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POall possible combinations from a set of sets (n choose k)
 

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  1. POall possible combinations from a set of sets (n choose k)
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    <p>Given several sets such as <code>{1,2,3,4}</code>,<code>{1,2}</code>,<code>{1}</code>,<code>{1,2,3,}</code>,..., and a number <code>k</code> such that the combination that ought to be formed is exactly of length <code>k</code>, <em>how would one go about generating a unique combination of length <code>k</code> if I can only choose one number from each set?</em></p> <p>There are exactly k number of sets to choose from. I'm looking for the most efficient way to do this in c#. </p> <p>Intuitively i tried(though i'm not sure it is correct) generating all possible combinations for each set then concatenating each i'th combination from each set with the corresponding i'th combination from subsequent sets to form a <code>k</code> long unique combination but I'm sure there is a general case for this type of question. </p> <p>Can anyone please offer some tips or advise? Specifically which math or computer science topic this falls under and how these questions are typically solved? </p> <p>in the snippet below a string in the array theSets would be for example "31" this means that k = 2 (length of a string in theSets) and there are two sets one of which is {1,2,3} and {1}. with these sets, generate all the unique combinations and provide a count</p> <pre><code>private int combicount(string[] theSets) { int size = theSets[0].Length; int count = 0; List&lt;HashSet&lt;int&gt;&gt; l = new List&lt;HashSet&lt;int&gt;&gt;(); foreach (string s in theSets) { foreach (char c in s) { HashSet&lt;int&gt; h = new HashSet&lt;int&gt;(); for (int n = 1; n &lt;= int.Parse(c.ToString()); n++) { h.Add(n); } l.Add(h); } //toDO - generate all unique combinations by picking exactly 1 from each set in l //toDO - count the number of unique combinations generated } return count; } </code></pre>
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    1. USTheJackal
    1. USTheJackal
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      1. POall possible combinations from a set of sets (n choose k)
      1. USRaymond Chen
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    1. COPost code you have tried.
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      1. USOndrej Janacek
    2. COin presented example sets are ordered, ex: {1,2,3..}. Is this is a true?
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      1. USTigran
    3. COAre you asking for one combination, or an enumeration of all possibilities? If you're picking one number from each set I don't understand why you are generating combinations from each set. What does unique mean here? Uniqueness surely relates to generating multiple combinations?
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      1. USdjna
 

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