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631 lines
23 KiB
631 lines
23 KiB
// <copyright file="Sorting.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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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2013 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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using System.Collections.Generic;
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namespace MathNet.Numerics
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{
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/// <summary>
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/// Sorting algorithms for single, tuple and triple lists.
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/// </summary>
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public static class Sorting
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{
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/// <summary>
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/// Sort a range of a list of keys, in place using the quick sort algorithm.
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/// </summary>
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/// <typeparam name="T">The type of elements in the key list.</typeparam>
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/// <param name="keys">List to sort.</param>
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/// <param name="index">The zero-based starting index of the range to sort.</param>
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/// <param name="count">The length of the range to sort.</param>
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public static void Sort<T>(IList<T> keys, int index, int count)
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{
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Sort(keys, index, count, Comparer<T>.Default);
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}
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/// <summary>
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/// Sort a list of keys, in place using the quick sort algorithm using the quick sort algorithm.
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/// </summary>
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/// <typeparam name="T">The type of elements in the key list.</typeparam>
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/// <param name="keys">List to sort.</param>
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/// <param name="comparer">Comparison, defining the sort order.</param>
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public static void Sort<T>(IList<T> keys, IComparer<T> comparer = null)
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{
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if (null == comparer)
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{
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comparer = Comparer<T>.Default;
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}
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// basic cases
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if (keys.Count <= 1)
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{
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return;
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}
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if (keys.Count == 2)
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{
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if (comparer.Compare(keys[0], keys[1]) > 0)
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{
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Swap(keys, 0, 1);
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}
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return;
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}
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// generic list case
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var keysList = keys as List<T>;
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if (null != keysList)
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{
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keysList.Sort(comparer);
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return;
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}
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// array case
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var keysArray = keys as T[];
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if (null != keysArray)
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{
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Array.Sort(keysArray, comparer);
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return;
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}
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// local sort implementation
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QuickSort(keys, comparer, 0, keys.Count - 1);
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}
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/// <summary>
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/// Sort a list of keys and items with respect to the keys, in place using the quick sort algorithm.
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/// </summary>
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/// <typeparam name="TKey">The type of elements in the key list.</typeparam>
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/// <typeparam name="TItem">The type of elements in the item list.</typeparam>
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/// <param name="keys">List to sort.</param>
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/// <param name="items">List to permute the same way as the key list.</param>
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/// <param name="comparer">Comparison, defining the sort order.</param>
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public static void Sort<TKey, TItem>(IList<TKey> keys, IList<TItem> items, IComparer<TKey> comparer = null)
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{
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if (null == comparer)
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{
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comparer = Comparer<TKey>.Default;
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}
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#if !PORTABLE
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// array case
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var keysArray = keys as TKey[];
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var itemsArray = items as TItem[];
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if ((null != keysArray) && (null != itemsArray))
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{
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Array.Sort(keysArray, itemsArray, comparer);
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return;
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}
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#endif
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// local sort implementation
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QuickSort(keys, items, comparer, 0, keys.Count - 1);
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}
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/// <summary>
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/// Sort a list of keys, items1 and items2 with respect to the keys, in place using the quick sort algorithm.
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/// </summary>
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/// <typeparam name="TKey">The type of elements in the key list.</typeparam>
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/// <typeparam name="TItem1">The type of elements in the first item list.</typeparam>
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/// <typeparam name="TItem2">The type of elements in the second item list.</typeparam>
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/// <param name="keys">List to sort.</param>
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/// <param name="items1">First list to permute the same way as the key list.</param>
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/// <param name="items2">Second list to permute the same way as the key list.</param>
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/// <param name="comparer">Comparison, defining the sort order.</param>
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public static void Sort<TKey, TItem1, TItem2>(IList<TKey> keys, IList<TItem1> items1, IList<TItem2> items2, IComparer<TKey> comparer = null)
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{
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if (null == comparer)
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{
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comparer = Comparer<TKey>.Default;
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}
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// local sort implementation
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QuickSort(keys, items1, items2, comparer, 0, keys.Count - 1);
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}
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/// <summary>
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/// Sort a list of keys and items with respect to the keys, in place using the quick sort algorithm.
