// 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 insert and delete-the-maximum
* operations, along with methods for peeking at the maximum key,
* testing if the priority queue is empty, and iterating through
* the keys.
*
* The insert and delete-the-maximum operations take
* logarithmic amortized time.
* The max, size, and is-empty operations take constant time.
* Construction takes time proportional to the specified capacity or the number of
* items used to initialize the data structure.
*
* This implementation uses a binary heap.
*
* For additional documentation, see Section 2.4 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*/
public class MaxPQ> implements Iterable {
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.
*
* The iterator doesn't implement {@code remove()} since it's optional.
*/
public Iterator iterator() { return new HeapIterator(); }
private class HeapIterator implements Iterator {
// create a new pq
private MaxPQ 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(size());
else copy = new MaxPQ(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 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)");
}
}