework>
-    <Version>1.0.5</Version>
+    <Version>1.0.6</Version>
     <PackageId>AlgorithmLib</PackageId>
     <Authors>Jiang Guogang</Authors>
     <Company></Company>
     <Description>一些常用的算法</Description>
     <RepositoryUrl>https://github.com/guogangj/AlgorithmLib.git</RepositoryUrl>
-    <PackageReleaseNotes>增加了RelationshipHelper.MakeRelationShip方法，用于处理整体对象和碎片对象的关联关系</PackageReleaseNotes>
+    <PackageReleaseNotes>修正了数值分摊算法之前一些不合理之处</PackageReleaseNotes>
     <PackageReadmeFile>README.md</PackageReadmeFile>
     <PackageProjectUrl>https://github.com/guogangj/AlgorithmLib</PackageProjectUrl>
     <RepositoryType>git</RepositoryType>

diff --git a/AlgorithmLib/NumberDivideHelper.cs b/AlgorithmLib/NumberDivideHelper.cs
@@ -19,7 +19,10 @@ public static decimal[] Divide(decimal total, decimal[] scale, int decimalNum =
                 throw new ArgumentException("Cannot divide the number due to its decimal number is more than specified value");
             }
             int partNum = scale.Length;
-            decimal[] result = new decimal[partNum];
+
+            decimal[] result = new decimal[partNum]; //要返回的结果（可能需要舍入）
+
+
             if (partNum == 0) {
                 return result;
             }
@@ -43,31 +46,57 @@ public static decimal[] Divide(decimal total, decimal[] scale, int decimalNum =
                 decimalNum = -1;
             }
 
+            decimal[] rawResult = new decimal[partNum]; //未经舍入的原始分摊结果
+
             //尝试执行分摊
             for (int i = 0; i < partNum; i++) {
-                result[i] = total * scale[i] / scaleSum;
-
+                rawResult[i] = total * scale[i] / scaleSum;
                 if (decimalNum != -1) {
 
-                    result[i] = decimal.Round(result[i], decimalNum);
+                    result[i] = decimal.Round(rawResult[i], decimalNum);
+                }
+                else {
+                    result[i] = rawResult[i];
                 }
             }
 
-            decimal totalTest = result.Sum();
-            decimal remainder = total - totalTest;
-            if (remainder == 0m) {
+            decimal totalRes = result.Sum();
+            decimal totalDiff = total - totalRes;
+            if (totalDiff == 0m) {
                 return result;
             }
 
-            //摊到最大的上面
-            int maxIdx = 0;
-            for (int i = 1; i < result.Length; i++) {
-                if (result[i] > result[maxIdx]) {
-                    maxIdx = i;
+            if (decimalNum == -1) {
+                //如果小数位不限，产生的误差就算有也极小，直接把误差值算到差距最大的一个值上即可
+                int maxDiffIdx = 0;
+                for (int i = 1; i < partNum; i++) {
+                    if (Math.Abs(result[i] - rawResult[i]) > Math.Abs(result[maxDiffIdx] - rawResult[maxDiffIdx])) {
+                        maxDiffIdx = i;
+                    }
                 }
+                result[maxDiffIdx] += totalDiff;
             }
-            result[maxIdx] += remainder;
+            else {
+                //平掉由于舍入引起的误差
+                //用差值来排个序，准备从差值大的开始调整
+                var sortedDiffs = totalDiff > 0
+                    ? rawResult.Select((r, i) => new { Index = i, Residual = r - result[i] }).ToArray().OrderByDescending(x => x.Residual).ToArray()
+                    : rawResult.Select((r, i) => new { Index = i, Residual = r - result[i] }).ToArray().OrderBy(x => x.Residual).ToArray();
+
+                //最小调整单元，根据小数位决定
+                decimal unit = 1m / (decimalNum >= 0 ? (decimal)Math.Pow(10, decimalNum) : 1m);
 
