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POList all possible combinations of k integers between 1...n (n choose k)
 

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    <p>Out of no particular reason I decided to look for an algorithm that produces all possible choices of k integers between 1...n, where the order amongst the k integer doesn't matter (the n choose k thingy). </p> <p>From the exact same reason, which is no reason at all, I also implemented it in C#. My question is:</p> <p><em>Do you see any mistake in my algorithm or code? And, more importantly, <strong>can you suggest a better algorithm?</em></strong></p> <p>Please pay more attention to the algorithm than the code itself. It's not the prettiest code I've ever written, although do tell if you see an error.</p> <p><strong>EDIT:</strong> Alogirthm explained - <br/></p> <ul> <li>We hold k indices.</li> <li>This creates k nested <em>for</em> loops, where loop i's index is indices[i]. </li> <li>It simulates k <em>for</em> loops where indices[i+1] belongs to a loop nested within the loop of indices[i].</li> <li>indices[i] runs from indices[i - 1] + 1 to n - k + i + 1.</li> </ul> <p>CODE:</p> <pre><code>public class AllPossibleCombination { int n, k; int[] indices; List&lt;int[]&gt; combinations = null; public AllPossibleCombination(int n_, int k_) { if (n_ &lt;= 0) { throw new ArgumentException("n_ must be in N+"); } if (k_ &lt;= 0) { throw new ArgumentException("k_ must be in N+"); } if (k_ &gt; n_) { throw new ArgumentException("k_ can be at most n_"); } n = n_; k = k_; indices = new int[k]; indices[0] = 1; } /// &lt;summary&gt; /// Returns all possible k combination of 0..n-1 /// &lt;/summary&gt; /// &lt;returns&gt;&lt;/returns&gt; public List&lt;int[]&gt; GetCombinations() { if (combinations == null) { combinations = new List&lt;int[]&gt;(); Iterate(0); } return combinations; } private void Iterate(int ii) { // // Initialize // if (ii &gt; 0) { indices[ii] = indices[ii - 1] + 1; } for (; indices[ii] &lt;= (n - k + ii + 1); indices[ii]++) { if (ii &lt; k - 1) { Iterate(ii + 1); } else { int[] combination = new int[k]; indices.CopyTo(combination, 0); combinations.Add(combination); } } } } </code></pre> <p>I apologize for the long question, it might be fit for a blog post, but I do want the community's opinion here.</p> <p>Thanks, <br/> Asaf</p>
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    1. CODuplicate of http://stackoverflow.com/questions/127704/algorithm-to-return-all-combinations-of-k-elements-from-n
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