/******************************************************************************
 *  Compilation:  javac MinPQ.java
 *  Execution:    java MinPQ < input.txt
 *  Dependencies: StdIn.java StdOut.java
 *  Data files:   http://algs4.cs.princeton.edu/24pq/tinyPQ.txt
 *  
 *  Generic min priority queue implementation with a binary heap.
 *  Can be used with a comparator instead of the natural order.
 *
 *  % java MinPQ < tinyPQ.txt
 *  E A E (6 left on pq)
 *
 *  We use a one-based array to simplify parent and child calculations.
 *
 *  Can be optimized by replacing full exchanges with half exchanges
 *  (ala insertion sort).
 *
 ******************************************************************************/

package edu.princeton.cs.algs4;

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

/**
 *  The {@code MinPQ} class represents a priority queue of generic keys.
 *  It supports the usual <em>insert</em> and <em>delete-the-minimum</em>
 *  operations, along with methods for peeking at the minimum key,
 *  testing if the priority queue is empty, and iterating through
 *  the keys.
 *  <p>
 *  This implementation uses a binary heap.
 *  The <em>insert</em> and <em>delete-the-minimum</em> operations take
 *  logarithmic amortized time.
 *  The <em>min</em>, <em>size</em>, and <em>is-empty</em> operations take constant time.
 *  Construction takes time proportional to the specified capacity or the number of
 *  items used to initialize the data structure.
 *  <p>
 *  For additional documentation, see <a href="http://algs4.cs.princeton.edu/24pq">Section 2.4</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 *
 *  @param <Key> the generic type of key on this priority queue
 */
public class MinPQ<Key> implements Iterable<Key> {
    private Key[] pq;                    // store items at indices 1 to n
    private int n;                       // number of items on priority queue
    private Comparator<Key> comparator;  // optional comparator

    /**
     * Initializes an empty priority queue with the given initial capacity.
     *
     * @param  initCapacity the initial capacity of this priority queue
     */
    public MinPQ(int initCapacity) {
        pq = (Key[]) new Object[initCapacity + 1];
        n = 0;
    }

    /**
     * Initializes an empty priority queue.
     */
    public MinPQ() {
        this(1);
    }

    /**
     * Initializes an empty priority queue with the given initial capacity,
     * using the given comparator.
     *
     * @param  initCapacity the initial capacity of this priority queue
     * @param  comparator the order to use when comparing keys
     */
    public MinPQ(int initCapacity, Comparator<Key> comparator) {
        this.comparator = comparator;
        pq = (Key[]) new Object[initCapacity + 1];
        n = 0;
    }

    /**
     * Initializes an empty priority queue using the given comparator.
     *
     * @param  comparator the order to use when comparing keys
     */
    public MinPQ(Comparator<Key> comparator) {
        this(1, comparator);
    }

    /**
     * Initializes a priority queue from the array of keys.
     * <p>
     * Takes time proportional to the number of keys, using sink-based heap construction.
     *
     * @param  keys the array of keys
     */
    public MinPQ(Key[] keys) {
        n = keys.length;
        pq = (Key[]) new Object[keys.length + 1];
        for (int i = 0; i < n; i++)
            pq[i+1] = keys[i];
        for (int k = n/2; k >= 1; k--)
            sink(k);
        assert isMinHeap();
    }

    /**
     * Returns true if this priority queue is empty.
     *
     * @return {@code true} if this priority queue is empty;
     *         {@code false} otherwise
     */
    public boolean isEmpty() {
        return n == 0;
    }

    /**
     * Returns the number of keys on this priority queue.
     *
     * @return the number of keys on this priority queue
     */
    public int size() {
        return n;
    }

    /**
     * Returns a smallest key on this priority queue.
     *
     * @return a smallest key on this priority queue
     * @throws NoSuchElementException if this priority queue is empty
     */
    public Key min() {
        if (isEmpty()) throw new NoSuchElementException("Priority queue underflow");
        return pq[1];
    }

