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POsemi-random set of subsets
 

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    <p>I'm trying to generate semi-random subsets with some restrictions.</p> <p>Here are the variable descriptions with example values:</p> <ul> <li>ObjCount - the number of objects (12)</li> <li>VisibleCount (AKA SetSize) - the number of objects per set (6)</li> <li>SetCount - the number of sets (12)</li> <li>ObjAppearances - the number of set in which an object appears = <code>SetCount * VisibleCount / ObjCount</code></li> </ul> <p>I need to produce a given number of sets (SetCount) that follow these rules:</p> <ol> <li>Each set is a collection of objects, but no object can be in a single set more than once. </li> <li>Furthermore, each object should be in the same number of sets. <em>If it doesn't devide evenly, then the number sets in which an object appears can be off by 1 (some objects are in 4 sets, and others are in 5). I'll try to avoid this situation, so it's not critical.</em></li> </ol> <p>It's turning out to be far less trivial than I initially thought. Could anyone help me with some code/psuedocode? A solution to a generalized version would be very helpful too.</p> <p>Thanks in advance.</p> <p><strong>Edit:</strong> VisibleCount is the set size. The number of times an object appears (ObjAppearances) is <code>SetCount * VisibleCount / ObjCount</code></p> <p><strong>Edit2:</strong> I should also add that I want the sets to be fairly random. If the sets all have sequential objects (e.g. set1:5,6,7 set2:3,4,5 set3:10,11,0), the solution isn't useful. Sorry for not making that clear.</p> <p><strong>Edit3:</strong> Here is a solution that DOES NOT work. (In C#)</p> <pre><code>static void Main(string[] args) { var ObjectCount = 12; var SetSize = 6; var SetCount = 12; var Sets = Enumerable.Range(0, SetCount).Select(i =&gt; new List&lt;int&gt;()).ToArray(); // a SetCount-sized array of lists var ObjectAppearances = SetSize * SetCount / ObjectCount; var rand = new Random(); // fill the sets for (int obj = 0; obj &lt; ObjectCount; obj++) { for (int a = 0; a &lt; ObjectAppearances; a++) { // get the collection of sets that are not full var nonFullSets = Sets.Where(s =&gt; s.Count &lt; SetSize); // get the collection of non-full sets without obj var setsWithoutObj = nonFullSets.Where(s =&gt; !s.Contains(obj)); /////////////////////// // Here is the problem. All of the non-full sets may already // have a copy of obj /////////////////////// // choose a set at random var currentSetIndex = rand.Next(setsWithoutObj.Count()); var currentSet = setsWithoutObj.ElementAt(currentSetIndex); // add the object currentSet.Add(obj); } } // randomize the order within each set and output each for (int i = 0; i &lt; SetCount; i++) { var randomlyOrderedSet = Sets[i].OrderBy(obj =&gt; rand.Next()); Sets[i] = new List&lt;int&gt;(randomlyOrderedSet); // output foreach (var obj in Sets[i]) Console.Write(string.Format("{0}, ", obj)); Console.WriteLine(); } Console.ReadLine(); } </code></pre> <p><strong>Here's the Solution - An implementation of MizardX's answer</strong></p> <pre><code>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 &lt; 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 &lt; SetCount; s++) { var firstObject = (int)Math.Ceiling((double)s * ObjectCount / SetCount); for (int i = 0; i &lt; SetSize; i++) { var o = (firstObject + i) % ObjectCount; Matrix[s][o] = 1; } } // output the result for (int s = 0; s &lt; SetCount; s++) { for (int o = 0; o &lt; ObjectCount; o++) { Console.Write(string.Format("{0}, ", Matrix[s][o])); } Console.WriteLine(); } Console.WriteLine(); // shuffle sets Matrix = Matrix.OrderBy(s =&gt; rand.Next()).ToArray(); // make a new matrix for shuffle objects var objOrder = Enumerable.Range(0, ObjectCount).OrderBy(o =&gt; rand.Next()).ToArray(); var MatrixSuffled = new int[SetCount][]; for (int s = 0; s &lt; SetCount; s++) MatrixSuffled[s] = Enumerable.Repeat(0, ObjectCount).ToArray(); for (int o = 0; o &lt; ObjectCount; o++) { var oldObj = o; var newObj = objOrder[o]; for (int s = 0; s &lt; 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 &lt; SetCount; s++) { var objectsInThisSet = 0; for (int o = 0; o &lt; 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 &lt; ObjectCount; o++) Console.Write(string.Format("{0} ", objectCounters[o])); Console.ReadLine(); } </code></pre>
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