// <copyright file="Sorting.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
//
// Copyright (c) 2009 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
// </copyright>

namespace MathNet.Numerics
{
    using System;
    using System.Collections.Generic;
    using System.Text;

    /// <summary>
    /// Sorting algorithms for single, tuple and triple lists.
    /// </summary>
    public static class Sorting
    {
        /// <summary>
        /// Sort a list of keys, inplace using the quick sort algorithm.
        /// </summary>
        /// <typeparam name="T">The type of elements stored in the list.</typeparam>
        /// <param name="keys">List to sort.</param>
        public static void Sort<T>(IList<T> keys)
        {
            Sort(keys, Comparer<T>.Default);
        }

        /// <summary>
        /// Sort a list of keys and items with respect to the keys, inplace using the quick sort algorithm.
        /// </summary>
        /// <typeparam name="TKey">The type of elements stored in the key list.</typeparam>
        /// <typeparam name="TItem">The type of elements stored in the item list.</typeparam>
        /// <param name="keys">List to sort.</param>
        /// <param name="items">List to permutate the same way as the key list.</param>
        public static void Sort<TKey, TItem>(IList<TKey> keys, IList<TItem> items)
        {
            Sort(keys, items, Comparer<TKey>.Default);
        }

        /// <summary>
        /// Sort a list of keys, items1 and items2 with respect to the keys, inplace using the quick sort algorithm.
        /// </summary>
        /// <typeparam name="TKey">The type of elements stored in the key list.</typeparam>
        /// <typeparam name="TItem1">The type of elements stored in the first item list.</typeparam>
        /// <typeparam name="TItem2">The type of elements stored in the second item list.</typeparam>
        /// <param name="keys">List to sort.</param>
        /// <param name="items1">First list to permutate the same way as the key list.</param>
        /// <param name="items2">Second list to permutate the same way as the key list.</param>
        public static void Sort<TKey, TItem1, TItem2>(IList<TKey> keys, IList<TItem1> items1, IList<TItem2> items2)
        {
            Sort(keys, items1, items2, Comparer<TKey>.Default);
        }

        /// <summary>
        /// Sort a range of a list of keys, inplace using the quick sort algorithm.
        /// </summary>
        /// <typeparam name="T">The type of elements in the key list.</typeparam>
        /// <param name="keys">List to sort.</param>
        /// <param name="index">The zero-based starting index of the range to sort.</param>
        /// <param name="count">The length of the range to sort.</param>
        public static void Sort<T>(IList<T> keys, int index, int count)
        {
            Sort(keys, index, count, Comparer<T>.Default);
        }

        /// <summary>
        /// Sort a list of keys, inplace using the quick sort algorithm using the quick sort algorithm.
        /// </summary>
        /// <typeparam name="T">The type of elements in the key list.</typeparam>
        /// <param name="keys">List to sort.</param>
        /// <param name="comparer">Comparison, defining the sort order.</param>
        public static void Sort<T>(IList<T> keys, IComparer<T> comparer)
        {
            if(null == keys)
            {
                throw new ArgumentNullException("keys");
            }

            if(null == comparer)
            {
                throw new ArgumentNullException("comparer");
            }

            // basic cases
            if(keys.Count <= 1)
            {
                return;
            }

            if(keys.Count == 2)
            {
                if(comparer.Compare(keys[0], keys[1]) > 0)
                {
                    Swap(keys, 0, 1);
                }

                return;
            }

            // generic list case
            List<T> list = keys as List<T>;
            if(null != list)
            {
                list.Sort(comparer);
                return;
            }

            // array case
            T[] array = keys as T[];
            if(null != array)
            {
                Array.Sort(array, comparer);
                return;
            }

            // local sort implementation
            QuickSort(keys, comparer, 0, keys.Count - 1);
        }

        /// <summary>
        /// Sort a list of keys and items with respect to the keys, inplace using the quick sort algorithm.
        /// </summary>
        /// <typeparam name="TKey">The type of elements in the key list.</typeparam>
        /// <typeparam name="TItem">The type of elements in the item list.</typeparam>
        /// <param name="keys">List to sort.</param>
        /// <param name="items">List to permutate the same way as the key list.</param>
        /// <param name="comparer">Comparison, defining the sort order.</param>
        public static void Sort<TKey, TItem>(IList<TKey> keys, IList<TItem> items, IComparer<TKey> comparer)
        {
            if(null == keys)
            {
                throw new ArgumentNullException("keys");
            }

            if(null == items)
            {
                throw new ArgumentNullException("items");
            }

            if(null == comparer)
            {
                throw new ArgumentNullException("comparer");
            }

