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661 lines
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661 lines
31 KiB
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<a href="../MathNet.Numerics/AppSwitches.htm">AppSwitches</a>
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<a href="../MathNet.Numerics/Combinatorics.htm" class="current">Combinatorics</a>
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<a href="../MathNet.Numerics/FindMinimum.htm">FindMinimum</a>
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<a href="../MathNet.Numerics/MemoryAllocationException.htm">MemoryAllocationException</a>
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<a href="../MathNet.Numerics/NumericalBreakdownException.htm">NumericalBreakdownException</a>
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<a href="../MathNet.Numerics/Permutation.htm">Permutation</a>
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<a href="../MathNet.Numerics/Polynomial.htm">Polynomial</a>
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<a href="../MathNet.Numerics/Precision.htm">Precision</a>
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<a href="../MathNet.Numerics/SingularUMatrixException.htm">SingularUMatrixException</a>
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<a href="../MathNet.Numerics/Sorting.htm">Sorting</a>
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<a href="../MathNet.Numerics/SpecialFunctions.htm">SpecialFunctions</a>
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<a href="../MathNet.Numerics/TestFunctions.htm">TestFunctions</a>
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<a href="../MathNet.Numerics/Trig.htm">Trig</a>
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<a href="../MathNet.Numerics/Window.htm">Window</a>
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</ul>
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</div>
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</div>
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<div class="header">
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<p class="class"><strong>Type</strong> Combinatorics</p>
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<p><strong>Namespace</strong> MathNet.Numerics</p>
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</div>
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<div class="sub-header">
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<div id="summary">Enumerative Combinatorics and Counting.
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</div>
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<h3 class="section">Static Functions</h3>
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<ul>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#Combinations">Combinations</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#CombinationsWithRepetition">CombinationsWithRepetition</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#GenerateCombination">GenerateCombination</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#GenerateCombination">GenerateCombination</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#GenerateCombinationWithRepetition">GenerateCombinationWithRepetition</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#GeneratePermutation">GeneratePermutation</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#GenerateVariation">GenerateVariation</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#GenerateVariationWithRepetition">GenerateVariationWithRepetition</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#Permutations">Permutations</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#SelectCombination``1">SelectCombination<T></a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#SelectCombinationWithRepetition``1">SelectCombinationWithRepetition<T></a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#SelectPermutation``1">SelectPermutation<T></a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#SelectPermutationInplace``1">SelectPermutationInplace<T></a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#SelectVariation``1">SelectVariation<T></a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#SelectVariationWithRepetition``1">SelectVariationWithRepetition<T></a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#Variations">Variations</a></li>
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<li><a href="../MathNet.Numerics/Combinatorics.htm#VariationsWithRepetition">VariationsWithRepetition</a></li>
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</ul>
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</div>
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<h3 class="section">Public Static Functions</h3>
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<div id="Combinations" class="method">
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<h4><span title="System.double">double</span> <strong>Combinations</strong>(<span title="System.int">int</span> n, <span title="System.int">int</span> k)</h4>
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<div class="content">Count the number of possible combinations without repetition.
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The order does not matter and each object can be chosen only once.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">Number of elements in the set. </p>
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<h6><code><span title="System.int">int</span></code> k</h6>
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<p class="comments">Number of elements to choose from the set. Each element is chosen at most once. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.double">double</span></code></h6>
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<p>Maximum number of combinations. </p>
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</div>
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</div>
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</div>
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<div id="CombinationsWithRepetition" class="method">
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<h4><span title="System.double">double</span> <strong>CombinationsWithRepetition</strong>(<span title="System.int">int</span> n, <span title="System.int">int</span> k)</h4>
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<div class="content">Count the number of possible combinations with repetition.