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/// </summary>
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/// <typeparam name="T1">The type of elements in the primary list.</typeparam>
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/// <typeparam name="T2">The type of elements in the secondary list.</typeparam>
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/// <param name="primary">List to sort.</param>
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/// <param name="secondary">List to to sort on duplicate primaty items, and permute the same way as the key list.</param>
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/// <param name="primaryComparer">Comparison, defining the primary sort order.</param>
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/// <param name="secondaryComparer">Comparison, defining the secondary sort order.</param>
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public static void SortAll<T1, T2>(IList<T1> primary, IList<T2> secondary, IComparer<T1> primaryComparer = null, IComparer<T2> secondaryComparer = null)
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{
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if (null == primaryComparer)
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{
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primaryComparer = Comparer<T1>.Default;
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}
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if (null == secondaryComparer)
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{
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secondaryComparer = Comparer<T2>.Default;
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}
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// local sort implementation
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QuickSortAll(primary, secondary, primaryComparer, secondaryComparer, 0, primary.Count - 1);
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}
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/// <summary>
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/// Sort a range of a list of keys, in place using the quick sort algorithm.
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/// </summary>
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/// <typeparam name="T">The type of element in the list.</typeparam>
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/// <param name="keys">List to sort.</param>
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/// <param name="index">The zero-based starting index of the range to sort.</param>
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/// <param name="count">The length of the range to sort.</param>
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/// <param name="comparer">Comparison, defining the sort order.</param>
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public static void Sort<T>(IList<T> keys, int index, int count, IComparer<T> comparer = null)
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{
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if (index < 0 || index >= keys.Count)
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{
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throw new ArgumentOutOfRangeException("index");
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}
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if (count < 0 || index + count > keys.Count)
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{
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throw new ArgumentOutOfRangeException("count");
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}
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if (null == comparer)
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{
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comparer = Comparer<T>.Default;
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}
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// basic cases
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if (count <= 1)
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{
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return;
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}
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if (count == 2)
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{
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if (comparer.Compare(keys[index], keys[index + 1]) > 0)
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{
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Swap(keys, index, index + 1);
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}
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return;
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}
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// generic list case
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var keysList = keys as List<T>;
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if (null != keysList)
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{
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keysList.Sort(index, count, comparer);
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return;
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}
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// array case
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var keysArray = keys as T[];
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if (null != keysArray)
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{
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Array.Sort(keysArray, index, count, comparer);
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return;
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}
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// local sort implementation
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QuickSort(keys, comparer, index, count - 1);
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}
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/// <summary>
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/// Recursive implementation for an in place quick sort on a list.
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/// </summary>
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/// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
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/// <param name="keys">The list which is sorted using quick sort.</param>
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/// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
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/// <param name="left">The left boundary of the quick sort.</param>
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/// <param name="right">The right boundary of the quick sort.</param>
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static void QuickSort<T>(IList<T> keys, IComparer<T> comparer, int left, int right)
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{
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do
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{
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// Pivoting
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int a = left;
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int b = right;
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int p = a + ((b - a) >> 1); // midpoint
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if (comparer.Compare(keys[a], keys[p]) > 0)
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{
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Swap(keys, a, p);
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}
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if (comparer.Compare(keys[a], keys[b]) > 0)
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{
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Swap(keys, a, b);
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}
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if (comparer.Compare(keys[p], keys[b]) > 0)
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{
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Swap(keys, p, b);
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}
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T pivot = keys[p];
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// Hoare Partitioning
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do
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{
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while (comparer.Compare(keys[a], pivot) < 0)
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{
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a++;
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}
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while (comparer.Compare(pivot, keys[b]) < 0)
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{
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b--;
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}
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if (a > b)
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{
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break;
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}
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if (a < b)
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{
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Swap(keys, a, b);
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}
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a++;
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b--;
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} while (a <= b);
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// In order to limit the recusion depth to log(n), we sort the
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// shorter partition recusively and the longer partition iteratively.
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if ((b - left) <= (right - a))
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{
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if (left < b)
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{
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QuickSort(keys, comparer, left, b);
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}
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left = a;
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}
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else
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{
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if (a < right)
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{
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QuickSort(keys, comparer, a, right);
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}
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right = b;
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}
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} while (left < right);
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}
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/// <summary>
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/// Recursive implementation for an in place quick sort on a list while reordering one other list accordingly.