    // helper function to double the size of the heap array
    private void resize(int capacity) {
        assert capacity > n;
        Key[] temp = (Key[]) new Object[capacity];
        for (int i = 1; i <= n; i++) {
            temp[i] = pq[i];
        }
        pq = temp;
    }

    /**
     * Adds a new key to this priority queue.
     *
     * @param  x the key to add to this priority queue
     */
    public void insert(Key x) {
        // double size of array if necessary
        if (n == pq.length - 1) resize(2 * pq.length);

        // add x, and percolate it up to maintain heap invariant
        pq[++n] = x;
        swim(n);
        assert isMinHeap();
    }

    /**
     * Removes and returns a smallest key on this priority queue.
     *
     * @return a smallest key on this priority queue
     * @throws NoSuchElementException if this priority queue is empty
     */
    public Key delMin() {
        if (isEmpty()) throw new NoSuchElementException("Priority queue underflow");
        exch(1, n);
        Key min = pq[n--];
        sink(1);
        pq[n+1] = null;         // avoid loitering and help with garbage collection
        if ((n > 0) && (n == (pq.length - 1) / 4)) resize(pq.length  / 2);
        assert isMinHeap();
        return min;
    }


   /***************************************************************************
    * Helper functions to restore the heap invariant.
    ***************************************************************************/

    private void swim(int k) {
        while (k > 1 && greater(k/2, k)) {
            exch(k, k/2);
            k = k/2;
        }
    }

    private void sink(int k) {
        while (2*k <= n) {
            int j = 2*k;
            if (j < n && greater(j, j+1)) j++;
            if (!greater(k, j)) break;
            exch(k, j);
            k = j;
        }
    }

   /***************************************************************************
    * Helper functions for compares and swaps.
    ***************************************************************************/
    private boolean greater(int i, int j) {
        if (comparator == null) {
            return ((Comparable<Key>) pq[i]).compareTo(pq[j]) > 0;
        }
        else {
            return comparator.compare(pq[i], pq[j]) > 0;
        }
    }

    private void exch(int i, int j) {
        Key swap = pq[i];
        pq[i] = pq[j];
        pq[j] = swap;
    }

    // is pq[1..N] a min heap?
    private boolean isMinHeap() {
        return isMinHeap(1);
    }

    // is subtree of pq[1..n] rooted at k a min heap?
    private boolean isMinHeap(int k) {
        if (k > n) return true;
        int left = 2*k;
        int right = 2*k + 1;
        if (left  <= n && greater(k, left))  return false;
        if (right <= n && greater(k, right)) return false;
        return isMinHeap(left) && isMinHeap(right);
    }


    /**
     * Returns an iterator that iterates over the keys on this priority queue
     * in ascending order.
     * <p>
     * The iterator doesn't implement {@code remove()} since it's optional.
     *
     * @return an iterator that iterates over the keys in ascending order
     */
    public Iterator<Key> iterator() { return new HeapIterator(); }

    private class HeapIterator implements Iterator<Key> {
        // create a new pq
        private MinPQ<Key> copy;

        // add all items to copy of heap
        // takes linear time since already in heap order so no keys move
        public HeapIterator() {
            if (comparator == null) copy = new MinPQ<Key>(size());
            else                    copy = new MinPQ<Key>(size(), comparator);
            for (int i = 1; i <= n; i++)
                copy.insert(pq[i]);
        }

        public boolean hasNext()  { return !copy.isEmpty();                     }
        public void remove()      { throw new UnsupportedOperationException();  }

        public Key next() {
            if (!hasNext()) throw new NoSuchElementException();
            return copy.delMin();
        }
    }

    /**
     * Unit tests the {@code MinPQ} data type.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        MinPQ<String> pq = new MinPQ<String>();
        while (!StdIn.isEmpty()) {
            String item = StdIn.readString();
            if (!item.equals("-")) pq.insert(item);
            else if (!pq.isEmpty()) StdOut.print(pq.delMin() + " ");
        }
        StdOut.println("(" + pq.size() + " left on pq)");
    }

}

/******************************************************************************
 *  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.
 ******************************************************************************/