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The order does not matter and an object can be chosen more than once.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">Number of elements in the set. </p>
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<h6><code><span title="System.int">int</span></code> k</h6>
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<p class="comments">Number of elements to choose from the set. Each element is chosen 0, 1 or multiple times. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.double">double</span></code></h6>
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<p>Maximum number of combinations with repetition. </p>
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</div>
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</div>
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</div>
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<div id="GenerateCombination" class="method">
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<h4><span title="System.Boolean[]">Boolean[]</span> <strong>GenerateCombination</strong>(<span title="System.int">int</span> n, <span title="System.int">int</span> k, <span title="System.Random">Random</span> randomSource)</h4>
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<div class="content">Generate a random combination, without repetition, by randomly selecting k of N elements.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">Number of elements in the set. </p>
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<h6><code><span title="System.int">int</span></code> k</h6>
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<p class="comments">Number of elements to choose from the set. Each element is chosen at most once. </p>
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<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
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<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.Boolean[]">Boolean[]</span></code></h6>
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<p>Boolean mask array of length <code>N</code> , for each item true if it is selected. </p>
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</div>
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</div>
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</div>
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<div id="GenerateCombination" class="method">
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<h4><span title="System.Boolean[]">Boolean[]</span> <strong>GenerateCombination</strong>(<span title="System.int">int</span> n, <span title="System.Random">Random</span> randomSource)</h4>
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<div class="content">Generate a random combination, without repetition, by randomly selecting some of N elements.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">Number of elements in the set. </p>
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<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
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<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.Boolean[]">Boolean[]</span></code></h6>
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<p>Boolean mask array of length <code>N</code> , for each item true if it is selected. </p>
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</div>
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</div>
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</div>
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<div id="GenerateCombinationWithRepetition" class="method">
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<h4><span title="System.Int32[]">Int32[]</span> <strong>GenerateCombinationWithRepetition</strong>(<span title="System.int">int</span> n, <span title="System.int">int</span> k, <span title="System.Random">Random</span> randomSource)</h4>
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<div class="content">Generates a random combination, with repetition, by randomly selecting k of N elements.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">Number of elements in the set. </p>
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<h6><code><span title="System.int">int</span></code> k</h6>
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<p class="comments">Number of elements to choose from the set. Elements can be chosen more than once. </p>
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<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
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<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.Int32[]">Int32[]</span></code></h6>
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<p>Integer mask array of length <code>N</code> , for each item the number of times it was selected. </p>
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</div>
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</div>
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</div>
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<div id="GeneratePermutation" class="method">
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<h4><span title="System.Int32[]">Int32[]</span> <strong>GeneratePermutation</strong>(<span title="System.int">int</span> n, <span title="System.Random">Random</span> randomSource)</h4>
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<div class="content">Generate a random permutation, without repetition, by generating the index numbers 0 to N-1 and shuffle them randomly.
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Implemented using Fisher-Yates Shuffling.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">Number of (distinguishable) elements in the set. </p>
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<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
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<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.Int32[]">Int32[]</span></code></h6>
|
|
<p>An array of length <code>N</code> that contains (in any order) the integers of the interval <code>[0, N)</code>. </p>
|
|
</div>
|
|
|
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</div>
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|
</div>
|
|
<div id="GenerateVariation" class="method">
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|
<h4><span title="System.Int32[]">Int32[]</span> <strong>GenerateVariation</strong>(<span title="System.int">int</span> n, <span title="System.int">int</span> k, <span title="System.Random">Random</span> randomSource)</h4>
|
|
<div class="content">Generate a random variation, without repetition, by randomly selecting k of n elements with order.
|
|
Implemented using partial Fisher-Yates Shuffling.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">Number of elements in the set. </p>
|
|
<h6><code><span title="System.int">int</span></code> k</h6>
|
|
<p class="comments">Number of elements to choose from the set. Each element is chosen at most once. </p>
|
|
<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
|
|
<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.Int32[]">Int32[]</span></code></h6>
|
|
<p>An array of length <code>K</code> that contains the indices of the selections as integers of the interval <code>[0, N)</code>. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="GenerateVariationWithRepetition" class="method">
|
|
<h4><span title="System.Int32[]">Int32[]</span> <strong>GenerateVariationWithRepetition</strong>(<span title="System.int">int</span> n, <span title="System.int">int</span> k, <span title="System.Random">Random</span> randomSource)</h4>
|
|
<div class="content">Generate a random variation, with repetition, by randomly selecting k of n elements with order.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">Number of elements in the set. </p>
|
|
<h6><code><span title="System.int">int</span></code> k</h6>
|
|
<p class="comments">Number of elements to choose from the set. Elements can be chosen more than once. </p>
|
|
<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
|
|
<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.Int32[]">Int32[]</span></code></h6>
|
|
<p>An array of length <code>K</code> that contains the indices of the selections as integers of the interval <code>[0, N)</code>. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Permutations" class="method">
|
|
<h4><span title="System.double">double</span> <strong>Permutations</strong>(<span title="System.int">int</span> n)</h4>
|
|
<div class="content">Count the number of possible permutations (without repetition).
