[7812] | 1 | #region License Information
|
---|
| 2 | /* HeuristicLab
|
---|
[16453] | 3 | * Copyright (C) 2002-2019 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
|
---|
[7812] | 4 | *
|
---|
| 5 | * This file is part of HeuristicLab.
|
---|
| 6 | *
|
---|
| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
|
---|
| 8 | * it under the terms of the GNU General Public License as published by
|
---|
| 9 | * the Free Software Foundation, either version 3 of the License, or
|
---|
| 10 | * (at your option) any later version.
|
---|
| 11 | *
|
---|
| 12 | * HeuristicLab is distributed in the hope that it will be useful,
|
---|
| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
|
---|
| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
---|
| 15 | * GNU General Public License for more details.
|
---|
| 16 | *
|
---|
| 17 | * You should have received a copy of the GNU General Public License
|
---|
| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
|
---|
| 19 | */
|
---|
| 20 | #endregion
|
---|
| 21 |
|
---|
| 22 | using System;
|
---|
| 23 | using System.Collections.Generic;
|
---|
| 24 | using System.Linq;
|
---|
| 25 |
|
---|
| 26 | namespace HeuristicLab.Common {
|
---|
| 27 | public static class EnumerableExtensions {
|
---|
| 28 | /// <summary>
|
---|
| 29 | /// Selects all elements in the sequence that are maximal with respect to the given value.
|
---|
| 30 | /// </summary>
|
---|
| 31 | /// <remarks>
|
---|
| 32 | /// Runtime complexity of the operation is O(N).
|
---|
| 33 | /// </remarks>
|
---|
| 34 | /// <typeparam name="T">The type of the elements.</typeparam>
|
---|
| 35 | /// <param name="source">The enumeration in which the items with a maximal value should be found.</param>
|
---|
| 36 | /// <param name="valueSelector">The function that selects the value to compare.</param>
|
---|
| 37 | /// <returns>All elements in the enumeration where the selected value is the maximum.</returns>
|
---|
| 38 | public static IEnumerable<T> MaxItems<T>(this IEnumerable<T> source, Func<T, IComparable> valueSelector) {
|
---|
| 39 | IEnumerator<T> enumerator = source.GetEnumerator();
|
---|
| 40 | if (!enumerator.MoveNext()) return Enumerable.Empty<T>();
|
---|
| 41 | IComparable max = valueSelector(enumerator.Current);
|
---|
| 42 | var result = new List<T>();
|
---|
| 43 | result.Add(enumerator.Current);
|
---|
| 44 |
|
---|
| 45 | while (enumerator.MoveNext()) {
|
---|
| 46 | T item = enumerator.Current;
|
---|
| 47 | IComparable comparison = valueSelector(item);
|
---|
| 48 | if (comparison.CompareTo(max) > 0) {
|
---|
| 49 | result.Clear();
|
---|
| 50 | result.Add(item);
|
---|
| 51 | max = comparison;
|
---|
| 52 | } else if (comparison.CompareTo(max) == 0) {
|
---|
| 53 | result.Add(item);
|
---|
| 54 | }
|
---|
| 55 | }
|
---|
| 56 | return result;
|
---|
| 57 | }
|
---|
| 58 |
|
---|
| 59 | /// <summary>
|
---|
| 60 | /// Selects all elements in the sequence that are minimal with respect to the given value.
|
---|
| 61 | /// </summary>
|
---|
| 62 | /// <remarks>
|
---|
| 63 | /// Runtime complexity of the operation is O(N).
|
---|
| 64 | /// </remarks>
|
---|
| 65 | /// <typeparam name="T">The type of the elements.</typeparam>
|
---|
| 66 | /// <param name="source">The enumeration in which items with a minimal value should be found.</param>
|
---|
| 67 | /// <param name="valueSelector">The function that selects the value.</param>
|
---|
| 68 | /// <returns>All elements in the enumeration where the selected value is the minimum.</returns>
|
---|
| 69 | public static IEnumerable<T> MinItems<T>(this IEnumerable<T> source, Func<T, IComparable> valueSelector) {
|
---|
| 70 | IEnumerator<T> enumerator = source.GetEnumerator();
|
---|
| 71 | if (!enumerator.MoveNext()) return Enumerable.Empty<T>();
|
---|
| 72 | IComparable min = valueSelector(enumerator.Current);
|
---|
| 73 | var result = new List<T>();
|
---|
| 74 | result.Add(enumerator.Current);
|
---|
| 75 |
|
---|
| 76 | while (enumerator.MoveNext()) {
|
---|
| 77 | T item = enumerator.Current;
|
---|
| 78 | IComparable comparison = valueSelector(item);
|
---|
| 79 | if (comparison.CompareTo(min) < 0) {
|
---|
| 80 | result.Clear();
|
---|
| 81 | result.Add(item);
|
---|
| 82 | min = comparison;
|
---|
| 83 | } else if (comparison.CompareTo(min) == 0) {
|
---|
| 84 | result.Add(item);
|
---|
| 85 | }
|
---|
| 86 | }
|
---|
| 87 | return result;
|
---|
| 88 | }
|
---|
[11309] | 89 |
|
---|
| 90 | /// <summary>
|
---|
| 91 | /// Compute the n-ary cartesian product of arbitrarily many sequences: http://blogs.msdn.com/b/ericlippert/archive/2010/06/28/computing-a-cartesian-product-with-linq.aspx
|
---|
| 92 | /// </summary>
|
---|
| 93 | /// <typeparam name="T">The type of the elements inside each sequence</typeparam>
|
---|
| 94 | /// <param name="sequences">The collection of sequences</param>
|
---|
| 95 | /// <returns>An enumerable sequence of all the possible combinations of elements</returns>
|
---|
| 96 | public static IEnumerable<IEnumerable<T>> CartesianProduct<T>(this IEnumerable<IEnumerable<T>> sequences) {
|
---|
| 97 | IEnumerable<IEnumerable<T>> result = new[] { Enumerable.Empty<T>() };
|
---|
[11347] | 98 | return sequences.Where(s => s.Any()).Aggregate(result, (current, s) => (from seq in current from item in s select seq.Concat(new[] { item })));
|
---|
[11309] | 99 | }
|
---|
[13802] | 100 |
|
---|
| 101 | /// <summary>
|
---|
| 102 | /// Compute all k-combinations of elements from the provided collection.
