using System;
using System.Collections.Generic;
using System.Text;

namespace Framework.Collections
{
    /// <summary>
    /// The IndexMinPriorityQueue class represents an indexed priority queue of generic keys.
    /// </summary>
    /// <seealso href="http://algs4.cs.princeton.edu/24pq/IndexMinPQ.java.html">IndexMinPQ class from Princeton University's Java Algorithms</seealso>
    /// <typeparam name="T">Type must implement IComparable interface</typeparam>
    public class IndexMinPriorityQueue<T> where T : IComparable<T>
    {
        private readonly T[] _keys;
        private readonly int _maxSize;
        private readonly int[] _pq;
        private readonly int[] _qp;
        /// <summary>
        /// Constructs an empty indexed priority queue with indices between 0 and the specified maxSize - 1
        /// </summary>
        /// <param name="maxSize">The maximum size of the indexed priority queue</param>
        public IndexMinPriorityQueue(int maxSize)
        {
            _maxSize = maxSize;
            Size = 0;
            _keys = new T[_maxSize + 1];
            _pq = new int[_maxSize + 1];
            _qp = new int[_maxSize + 1];
            for (int i = 0; i < _maxSize; i++)
            {
                _qp[i] = -1;
            }
        }
        /// <summary>
        /// The number of keys on this indexed priority queue
        /// </summary>
        public int Size { get; private set; }
        /// <summary>
        /// Is the indexed priority queue empty?
        /// </summary>
        /// <returns>True if the indexed priority queue is empty, false otherwise</returns>
        public bool IsEmpty()
        {
            return Size == 0;
        }
        /// <summary>
        /// Is the specified parameter i an index on the priority queue?
        /// </summary>
        /// <param name="i">An index to check for on the priority queue</param>
        /// <returns>True if the specified parameter i is an index on the priority queue, false otherwise</returns>
        public bool Contains(int i)
        {
            return _qp[i] != -1;
        }
        /// <summary>
        /// Associates the specified key with the specified index
        /// </summary>
        /// <param name="index">The index to associate the key with</param>
        /// <param name="key">The key to associate with the index</param>
        public void Insert(int index, T key)
        {
            Size++;
            _qp[index] = Size;
            _pq[Size] = index;
            _keys[index] = key;
            Swim(Size);
        }
        /// <summary>
        /// Returns an index associated with a minimum key
        /// </summary>
        /// <returns>An index associated with a minimum key</returns>
        public int MinIndex()
        {
            return _pq[1];
        }
        /// <summary>
        /// Returns a minimum key
        /// </summary>
        /// <returns>A minimum key</returns>
        public T MinKey()
        {
            return _keys[_pq[1]];
        }
        /// <summary>
        /// Removes a minimum key and returns its associated index
        /// </summary>
        /// <returns>An index associated with a minimum key that was removed</returns>
        public int DeleteMin()
        {
            int min = _pq[1];
            Exchange(1, Size--);
            Sink(1);
            _qp[min] = -1;
            _keys[_pq[Size + 1]] = default(T);
            _pq[Size + 1] = -1;
            return min;
        }
        /// <summary>
        /// Returns the key associated with the specified index
        /// </summary>
        /// <param name="index">The index of the key to return</param>
        /// <returns>The key associated with the specified index</returns>
        public T KeyAt(int index)
        {
            return _keys[index];
        }
        /// <summary>
        /// Change the key associated with the specified index to the specified value
        /// </summary>
        /// <param name="index">The index of the key to change</param>
        /// <param name="key">Change the key associated with the specified index to this key</param>
        public void ChangeKey(int index, T key)
        {
            _keys[index] = key;
            Swim(_qp[index]);
            Sink(_qp[index]);
        }
        /// <summary>
        /// Decrease the key associated with the specified index to the specified value
        /// </summary>
        /// <param name="index">The index of the key to decrease</param>
        /// <param name="key">Decrease the key associated with the specified index to this key</param>
        public void DecreaseKey(int index, T key)
        {
            _keys[index] = key;
            Swim(_qp[index]);
        }
        /// <summary>
        /// Increase the key associated with the specified index to the specified value
        /// </summary>
        /// <param name="index">The index of the key to increase</param>
        /// <param name="key">Increase the key associated with the specified index to this key</param>
        public void IncreaseKey(int index, T key)
        {
            _keys[index] = key;
            Sink(_qp[index]);
        }
        /// <summary>
        /// Remove the key associated with the specified index
        /// </summary>
        /// <param name="index">The index of the key to remove</param>
        public void Delete(int index)
        {
            int i = _qp[index];
            Exchange(i, Size--);
            Swim(i);
            Sink(i);
            _keys[index] = default(T);
            _qp[index] = -1;
        }
        private bool Greater(int i, int j)
        {
            return _keys[_pq[i]].CompareTo(_keys[_pq[j]]) > 0;
        }
        private void Exchange(int i, int j)
        {
            int swap = _pq[i];
            _pq[i] = _pq[j];
            _pq[j] = swap;
            _qp[_pq[i]] = i;
            _qp[_pq[j]] = j;
        }
        private void Swim(int k)
        {
            while (k > 1 && Greater(k / 2, k))
            {
                Exchange(k, k / 2);
                k = k / 2;
            }
        }
        private void Sink(int k)
        {
            while (2 * k <= Size)
            {
                int j = 2 * k;
                if (j < Size && Greater(j, j + 1))
                {
                    j++;
                }
                if (!Greater(k, j))
                {
                    break;
                }
                Exchange(k, j);
                k = j;
            }
        }
    }
}