            // array case
            TKey[] keysArray = keys as TKey[];
            TItem[] itemsArray = items as TItem[];
            if((null != keysArray) && (null != itemsArray))
            {
                Array.Sort(keysArray, itemsArray, comparer);
                return;
            }

            // local sort implementation
            QuickSort(keys, items, comparer, 0, keys.Count - 1);
        }

        /// <summary>
        /// Sort a list of keys, items1 and items2 with respect to the keys, inplace using the quick sort algorithm.
        /// </summary>
        /// <typeparam name="TKey">The type of elements in the key list.</typeparam>
        /// <typeparam name="TItem1">The type of elements in the first item list.</typeparam>
        /// <typeparam name="TItem2">The type of elements in the second item list.</typeparam>
        /// <param name="keys">List to sort.</param>
        /// <param name="items1">First list to permutate the same way as the key list.</param>
        /// <param name="items2">Second list to permutate the same way as the key list.</param>
        /// <param name="comparer">Comparison, defining the sort order.</param>
        public static void Sort<TKey, TItem1, TItem2>(
            IList<TKey> keys, IList<TItem1> items1, IList<TItem2> items2, IComparer<TKey> comparer)
        {
            if(null == keys)
            {
                throw new ArgumentNullException("keys");
            }

            if(null == items1)
            {
                throw new ArgumentNullException("items1");
            }

            if(null == items2)
            {
                throw new ArgumentNullException("items2");
            }

            if(null == comparer)
            {
                throw new ArgumentNullException("comparer");
            }

            // local sort implementation
            QuickSort(keys, items1, items2, comparer, 0, keys.Count - 1);
        }

        /// <summary>
        /// Sort a range of a list of keys, inplace using the quick sort algorithm.
        /// </summary>
        /// <typeparam name="T">The type of element in the list.</typeparam>
        /// <param name="keys">List to sort.</param>
        /// <param name="index">The zero-based starting index of the range to sort.</param>
        /// <param name="count">The length of the range to sort.</param>
        /// <param name="comparer">Comparison, defining the sort order.</param>
        public static void Sort<T>(IList<T> keys, int index, int count, IComparer<T> comparer)
        {
            if(null == keys)
            {
                throw new ArgumentNullException("keys");
            }

            if(null == comparer)
            {
                throw new ArgumentNullException("comparer");
            }

            if(index < 0 || index >= keys.Count)
            {
                throw new ArgumentOutOfRangeException("index");
            }

            if(count < 0 || index + count > keys.Count)
            {
                throw new ArgumentOutOfRangeException("count");
            }

            // basic cases
            if(count <= 1)
            {
                return;
            }

            if(count == 2)
            {
                if(comparer.Compare(keys[index], keys[index + 1]) > 0)
                {
                    Swap(keys, index, index + 1);
                }

                return;
            }

            // generic list case
            List<T> list = keys as List<T>;
            if(null != list)
            {
                list.Sort(index, count, comparer);
                return;
            }

            // array case
            T[] array = keys as T[];
            if(null != array)
            {
                Array.Sort(array, index, count, comparer);
                return;
            }

            // local sort implementation
            QuickSort(keys, comparer, index, count - 1);
        }

        /// <summary>
        /// Recursive implementation for an inplace quick sort on a list.
        /// </summary>
        /// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
        /// <param name="keys">The list which is sorted using quick sort.</param>
        /// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
        /// <param name="left">The left boundary of the quick sort.</param>
        /// <param name="right">The right boundary of the quick sort.</param>
        private static void QuickSort<T>(IList<T> keys, IComparer<T> comparer, int left, int right)
        {
            do
            {
                // Pivoting
                int a = left;
                int b = right;
                int p = a + ((b - a) >> 1); // midpoint

                if(comparer.Compare(keys[a], keys[p]) > 0)
                {
                    Swap(keys, a, p);
                }

                if(comparer.Compare(keys[a], keys[b]) > 0)
                {
                    Swap(keys, a, b);
                }

                if(comparer.Compare(keys[p], keys[b]) > 0)
                {
                    Swap(keys, p, b);
                }

                T pivot = keys[p];

