Algorithm 半随机子集集

我试图生成带有一些限制的半随机子集

以下是变量说明和示例值：

• ObjCount—对象数（12）
• VisibleCount（又名SetSize）-每组对象的数量（6）
• SetCount—集合数（12）
• ObjAppearances—对象出现的集合数=

  SetCount*VisibleCount/ObjCount

我需要生成符合以下规则的给定数量的集合（集合计数）：

每个集合都是对象的集合，但没有对象可以在单个集合中多次出现

此外，每个对象应位于相同数量的集合中。如果不均匀划分，则对象出现的数量集可以减少1（一些对象在4个集中，其他对象在5个集中）。我会尽量避免这种情况，所以这不是关键

事实证明，这远没有我最初想象的那么琐碎。有人能帮我写些代码吗？通用版本的解决方案也会非常有用

提前谢谢

编辑：VisibleCount是设置的大小。对象出现的次数（ObjAppearances）为

SetCount*VisibleCount/ObjCount

Edit2:我还应该补充一点，我希望集合是相当随机的。如果所有集合都有顺序对象（例如set1:5,6,7 set2:3,4,5 set3:10,11,0），则解决方案无效。很抱歉没有说清楚

Edit3:这里有一个不起作用的解决方案。（用C#表示）

static void Main（字符串[]args）
{
var-ObjectCount=12；
var SetSize=6；
var SetCount=12；
var Sets=Enumerable.Range（0，SetCount）.Select（i=>newlist（））.ToArray（）；//一个SetCount大小的列表数组
var objectappearancess=SetSize*SetCount/ObjectCount；
var rand=new Random（）；
//填空
for（int-obj=0；objs.Count！s.Contains（obj））；
///////////////////////
//问题是，所有的非全套可能已经
//有一份obj
///////////////////////
//随机选择一组
var currentSetIndex=rand.Next（setwithoutobj.Count（））；
var currentSet=设置无对象元素（currentSetIndex）；
//添加对象
currentSet.Add（obj）；
}
}
//随机化每个集合内的顺序并输出每个
对于（int i=0；irand.Next（））；
集合[i]=新列表（随机有序集合）；
//输出
foreach（集合[i]中的var obj）
Write（string.Format（“{0}，”，obj））；
Console.WriteLine（）；
}
Console.ReadLine（）；
}

以下是解决方案-MizardX答案的实现

static void Main(string[] args)
{
    var ObjectCount = 12;
    var SetSize = 6;
    var SetCount = 10;
    var rand = new Random();

    // make a matrix [SetCount][ObjectCount]
    var Matrix = new int[SetCount][];
    for (int s = 0; s < SetCount; s++)
        Matrix[s] = Enumerable.Repeat(0, ObjectCount).ToArray();

    // put approximately the same number of objects in each set by
    // adding sequential objects to sequential sets (not random)
    for (int s = 0; s < SetCount; s++)
    {
        var firstObject = (int)Math.Ceiling((double)s * ObjectCount / SetCount);
        for (int i = 0; i < SetSize; i++)
        {
            var o = (firstObject + i) % ObjectCount;
            Matrix[s][o] = 1;
        }
    }

    // output the result
    for (int s = 0; s < SetCount; s++)
    {
        for (int o = 0; o < ObjectCount; o++)
        {
            Console.Write(string.Format("{0}, ", Matrix[s][o]));
        }
        Console.WriteLine();
    }
    Console.WriteLine();

    // shuffle sets
    Matrix = Matrix.OrderBy(s => rand.Next()).ToArray();
    // make a new matrix for shuffle objects
    var objOrder = Enumerable.Range(0, ObjectCount).OrderBy(o => rand.Next()).ToArray();
    var MatrixSuffled = new int[SetCount][];
    for (int s = 0; s < SetCount; s++)
        MatrixSuffled[s] = Enumerable.Repeat(0, ObjectCount).ToArray();
    for (int o = 0; o < ObjectCount; o++)
    {
        var oldObj = o;
        var newObj = objOrder[o];
        for (int s = 0; s < SetCount; s++)
        {
            MatrixSuffled[s][newObj] = Matrix[s][oldObj];
        }
    }

    // check and output the result
    var objectCounters = Enumerable.Repeat(0, ObjectCount).ToArray();
    for (int s = 0; s < SetCount; s++)
    {
        var objectsInThisSet = 0;
        for (int o = 0; o < ObjectCount; o++)
        {
            objectsInThisSet += MatrixSuffled[s][o];
            objectCounters[o] += MatrixSuffled[s][o];
            Console.Write(string.Format("{0}, ", MatrixSuffled[s][o]));
        }
        Console.Write(string.Format("  {0}", objectsInThisSet));
        Console.WriteLine();
    }
    // output object count
    Console.WriteLine();
    for (int o = 0; o < ObjectCount; o++)
        Console.Write(string.Format("{0}  ", objectCounters[o]));
    Console.ReadLine();
}