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/// </summary>
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/// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
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/// <typeparam name="TItems">The type of the list which is automatically reordered accordingly.</typeparam>
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/// <param name="keys">The list which is sorted using quick sort.</param>
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/// <param name="items">The list which is automatically reordered accordingly.</param>
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/// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
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/// <param name="left">The left boundary of the quick sort.</param>
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/// <param name="right">The right boundary of the quick sort.</param>
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static void QuickSort<T, TItems>(IList<T> keys, IList<TItems> items, IComparer<T> comparer, int left, int right)
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{
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do
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{
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// Pivoting
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int a = left;
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int b = right;
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int p = a + ((b - a) >> 1); // midpoint
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if (comparer.Compare(keys[a], keys[p]) > 0)
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{
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Swap(keys, a, p);
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Swap(items, a, p);
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}
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if (comparer.Compare(keys[a], keys[b]) > 0)
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{
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Swap(keys, a, b);
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Swap(items, a, b);
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}
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if (comparer.Compare(keys[p], keys[b]) > 0)
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{
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Swap(keys, p, b);
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Swap(items, p, b);
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}
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T pivot = keys[p];
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// Hoare Partitioning
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do
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{
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while (comparer.Compare(keys[a], pivot) < 0)
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{
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a++;
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}
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while (comparer.Compare(pivot, keys[b]) < 0)
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{
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b--;
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}
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if (a > b)
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{
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break;
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}
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if (a < b)
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{
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Swap(keys, a, b);
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Swap(items, a, b);
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}
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a++;
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b--;
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} while (a <= b);
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// In order to limit the recusion depth to log(n), we sort the
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// shorter partition recusively and the longer partition iteratively.
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if ((b - left) <= (right - a))
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{
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if (left < b)
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{
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QuickSort(keys, items, comparer, left, b);
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}
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left = a;
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}
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else
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{
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if (a < right)
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{
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QuickSort(keys, items, comparer, a, right);
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}
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right = b;
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}
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} while (left < right);
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}
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/// <summary>
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/// Recursive implementation for an in place quick sort on one list while reordering two other lists accordingly.
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/// </summary>
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/// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
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/// <typeparam name="TItems1">The type of the first list which is automatically reordered accordingly.</typeparam>
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/// <typeparam name="TItems2">The type of the second list which is automatically reordered accordingly.</typeparam>
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/// <param name="keys">The list which is sorted using quick sort.</param>
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/// <param name="items1">The first list which is automatically reordered accordingly.</param>
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/// <param name="items2">The second list which is automatically reordered accordingly.</param>
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/// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
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/// <param name="left">The left boundary of the quick sort.</param>
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/// <param name="right">The right boundary of the quick sort.</param>
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static void QuickSort<T, TItems1, TItems2>(
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IList<T> keys, IList<TItems1> items1, IList<TItems2> items2,
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IComparer<T> comparer,
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int left, int right)
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{
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do
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{
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// Pivoting
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int a = left;
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int b = right;
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int p = a + ((b - a) >> 1); // midpoint
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|
|
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if (comparer.Compare(keys[a], keys[p]) > 0)
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{
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Swap(keys, a, p);
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Swap(items1, a, p);
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Swap(items2, a, p);
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}
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|
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if (comparer.Compare(keys[a], keys[b]) > 0)
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{
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Swap(keys, a, b);
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Swap(items1, a, b);
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Swap(items2, a, b);
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}
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|
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if (comparer.Compare(keys[p], keys[b]) > 0)
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{
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Swap(keys, p, b);
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Swap(items1, p, b);
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Swap(items2, p, b);
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}
|
|
|
|
T pivot = keys[p];
|
|
|
|
// Hoare Partitioning
|
|
do
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|
{
|
|
while (comparer.Compare(keys[a], pivot) < 0)
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|
{
|
|
a++;
|
|
}
|
|
|
|
while (comparer.Compare(pivot, keys[b]) < 0)
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|
{
|
|
b--;
|
|
}
|
|
|
|
if (a > b)
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|
{
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break;
|
|
}
|
|
|
|
if (a < b)
|
|
{
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|
Swap(keys, a, b);
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Swap(items1, a, b);
|
|
Swap(items2, a, b);
|
|
}
|
|
|
|
a++;
|
|
b--;
|
|
} while (a <= b);
|
|
|
|
// In order to limit the recusion depth to log(n), we sort the
|
|
// shorter partition recusively and the longer partition iteratively.
|
|
if ((b - left) <= (right - a))
|
|
{
|
|
if (left < b)
|
|
{
|
|
QuickSort(keys, items1, items2, comparer, left, b);
|
|
}
|
|
|
|
left = a;
|
|
}
|
|
else
|
|
{
|
|
if (a < right)
|
|
{
|
|
QuickSort(keys, items1, items2, comparer, a, right);
|
|
}
|
|
|
|
right = b;
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}
|
|
} while (left < right);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Recursive implementation for an in place quick sort on the primary and then by the secondary list while reordering one secondary list accordingly.