                // Hoare Partitioning
                do
                {
                    while(comparer.Compare(keys[a], pivot) < 0)
                    {
                        a++;
                    }

                    while(comparer.Compare(pivot, keys[b]) < 0)
                    {
                        b--;
                    }

                    if(a > b)
                    {
                        break;
                    }

                    if(a < b)
                    {
                        Swap(keys, 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, comparer, left, b);
                    }

                    left = a;
                }
                else
                {
                    if(a < right)
                    {
                        QuickSort(keys, comparer, a, right);
                    }

                    right = b;
                }
            }
            while(left < right);
        }

        /// <summary>
        /// Recursive implementation for an inplace quick sort on a list while reordering one other list accordingly.
        /// </summary>
        /// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
        /// <typeparam name="TItems">The type of the list which is automatically reordered accordingly.</typeparam>
        /// <param name="keys">The list which is sorted using quick sort.</param>
        /// <param name="items">The list which is automatically reordered accordingly.</param>
        /// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
        /// <param name="left">The left boundary of the quick sort.</param>
        /// <param name="right">The right boundary of the quick sort.</param>
        private static void QuickSort<T, TItems>(IList<T> keys, IList<TItems> items, IComparer<T> comparer, int left, int right)
        {
            do
            {
                // Pivoting
                int a = left;
                int b = right;
                int p = a + ((b - a) >> 1); // midpoint

                if(comparer.Compare(keys[a], keys[p]) > 0)
                {
                    Swap(keys, a, p);
                    Swap(items, a, p);
                }

                if(comparer.Compare(keys[a], keys[b]) > 0)
                {
                    Swap(keys, a, b);
                    Swap(items, a, b);
                }

                if(comparer.Compare(keys[p], keys[b]) > 0)
                {
                    Swap(keys, p, b);
                    Swap(items, p, b);
                }

                T pivot = keys[p];

                // Hoare Partitioning
                do
                {
                    while(comparer.Compare(keys[a], pivot) < 0)
                    {
                        a++;
                    }

                    while(comparer.Compare(pivot, keys[b]) < 0)
                    {
                        b--;
                    }

                    if(a > b)
                    {
                        break;
                    }

                    if(a < b)
                    {
                        Swap(keys, a, b);
                        Swap(items, 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, items, comparer, left, b);
                    }

                    left = a;
                }
                else
                {
                    if(a < right)
                    {
                        QuickSort(keys, items, comparer, a, right);
                    }

                    right = b;
                }
            }
            while(left < right);
        }

        /// <summary>
        /// Recursive implementation for an inplace quick sort on one list while reordering two other lists accordingly.
        /// </summary>
        /// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
        /// <typeparam name="TItems1">The type of the first list which is automatically reordered accordingly.</typeparam>
        /// <typeparam name="TItems2">The type of the second list which is automatically reordered accordingly.</typeparam>
        /// <param name="keys">The list which is sorted using quick sort.</param>
        /// <param name="items1">The first list which is automatically reordered accordingly.</param>
        /// <param name="items2">The second list which is automatically reordered accordingly.</param>
        /// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
        /// <param name="left">The left boundary of the quick sort.</param>
        /// <param name="right">The right boundary of the quick sort.</param>
        private static void QuickSort<T, TItems1, TItems2>(
            IList<T> keys, IList<TItems1> items1, IList<TItems2> items2, IComparer<T> comparer, int left, int right)
        {
            do
            {
                // Pivoting
                int a = left;
                int b = right;
                int p = a + ((b - a) >> 1); // midpoint

                if(comparer.Compare(keys[a], keys[p]) > 0)
                {
                    Swap(keys, a, p);
                    Swap(items1, a, p);
                    Swap(items2, a, p);
                }

                if(comparer.Compare(keys[a], keys[b]) > 0)
                {
                    Swap(keys, a, b);
                    Swap(items1, a, b);
                    Swap(items2, a, b);
                }

                if(comparer.Compare(keys[p], keys[b]) > 0)
                {
                    Swap(keys, p, b);
                    Swap(items1, p, b);
                    Swap(items2, p, b);
                }

                T pivot = keys[p];

                // Hoare Partitioning
                do
                {
                    while(comparer.Compare(keys[a], pivot) < 0)
                    {
                        a++;
                    }

                    while(comparer.Compare(pivot, keys[b]) < 0)
                    {
                        b--;
                    }

                    if(a > b)
                    {
                        break;
                    }

                    if(a < b)
                    {
                        Swap(keys, a, b);
                        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;
                }
            }
            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)
            {
                T local = keys[a];
                keys[a] = keys[b];
                keys[b] = local;
            }
        }
    }
}