// Exercise 2.4.15 (Solution published at http://algs4.cs.princeton.edu/)
package algs24;
import stdlib.*;
import java.util.Comparator;
import java.util.Iterator;
import java.util.NoSuchElementException;
/* ***********************************************************************
 *  Compilation:  javac MaxPQ.java
 *  Execution:    java MaxPQ < input.txt
 *
 *  Generic max priority queue implementation with a binary heap.
 *  Can be used with a comparator instead of the natural order,
 *  but the generic key type must still be Comparable.
 *
 *  % java MaxPQ < tinyPQ.txt
 *  Q X P (6 left on pq)
 *
 *  We use a one-based array to simplify parent and child calculations.
 *
 *************************************************************************/

/**
 *  The {@code MaxPQ} class represents a priority queue of generic keys.
 *  It supports the usual <em>insert</em> and <em>delete-the-maximum</em>
 *  operations, along with methods for peeking at the maximum key,
 *  testing if the priority queue is empty, and iterating through
 *  the keys.
 *  <p>
 *  The <em>insert</em> and <em>delete-the-maximum</em> operations take
 *  logarithmic amortized time.
 *  The <em>max</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>
 *  This implementation uses a binary heap.
 *  <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.
 */
public class MaxPQ<K extends Comparable<? super K>> implements Iterable<K> {
  private K[] pq; // store items at indices 1 to N
  private int N;  // number of items on priority queue
  private Comparator<? super K> comparator;  // optional Comparator

  // helper function to double the size of the heap array
  @SuppressWarnings("unchecked")
  private void resize(int capacity) {
    if (capacity <= N) throw new IllegalArgumentException ();
    K[] temp = (K[]) new Comparable[capacity];
    for (int i = 1; i <= N; i++) temp[i] = pq[i];
    pq = temp;
  }

  @SuppressWarnings("unchecked")
  /** Create an empty priority queue with the given initial capacity, using the given comparator. */
  public MaxPQ(int initCapacity, Comparator<? super K> comparator) {
    pq = (K[]) new Comparable[initCapacity + 1];
    N = 0;
    this.comparator = comparator;
  }
  /** Create an empty priority queue with the given initial capacity. */
  public MaxPQ(int initCapacity) { this(initCapacity, null); }
  /** Create an empty priority queue using the given comparator. */
  public MaxPQ(Comparator<? super K> comparator) { this(1, comparator); }
  /** Create an empty priority queue. */
  public MaxPQ() { this(1, null); }

  /**
   * Create a priority queue with the given items.
   * Takes time proportional to the number of items using sink-based heap construction.
   */
  public MaxPQ(K[] keys) {
    this(keys.length, null);
    N = keys.length;
    for (int i = 0; i < N; i++)
      pq[i+1] = keys[i];
    for (int k = N/2; k >= 1; k--)
      sink(k);
    //assert isMaxHeap();
  }

  /** Is the priority queue empty? */
  public boolean isEmpty() { return N == 0; }

  /** Return the number of items on the priority queue. */
  public int size() { return N; }

  /**
   * Return the largest key on the priority queue.
   * @throws java.util.NoSuchElementException if the priority queue is empty.
   */
  public K max() {
    if (isEmpty()) throw new NoSuchElementException("Priority queue underflow");
    return pq[1];
  }

  /** Add a new key to the priority queue. */
  public void insert(K 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 isMaxHeap();
  }

  /**
   * Delete and return the largest key on the priority queue.
   * @throws java.util.NoSuchElementException if the priority queue is empty.
   */
  public K delMax() {
    if (isEmpty()) throw new NoSuchElementException("Priority queue underflow");
    exch(1, N);
    N = N - 1;
    sink(1);
    K max = pq[N+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 isMaxHeap();
    return max;
  }


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

  private void swim(int k) {
    while (k > 1 && less(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 && less(j, j+1)) j++;
      if (!less(k, j)) break;
      exch(k, j);
      k = j;
    }
  }

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

  private void exch(int i, int j) {
    if (DEBUG) GraphvizBuilder.binaryHeapToFile (pq, N);
    K swap = pq[i];
    pq[i] = pq[j];
    pq[j] = swap;
  }

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

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


  /* *********************************************************************
   * Iterator
   **********************************************************************/

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

  private class HeapIterator implements Iterator<K> {
    // create a new pq
    private MaxPQ<K> 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 MaxPQ<K>(size());
      else                    copy = new MaxPQ<K>(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 K next() {
      if (!hasNext()) throw new NoSuchElementException();
      return copy.delMax();
    }
  }

  void showHeap() {
    for (int i = 1; i <= N; i++)
      StdOut.print (pq[i] + " ");
    StdOut.println ();
  }

  /**
   * A test client.
   */
  public static boolean DEBUG = false;
  public static void main(String[] args) {
    DEBUG = true;
    MaxPQ<String> pq = new MaxPQ<>(100);
    StdIn.fromString("10 20 30 40 50 - - - 05 25 35 - - - 70 80 05 - - - - ");
    //StdIn.fromString("E A S Y Q U E S T I O N - - - - - - - - - - - -");
    while (!StdIn.isEmpty()) {
      String item = StdIn.readString();
      if (item.equals("-")) StdOut.println("min: " + pq.delMax());
      else pq.insert(item);
      StdOut.print ("pq:  "); pq.showHeap();
      GraphvizBuilder.binaryHeapToFile (pq.pq, pq.N);
    }
    StdOut.println("(" + pq.size() + " left on pq)");
  }
}