+                int idx = 0;
+                while (totalDiff != 0) {
+                    int index = sortedDiffs[idx].Index;
+                    decimal adjustment = totalDiff > 0 ? unit : -unit;
+                    if (result[index] + adjustment >= 0) {
+                        result[index] += adjustment;
+                        totalDiff -= adjustment;
+                    }
+                    idx = (idx + 1) % sortedDiffs.Length; //按道理应该不会出现idx比数组长度大的情形，这里的取模应该是不需要的
+                }
+            }
             return result;
         }
     }

diff --git a/AlgorithmLibDemo/Demos.cs b/AlgorithmLibDemo/Demos.cs
@@ -1,6 +1,7 @@
 using AlgorithmLib;
 using System;
 using System.Diagnostics;
+using System.Linq;
 
 namespace AlgorithmLibDemo;
 
@@ -111,6 +112,7 @@ public static void NumberDivideDemo() {
         void PrintDivInfo() {
             Utils.SimplePrintArray(ratioArray, $"\n以此比例分摊 [{toDivide}] (小数位{decimalNum}): ");
         }
+
         PrintDivInfo();
         Utils.SimplePrintArray(NumberDivideHelper.Divide(toDivide, ratioArray, decimalNum));
 
@@ -154,6 +156,15 @@ void PrintDivInfo() {
         catch (ArgumentException ex) {
             Console.WriteLine("出错了: " + ex.Message);
         }
+
+        //一个实际的分摊案例
+        toDivide = 26;
+        decimalNum = 3;
+        ratioArray = new[] { 0.001m, 0.001m, 0.001m, 0.0022m, 0.001m, 0.0022m, 0.001m, 0.0011m, 0.0011m, 0.001m, 0.0011m, 0.0022m, 0.0011m, 0.001m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.001m, 0.0022m, 0.0022m, 0.001m, 0.0011m, 0.0105m, 0.0111m, 0.0022m, 0.0022m, 0.0011m, 0.0022m, 0.001m, 0.001m, 0.0011m, 0.001m, 0.0011m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.0011m, 0.001m, 0.0011m, 0.0011m, 0.001m, 0.001m, 0.001m, 0.001m, 0.0011m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.001m, 0.001m, 0.001m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.0011m, 0.0022m, 0.0022m, 0.0022m, 0.0022m, 0.001m, 0.0011m, 0.0011m, 0.0011m, 0.0011m, 0.001m, 0.0022m, 0.0022m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.0011m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.0022m, 0.001m, 0.0011m, 0.001m, 0.001m, 0.001m, 0.0022m, 0.0022m, 0.001m, 0.001m, 0.0022m, 0.0022m, 0.001m, 0.001m, 0.0022m, 0.001m, 0.001m, 0.001m, 0.001m, 0.0022m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.001m, 0.0012m, 0.0012m, 0.001m, 0.001m, 0.001m, 0.001m };
+        Console.WriteLine("\n一个实际出现的例子，特点是：数值多，比例值小且小数位多，但结果舍进保留位数却少，这可能引起较大的分摊误差");
+        decimal[] result = NumberDivideHelper.Divide(toDivide, ratioArray, decimalNum);
+        Utils.SimplePrintArray(result);
+        Console.WriteLine(result.Sum());
     }
 
     /// <summary>

diff --git a/AlgorithmLibDemo/Program.cs b/AlgorithmLibDemo/Program.cs
@@ -12,7 +12,7 @@ class DemoItem {
         public DemoFun Fun { get; set; }
         public string Desc { get; set; }
     }
-
+    
 
     static void Main(string[] args) {
-Original file line number
+Diff line change
@@ Expand Up / @@ -12,7 +12,7 @@ class DemoItem { @@
             public DemoFun Fun { get; set; }
             public string Desc { get; set; }
         }
         static void Main(string[] args) {
@@ Expand Down @@