|
---|
| 103 | /// <param name="elements">The collection of elements</param>
|
---|
| 104 | /// <param name="k">The combination group size</param>
|
---|
| 105 | /// <returns>An enumerable sequence of all the possible k-combinations of elements</returns>
|
---|
| 106 | /// </summary>
|
---|
| 107 | public static IEnumerable<IEnumerable<T>> Combinations<T>(this IList<T> elements, int k) {
|
---|
| 108 | if (k > elements.Count)
|
---|
| 109 | throw new ArgumentException();
|
---|
[13899] | 110 |
|
---|
[13802] | 111 | if (k == 1) {
|
---|
[13899] | 112 | foreach (var element in elements)
|
---|
| 113 | yield return new[] { element };
|
---|
| 114 | yield break;
|
---|
| 115 | }
|
---|
[13802] | 116 |
|
---|
[13899] | 117 | int n = elements.Count;
|
---|
| 118 | var range = Enumerable.Range(0, k).ToArray();
|
---|
| 119 | var length = BinomialCoefficient(n, k);
|
---|
[13802] | 120 |
|
---|
[13899] | 121 | for (int i = 0; i < length; ++i) {
|
---|
[14769] | 122 | yield return range.Select(x => elements[x]).ToArray();
|
---|
[13899] | 123 |
|
---|
| 124 | if (i == length - 1) break;
|
---|
| 125 | var m = k - 1;
|
---|
| 126 | var max = n - 1;
|
---|
| 127 |
|
---|
| 128 | while (range[m] == max) { --m; --max; }
|
---|
| 129 | range[m]++;
|
---|
| 130 | for (int j = m + 1; j < k; ++j) {
|
---|
| 131 | range[j] = range[j - 1] + 1;
|
---|
[13802] | 132 | }
|
---|
| 133 | }
|
---|
| 134 | }
|
---|
| 135 |
|
---|
| 136 | /// <summary>
|
---|
| 137 | /// This function gets the total number of unique combinations based upon N and K,
|
---|
| 138 | /// where N is the total number of items and K is the size of the group.
|
---|
| 139 | /// It calculates the total number of unique combinations C(N, K) = N! / ( K! (N - K)! )
|
---|
| 140 | /// using the recursion C(N+1, K+1) = (N+1 / K+1) * C(N, K).
|
---|
| 141 | /// <remarks>http://blog.plover.com/math/choose.html</remarks>
|
---|
[13899] | 142 | /// <remark>https://en.wikipedia.org/wiki/Binomial_coefficient#Multiplicative_formula</remark>
|
---|
[13802] | 143 | /// <param name="n">The number of elements</param>
|
---|
| 144 | /// <param name="k">The size of the group</param>
|
---|
| 145 | /// <returns>The binomial coefficient C(N, K)</returns>
|
---|
| 146 | /// </summary>
|
---|
[13899] | 147 | public static long BinomialCoefficient(long n, long k) {
|
---|
[13802] | 148 | if (k > n) return 0;
|
---|
| 149 | if (k == n) return 1;
|
---|
| 150 | if (k > n - k)
|
---|
| 151 | k = n - k;
|
---|
[14750] | 152 |
|
---|
| 153 | // enable explicit overflow checking for very large coefficients
|
---|
| 154 | checked {
|
---|
| 155 | long r = 1;
|
---|
| 156 | for (long d = 1; d <= k; d++) {
|
---|
| 157 | r *= n--;
|
---|
| 158 | r /= d;
|
---|
| 159 | }
|
---|
| 160 | return r;
|
---|
[13802] | 161 | }
|
---|
| 162 | }
|
---|
[7812] | 163 | }
|
---|
| 164 | }
|
---|