|
|
/// </summary>
|
|
/// <typeparam name="T1">The type of the primary list.</typeparam>
|
|
/// <typeparam name="T2">The type of the secondary list.</typeparam>
|
|
/// <param name="primary">The list which is sorted using quick sort.</param>
|
|
/// <param name="secondary">The list which is sorted secondarily (on primary duplicates) and automatically reordered accordingly.</param>
|
|
/// <param name="primaryComparer">The method with which to compare two elements of the primary list.</param>
|
|
/// <param name="secondaryComparer">The method with which to compare two elements of the secondary list.</param>
|
|
/// <param name="left">The left boundary of the quick sort.</param>
|
|
/// <param name="right">The right boundary of the quick sort.</param>
|
|
static void QuickSortAll<T1, T2>(
|
|
IList<T1> primary, IList<T2> secondary,
|
|
IComparer<T1> primaryComparer, IComparer<T2> secondaryComparer,
|
|
int left, int right)
|
|
{
|
|
do
|
|
{
|
|
// Pivoting
|
|
int a = left;
|
|
int b = right;
|
|
int p = a + ((b - a) >> 1); // midpoint
|
|
|
|
int ap = primaryComparer.Compare(primary[a], primary[p]);
|
|
if (ap > 0 || ap == 0 && secondaryComparer.Compare(secondary[a], secondary[p]) > 0)
|
|
{
|
|
Swap(primary, a, p);
|
|
Swap(secondary, a, p);
|
|
}
|
|
|
|
int ab = primaryComparer.Compare(primary[a], primary[b]);
|
|
if (ab > 0 || ab == 0 && secondaryComparer.Compare(secondary[a], secondary[b]) > 0)
|
|
{
|
|
Swap(primary, a, b);
|
|
Swap(secondary, a, b);
|
|
}
|
|
|
|
int pb = primaryComparer.Compare(primary[p], primary[b]);
|
|
if (pb > 0 || pb == 0 && secondaryComparer.Compare(secondary[p], secondary[b]) > 0)
|
|
{
|
|
Swap(primary, p, b);
|
|
Swap(secondary, p, b);
|
|
}
|
|
|
|
T1 pivot1 = primary[p];
|
|
T2 pivot2 = secondary[p];
|
|
|
|
// Hoare Partitioning
|
|
do
|
|
{
|
|
int ax;
|
|
while ((ax = primaryComparer.Compare(primary[a], pivot1)) < 0 || ax == 0 && secondaryComparer.Compare(secondary[a], pivot2) < 0)
|
|
{
|
|
a++;
|
|
}
|
|
|
|
int xb;
|
|
while ((xb = primaryComparer.Compare(pivot1, primary[b])) < 0 || xb == 0 && secondaryComparer.Compare(pivot2, secondary[b]) < 0)
|
|
{
|
|
b--;
|
|
}
|
|
|
|
if (a > b)
|
|
{
|
|
break;
|
|
}
|
|
|
|
if (a < b)
|
|
{
|
|
Swap(primary, a, b);
|
|
Swap(secondary, a, b);
|
|
}
|
|
|
|
a++;
|
|
b--;
|
|
} while (a <= b);
|
|
|
|
// In order to limit the recusion depth to log(n), we sort the
|
|
// shorter partition recusively and the longer partition iteratively.
|
|
if ((b - left) <= (right - a))
|
|
{
|
|
if (left < b)
|
|
{
|
|
QuickSortAll(primary, secondary, primaryComparer, secondaryComparer, left, b);
|
|
}
|
|
|
|
left = a;
|
|
}
|
|
else
|
|
{
|
|
if (a < right)
|
|
{
|
|
QuickSortAll(primary, secondary, primaryComparer, secondaryComparer, a, right);
|
|
}
|
|
|
|
right = b;
|
|
}
|
|
} while (left < right);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an in place swap of two elements in a list.
|
|
/// </summary>
|
|
/// <typeparam name="T">The type of elements stored in the list.</typeparam>
|
|
/// <param name="keys">The list in which the elements are stored.</param>
|
|
/// <param name="a">The index of the first element of the swap.</param>
|
|
/// <param name="b">The index of the second element of the swap.</param>
|
|
internal static void Swap<T>(IList<T> keys, int a, int b)
|
|
{
|
|
if (a == b)
|
|
{
|
|
return;
|
|
}
|
|
|
|
T local = keys[a];
|
|
keys[a] = keys[b];
|
|
keys[b] = local;
|
|
}
|
|
}
|
|
}
|
|
|