/******************************************************************************
 *  Compilation: javac IndexMultiwayMinPQ.java
 *  Execution:
 *
 *  An inde  multiway heap.
 *
 ******************************************************************************/

package edu.princeton.cs.algs4;

import java.util.Comparator;
import java.util.Iterator;
import java.util.NoSuchElementException;

/**
 *  The IndexMultiwayMinPQ class represents an indexed priority queue of generic keys.
 *  It supports the usual insert and delete-the-minimum operations,
 *  along with delete and change-the-key methods. 
 *  In order to let the client refer to keys on the priority queue,
 *  an integer between 0 and N-1 is associated with each key ; the client
 *  uses this integer to specify which key to delete or change.
 *  It also supports methods for peeking at the minimum key,
 *  testing if the priority queue is empty, and iterating through
 *  the keys.
 *  
 *  This implementation uses a multiway heap along with an array to associate
 *  keys with integers in the given range.
 *  For simplified notations, logarithm in base d will be referred as log-d
 *  The delete-the-minimum, delete, change-key and increase-key operations
 *  take time proportional to d*log-d(n)
 *  The insert and decrease-key take time proportional to log-d(n)
 *  The is-empty, min-index, min-key, size, contains and key-of operations take constant time.
 *  Construction takes time proportional to the specified capacity.
 *  
 *  The arrays used in this structure have the first d indices empty,
 *  it apparently helps with caching effects.
 *
 *  @author Tristan Claverie
 */
public class IndexMultiwayMinPQ<Key> implements Iterable<Integer> {
	private final int d;				//Dimension of the heap
	private int n;						//Number of keys currently in the queue
	private int nmax;					//Maximum number of items in the queue
	private int[] pq;					//Multiway heap
	private int[] qp;					//Inverse of pq : qp[pq[i]] = pq[qp[i]] = i
	private Key[] keys;					//keys[i] = priority of i
	private final Comparator<Key> comp; //Comparator over the keys
	
	
    /**
     * Initializes an empty indexed priority queue with indices between {@code 0} to {@code N-1}
     * Worst case is O(n)
     * @param N number of keys in the priority queue, index from {@code 0} to {@code N-1}
     * @param D dimension of the heap
     * @throws java.lang.IllegalArgumentException if {@code N < 0}
     * @throws java.lang.IllegalArgumentException if {@code D < 2}
     */
	public IndexMultiwayMinPQ(int N, int D) {
		if (N < 0) throw new IllegalArgumentException("Maximum number of elements cannot be negative");
		if (D < 2) throw new IllegalArgumentException("Dimension should be 2 or over");
		this.d = D;
		nmax = N;
		pq = new int[nmax+D];
		qp = new int[nmax+D];
		keys = (Key[]) new Comparable[nmax+D];
		for (int i = 0; i < nmax+D; qp[i++] = -1);
		comp = new MyComparator();
	}
	
    /**
     * Initializes an empty indexed priority queue with indices between {@code 0} to {@code N-1}
     * Worst case is O(n)
     * @param N number of keys in the priority queue, index from {@code 0} to {@code N-1}
     * @param D dimension of the heap
     * @param C a Comparator over the keys
     * @throws java.lang.IllegalArgumentException if {@code N < 0}
     * @throws java.lang.IllegalArgumentException if {@code D < 2}
     */
	public IndexMultiwayMinPQ(int N, Comparator<Key> C, int D) {
		if (N < 0) throw new IllegalArgumentException("Maximum number of elements cannot be negative");
		if (D < 2) throw new IllegalArgumentException("Dimension should be 2 or over");
		this.d = D;
		nmax = N;
		pq = new int[nmax+D];
		qp = new int[nmax+D];
		keys = (Key[]) new Comparable[nmax+D];
		for (int i = 0; i < nmax+D; qp[i++] = -1);
		comp = C;
	}

	/**
	 * Whether the priority queue is empty
	 * Worst case is O(1)
	 * @return true if the priority queue is empty, false if not
	 */
	public boolean isEmpty() {
		return n == 0;
	}

	/**
	 * Does the priority queue contains the index i ?
	 * Worst case is O(1)
	 * @param i an index
	 * @throws java.lang.IndexOutOfBoundsException if the specified index is invalid
	 * @return true if i is on the priority queue, false if not
	 */
	public boolean contains(int i) {
		if (i < 0 ||i >= nmax) throw new IndexOutOfBoundsException();
		return qp[i+d] != -1;
	}

