// <copyright file="Permutation.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2010 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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namespace IStation.Numerics
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{
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/// <summary>
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/// Class to represent a permutation for a subset of the natural numbers.
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/// </summary>
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[Serializable]
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public class Permutation
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{
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#region fields
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/// <summary>
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/// Entry _indices[i] represents the location to which i is permuted to.
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/// </summary>
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private readonly int[] _indices;
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#endregion fields
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#region Constructor
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/// <summary>
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/// Initializes a new instance of the Permutation class.
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/// </summary>
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/// <param name="indices">An array which represents where each integer is permuted too: indices[i] represents that integer i
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/// is permuted to location indices[i].</param>
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public Permutation(int[] indices)
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{
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if (!CheckForProperPermutation(indices))
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{
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throw new ArgumentException("The integer array does not represent a valid permutation.", nameof(indices));
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}
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_indices = (int[])indices.Clone();
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}
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#endregion
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/// <summary>
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/// Gets the number of elements this permutation is over.
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/// </summary>
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public int Dimension => _indices.Length;
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/// <summary>
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/// Computes where <paramref name="idx"/> permutes too.
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/// </summary>
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/// <param name="idx">The index to permute from.</param>
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/// <returns>The index which is permuted to.</returns>
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public int this[int idx] => _indices[idx];
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/// <summary>
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/// Computes the inverse of the permutation.
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/// </summary>
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/// <returns>The inverse of the permutation.</returns>
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public Permutation Inverse()
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{
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var invIdx = new int[Dimension];
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for (int i = 0; i < invIdx.Length; i++)
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{
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invIdx[_indices[i]] = i;
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}
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return new Permutation(invIdx);
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}
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/// <summary>
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/// Construct an array from a sequence of inversions.
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/// </summary>
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/// <example>
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/// From wikipedia: the permutation 12043 has the inversions (0,2), (1,2) and (3,4). This would be
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/// encoded using the array [22244].
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/// </example>
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/// <param name="inv">The set of inversions to construct the permutation from.</param>
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/// <returns>A permutation generated from a sequence of inversions.</returns>
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public static Permutation FromInversions(int[] inv)
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{
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var idx = new int[inv.Length];
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for (int i = 0; i < inv.Length; i++)
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{
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idx[i] = i;
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}
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for (int i = inv.Length - 1; i >= 0; i--)
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{
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if (idx[i] != inv[i])
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{
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int t = idx[i];
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idx[i] = idx[inv[i]];
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idx[inv[i]] = t;
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}
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}
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return new Permutation(idx);
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}
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/// <summary>
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/// Construct a sequence of inversions from the permutation.
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/// </summary>
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/// <example>
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/// From wikipedia: the permutation 12043 has the inversions (0,2), (1,2) and (3,4). This would be
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/// encoded using the array [22244].
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/// </example>
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/// <returns>A sequence of inversions.</returns>
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public int[] ToInversions()
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{
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var idx = (int[])_indices.Clone();
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for (int i = 0; i < idx.Length; i++)
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{
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if (idx[i] != i)
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{
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int q = Array.FindIndex(idx, i + 1, x => x == i);
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var t = idx[i];
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idx[i] = q;
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idx[q] = t;
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}
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}
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return idx;
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}
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/// <summary>
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/// Checks whether the <paramref name="indices"/> array represents a proper permutation.
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/// </summary>
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/// <param name="indices">An array which represents where each integer is permuted too: indices[i] represents that integer i
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/// is permuted to location indices[i].</param>
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/// <returns>True if <paramref name="indices"/> represents a proper permutation, <c>false</c> otherwise.</returns>
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static bool CheckForProperPermutation(int[] indices)
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{
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var idxCheck = new bool[indices.Length];
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for (int i = 0; i < indices.Length; i++)
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{
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if (indices[i] >= indices.Length || indices[i] < 0)
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{
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return false;
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}
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idxCheck[indices[i]] = true;
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}
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for (int i = 0; i < indices.Length; i++)
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{
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if (idxCheck[i] == false)
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{
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return false;
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}
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}
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return true;
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}
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}
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}
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