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">Number of (distinguishable) elements in the set. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>Maximum number of permutations without repetition. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="SelectCombination``1" class="method">
|
|
<h4><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> <strong>SelectCombination<T></strong>(this <span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> data, <span title="System.int">int</span> elementsToChoose, <span title="System.Random">Random</span> randomSource)</h4>
|
|
<div class="content">Select a random combination, without repetition, from a data sequence by selecting k elements in original order.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code> data</h6>
|
|
<p class="comments">The data source to choose from. </p>
|
|
<h6><code><span title="System.int">int</span></code> elementsToChoose</h6>
|
|
<p class="comments">Number of elements (k) to choose from the data set. Each element is chosen at most once. </p>
|
|
<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
|
|
<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code></h6>
|
|
<p>The chosen combination, in the original order. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="SelectCombinationWithRepetition``1" class="method">
|
|
<h4><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> <strong>SelectCombinationWithRepetition<T></strong>(this <span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> data, <span title="System.int">int</span> elementsToChoose, <span title="System.Random">Random</span> randomSource)</h4>
|
|
<div class="content">Select a random combination, with repetition, from a data sequence by selecting k elements in original order.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code> data</h6>
|
|
<p class="comments">The data source to choose from. </p>
|
|
<h6><code><span title="System.int">int</span></code> elementsToChoose</h6>
|
|
<p class="comments">Number of elements (k) to choose from the data set. Elements can be chosen more than once. </p>
|
|
<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
|
|
<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code></h6>
|
|
<p>The chosen combination with repetition, in the original order. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="SelectPermutation``1" class="method">
|
|
<h4><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> <strong>SelectPermutation<T></strong>(this <span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> data, <span title="System.Random">Random</span> randomSource)</h4>
|
|
<div class="content">Select a random permutation from a data sequence by returning the provided data in random order.
|
|
Implemented using Fisher-Yates Shuffling.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code> data</h6>
|
|
<p class="comments">The data elements to be reordered. </p>
|
|
<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
|
|
<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="SelectPermutationInplace``1" class="method">
|
|
<h4><span title="System.void">void</span> <strong>SelectPermutationInplace<T></strong>(<span title="MathNet.Numerics.T[]">T[]</span> data, <span title="System.Random">Random</span> randomSource)</h4>
|
|
<div class="content">Select a random permutation, without repetition, from a data array by reordering the provided array in-place.
|
|
Implemented using Fisher-Yates Shuffling. The provided data array will be modified.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="MathNet.Numerics.T[]">T[]</span></code> data</h6>
|
|
<p class="comments">The data array to be reordered. The array will be modified by this routine. </p>
|
|
<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
|
|
<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="SelectVariation``1" class="method">
|
|
<h4><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> <strong>SelectVariation<T></strong>(this <span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> data, <span title="System.int">int</span> elementsToChoose, <span title="System.Random">Random</span> randomSource)</h4>
|
|
<div class="content">Select a random variation, without repetition, from a data sequence by randomly selecting k elements in random order.
|
|
Implemented using partial Fisher-Yates Shuffling.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code> data</h6>
|
|
<p class="comments">The data source to choose from. </p>
|
|
<h6><code><span title="System.int">int</span></code> elementsToChoose</h6>
|
|
<p class="comments">Number of elements (k) to choose from the set. Each element is chosen at most once. </p>
|
|
<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
|
|
<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code></h6>
|
|
<p>The chosen variation, in random order. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="SelectVariationWithRepetition``1" class="method">
|
|
<h4><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> <strong>SelectVariationWithRepetition<T></strong>(this <span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span> data, <span title="System.int">int</span> elementsToChoose, <span title="System.Random">Random</span> randomSource)</h4>
|
|
<div class="content">Select a random variation, with repetition, from a data sequence by randomly selecting k elements in random order.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code> data</h6>
|
|
<p class="comments">The data source to choose from. </p>
|
|
<h6><code><span title="System.int">int</span></code> elementsToChoose</h6>
|
|
<p class="comments">Number of elements (k) to choose from the data set. Elements can be chosen more than once. </p>
|
|
<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
|
|
<p class="comments">The random number generator to use. Optional; the default random source will be used if null. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<T>">IEnumerable<T></span></code></h6>
|
|
<p>The chosen variation with repetition, in random order. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Variations" class="method">
|
|
<h4><span title="System.double">double</span> <strong>Variations</strong>(<span title="System.int">int</span> n, <span title="System.int">int</span> k)</h4>
|
|
<div class="content">Count the number of possible variations without repetition.
|
|
The order matters and each object can be chosen only once.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">Number of elements in the set. </p>
|
|
<h6><code><span title="System.int">int</span></code> k</h6>
|
|
<p class="comments">Number of elements to choose from the set. Each element is chosen at most once. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>Maximum number of distinct variations. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="VariationsWithRepetition" class="method">
|
|
<h4><span title="System.double">double</span> <strong>VariationsWithRepetition</strong>(<span title="System.int">int</span> n, <span title="System.int">int</span> k)</h4>
|
|
<div class="content">Count the number of possible variations with repetition.
|
|
The order matters and each object can be chosen more than once.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">Number of elements in the set. </p>
|
|
<h6><code><span title="System.int">int</span></code> k</h6>
|
|
<p class="comments">Number of elements to choose from the set. Each element is chosen 0, 1 or multiple times. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>Maximum number of distinct variations with repetition. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="footer">
|
|
<p>Based on v5.0.0.0 of MathNet.Numerics (Math.NET Numerics)</p>
|
|
<p>Generated by <a href="http://docu.jagregory.com">docu</a></p>
|
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