	/**
	 * Number of elements currently on the priority queue
	 * Worst case is O(1)
	 * @return the number of elements on the priority queue
	 */
	public int size() {
		return n;
	}

	/**
	 * Associates a key with an index
	 * Worst case is O(log-d(n))
	 * @param i an index
	 * @param key a Key associated with i
	 * @throws java.lang.IndexOutOfBoundsException if the specified index is invalid
	 * @throws java.lang.IllegalArgumentException if the index is already in the queue
	 */
	public void insert(int i, Key key) {
		if (i < 0 || i >= nmax) throw new IndexOutOfBoundsException();
		if (contains(i)) throw new IllegalArgumentException("Index already there");
		keys[i+d] = key;
		pq[n+d] = i;
		qp[i+d] = n;
		swim(n++);
	}

	/**
	 * Gets the index associated with the minimum key
	 * Worst case is O(1)
	 * @throws java.util.NoSuchElementException if the priority queue is empty
	 * @return the index associated with the minimum key
	 */
	public int minIndex() {
		if (isEmpty()) throw new NoSuchElementException("Priority queue is empty");
		return pq[d];
	}

	/**
	 * Gets the minimum key currently in the queue
	 * Worst case is O(1)
	 * @throws java.util.NoSuchElementException if the priority queue is empty
	 * @return the minimum key currently in the priority queue
	 */
	public Key minKey() {
		if (isEmpty()) throw new NoSuchElementException("Priority queue is empty");
		return keys[pq[d]+d];
	}

	/**
	 * Deletes the minimum key
	 * Worst case is O(d*log-d(n))
	 * @throws java.util.NoSuchElementException if the priority queue is empty
	 * @return the index associated with the minimum key
	 */
	public int delMin() {
		if (isEmpty()) throw new NoSuchElementException("Priority queue is empty");
		int min = pq[d];
		exch(0, --n);
		sink(0);
		qp[min+d] = -1;
		keys[pq[n+d]+d] = null;
		pq[n+d] = -1;
		return min;
	}

	/**
	 * Gets the key associated with index i
	 * Worst case is O(1)
	 * @param i an index
	 * @throws java.lang.IndexOutOfBoundsException if the specified index is invalid
	 * @throws java.lang.IllegalArgumentException if the index is not in the queue
	 * @return the key associated with index i
	 */
	public Key keyOf(int i) {
		if (i < 0 || i >= nmax) throw new IndexOutOfBoundsException();
		if (! contains(i)) throw new NoSuchElementException("Specified index is not in the queue");
		return keys[i+d];
	}

	/**
	 * Changes the key associated with index i to the given key
	 * If the given key is greater, Worst case is O(d*log-d(n))
	 * If the given key is lower,   Worst case is O(log-d(n))
	 * @param i an index
	 * @param key the key to associate with i
	 * @throws java.lang.IndexOutOfBoundsException if the specified index is invalid
	 * @throws java.lang.IllegalArgumentException if the index has no key associated with
	 */
	public void changeKey(int i, Key key) {
		if (i < 0 || i >= nmax) throw new IndexOutOfBoundsException();
		if (! contains(i)) throw new NoSuchElementException("Specified index is not in the queue");
		Key tmp = keys[i+d];
		keys[i+d] = key;
		if (comp.compare(key, tmp) <= 0) { swim(qp[i+d]);}
		else 							 { sink(qp[i+d]);}
	}

	/**
	 * Decreases the key associated with index i to the given key
	 * Worst case is O(log-d(n))
	 * @param i an index
	 * @param key the key to associate with i
	 * @throws java.lang.IndexOutOfBoundsException if the specified index is invalid
	 * @throws java.util.NoSuchElementException if the index has no key associated with
	 * @throws java.lang.IllegalArgumentException if the given key is greater than the current key
	 */
	public void decreaseKey(int i, Key key) {
		if (i < 0 || i >=nmax) throw new IndexOutOfBoundsException();
		if (! contains(i)) throw new NoSuchElementException("Specified index is not in the queue");
		if (comp.compare(keys[i+d], key) <= 0) throw new IllegalArgumentException("Calling with this argument would not decrease the Key");
		keys[i+d] = key;
		swim(qp[i+d]);
	}