static void Main（字符串[]args）
{
var-ObjectCount=12；
var SetSize=6；
var SetCount=10；
var rand=new Random（）；
//制作一个矩阵[SetCount][ObjectCount]
var矩阵=新整数[SetCount][]；
对于（int s=0；srand.Next（））.ToArray（）；
//为洗牌对象创建新矩阵
var objOrder=Enumerable.Range（0，ObjectCount）.OrderBy（o=>rand.Next（））.ToArray（）；
var MatrixSuffled=new int[SetCount][]；
对于（int s=0；s

resultSets=新集合[SetCount]；//创建一个集合数组以保存结果
totalObjectsPlaced=0；
currentObjectIndex=0；
而（totalObjectsPlaced<（对象计数*可见计数））{
做{
randomSet=rand（SetCount）；
}而（！resultSets[randomSet].contains（object[currentObjectIndex]）；
结果集[randomSet].add（对象[currentObjectIndex]）；
currentObjectIndex=（currentObjectIndex+1）%ObjCount；
totalObjectsPlac
static void Main(string[] args)
{
    var ObjectCount = 12;
    var SetSize = 6;
    var SetCount = 10;
    var rand = new Random();

    // make a matrix [SetCount][ObjectCount]
    var Matrix = new int[SetCount][];
    for (int s = 0; s < SetCount; s++)
        Matrix[s] = Enumerable.Repeat(0, ObjectCount).ToArray();

    // put approximately the same number of objects in each set by
    // adding sequential objects to sequential sets (not random)
    for (int s = 0; s < SetCount; s++)
    {
        var firstObject = (int)Math.Ceiling((double)s * ObjectCount / SetCount);
        for (int i = 0; i < SetSize; i++)
        {
            var o = (firstObject + i) % ObjectCount;
            Matrix[s][o] = 1;
        }
    }

    // output the result
    for (int s = 0; s < SetCount; s++)
    {
        for (int o = 0; o < ObjectCount; o++)
        {
            Console.Write(string.Format("{0}, ", Matrix[s][o]));
        }
        Console.WriteLine();
    }
    Console.WriteLine();

    // shuffle sets
    Matrix = Matrix.OrderBy(s => rand.Next()).ToArray();
    // make a new matrix for shuffle objects
    var objOrder = Enumerable.Range(0, ObjectCount).OrderBy(o => rand.Next()).ToArray();
    var MatrixSuffled = new int[SetCount][];
    for (int s = 0; s < SetCount; s++)
        MatrixSuffled[s] = Enumerable.Repeat(0, ObjectCount).ToArray();
    for (int o = 0; o < ObjectCount; o++)
    {
        var oldObj = o;
        var newObj = objOrder[o];
        for (int s = 0; s < SetCount; s++)
        {
            MatrixSuffled[s][newObj] = Matrix[s][oldObj];
        }
    }

    // check and output the result
    var objectCounters = Enumerable.Repeat(0, ObjectCount).ToArray();
    for (int s = 0; s < SetCount; s++)
    {
        var objectsInThisSet = 0;
        for (int o = 0; o < ObjectCount; o++)
        {
            objectsInThisSet += MatrixSuffled[s][o];
            objectCounters[o] += MatrixSuffled[s][o];
            Console.Write(string.Format("{0}, ", MatrixSuffled[s][o]));
        }
        Console.Write(string.Format("  {0}", objectsInThisSet));
        Console.WriteLine();
    }
    // output object count
    Console.WriteLine();
    for (int o = 0; o < ObjectCount; o++)
        Console.Write(string.Format("{0}  ", objectCounters[o]));
    Console.ReadLine();
}

resultSets = new Set[SetCount];  // create an array of sets to hold the results

totalObjectsPlaced = 0;
currentObjectIndex = 0;

while (totalObjectsPlaced < (ObjCount * VisibleCount)) {
  do {
    randomSet = rand(SetCount);
  } while (!resultSets[randomSet].contains(object[currentObjectIndex]));
  resultSets[randomSet].add(object[currentObjectIndex]);
  currentObjectIndex = (currentObjectIndex + 1) % ObjCount;
  totalObjectsPlaced++;
}

1 0 0 0 0 0
1 0 0 0 0 0
1 1 0 0 0 0
0 1 0 0 0 0
0 1 1 0 0 0
0 0 1 0 0 0
0 0 1 1 0 0
0 0 0 1 0 0
0 0 0 1 1 0
0 0 0 0 1 1
0 0 0 0 1 1
0 0 0 0 0 1

1 0 1 0 0 0
0 0 0 0 1 0
1 1 0 0 0 0
0 0 0 1 1 0
0 1 0 0 0 0
0 0 0 1 0 0
0 0 1 0 0 0
1 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 1
0 1 0 0 0 1
0 0 0 0 0 1

{1,3,8}
{3,5,11}
{1,7,8}
{4,6,9}
{2,4,10}
{10,11,12}