	/**
	 * Increases the key associated with index i to the given key
	 * Worst case is O(d*log-d(n))
	 * @param i an index
	 * @param key the key to associate with i
	 * @throws java.lang.IndexOutOfBoundsException if the specified index is invalid
	 * @throws java.util.NoSuchElementException if the index has no key associated with
	 * @throws java.lang.IllegalArgumentException if the given key is lower than the current key
	 */
	public void increaseKey(int i, Key key) {
		if (i < 0 || i >=nmax) throw new IndexOutOfBoundsException();
		if (! contains(i)) throw new NoSuchElementException("Specified index is not in the queue");
		if (comp.compare(keys[i+d], key) >= 0) throw new IllegalArgumentException("Calling with this argument would not increase the Key");
		keys[i+d] = key;
		sink(qp[i+d]);
	}

	/**
	 * Deletes the key associated to the given index
	 * Worst case is O(d*log-d(n))
	 * @param i an index
	 * @throws java.lang.IndexOutOfBoundsException if the specified index is invalid
	 * @throws java.util.NoSuchElementException if the given index has no key associated with
	 */
	public void delete(int i) {
		if (i < 0 || i >= nmax) throw new IndexOutOfBoundsException();
		if (! contains(i)) throw new NoSuchElementException("Specified index is not in the queue");
		int idx = qp[i+d];
		exch(idx, --n);
		swim(idx);
		sink(idx);
		keys[i+d] = null;
		qp[i+d] = -1;
	}
	
	/***************************
	 * General helper functions
	 **************************/
	
	//Compares two keys
	private boolean greater(int i, int j) {
		return comp.compare(keys[pq[i+d]+d], keys[pq[j+d]+d]) > 0;
	}
	
	//Exchanges two keys
	private void exch(int x, int y) {
		int i = x+d, j = y+d;
		int swap = pq[i];
		pq[i] = pq[j];
		pq[j] = swap;
		qp[pq[i]+d] = x;
		qp[pq[j]+d] = y;
	}
	
	/***************************
	 * Functions for moving upward or downward
	 **************************/
	
	//Moves upward
	private void swim(int i) {
		if (i > 0 && greater((i-1)/d, i)) {
			exch(i, (i-1)/d);
			swim((i-1)/d);
		}
	}
	
	//Moves downward
	private void sink(int i) {
		if (d*i+1 >= n) return;
		int min = minChild(i);
		while (min < n && greater(i, min)) {
			exch(i, min);
			i = min;
			min = minChild(i);
		}
	}
	
	/***************************
	 * Deletes the minimum child
	 **************************/
	
	//Return the minimum child of i
	private int minChild(int i) {
		int loBound = d*i+1, hiBound = d*i+d;
		int min = loBound;
		for (int cur = loBound; cur <= hiBound; cur++) {
			if (cur < n && greater(min, cur)) min = cur;
		}
		return min;
	}
	
	/***************************
	 * Iterator
	 **************************/
	
	/**
	 * Gets an Iterator over the indexes in the priority queue in ascending order
	 * The Iterator does not implement the remove() method
	 * iterator() : Worst case is O(n)
	 * next() : 	Worst case is O(d*log-d(n))
	 * hasNext() : 	Worst case is O(1)
	 * @return an Iterator over the indexes in the priority queue in ascending order
	 */
	
	public Iterator<Integer> iterator() {
		return new MyIterator();
	}
	
	//Constructs an Iterator over the indices in linear time
	private class MyIterator implements Iterator<Integer> {
		IndexMultiwayMinPQ<Key> clone;
		
		public MyIterator() {
			clone = new IndexMultiwayMinPQ<Key>(nmax, comp, d);
			for (int i = 0; i < n; i++) {
				clone.insert(pq[i+d], keys[pq[i+d]+d]);
			}
		}

		public boolean hasNext() {
			return !clone.isEmpty();
		}
		
		public Integer next() {
                        if (!hasNext()) throw new NoSuchElementException();
			return clone.delMin();
		}
		
		public void remove() {
			throw new UnsupportedOperationException();
		}
	}
	
	/***************************
	 * Comparator
	 **************************/
	
	//default Comparator
	private class MyComparator implements Comparator<Key> {
		@Override
		public int compare(Key key1, Key key2) {
			return ((Comparable<Key>) key1).compareTo(key2);
		}
	}

}

/******************************************************************************
 *  Copyright 2002-2016, Robert Sedgewick and Kevin Wayne.
 *
 *  This file is part of algs4.jar, which accompanies the textbook
 *
 *      Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
 *      Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
 *      http://algs4.cs.princeton.edu
 *
 *
 *  algs4.jar is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  algs4.jar is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with algs4.jar.  If not, see http://www.gnu.org/licenses.
 ******************************************************************************/