package edu.princeton.cs.algs4.ch24;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* Compilation: javac MinPQ.java
* Execution: java MinPQ < input.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).
*
*************************************************************************/
import java.util.Comparator;
import java.util.Iterator;
import java.util.NoSuchElementException;
/**
* The <tt>MinPQ</tt> 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
*/
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 the 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 the 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.
* 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();
}
/**
* Is the priority queue empty?
* @return true if the priority queue is empty; false otherwise
*/
public boolean isEmpty() {
return N == 0;
}
/**
* Returns the number of keys on the priority queue.
* @return the number of keys on the priority queue
*/
public int size() {
return N;
}
/**
* Returns a smallest key on the priority queue.
* @return a smallest key on the priority queue
* @throws java.util.NoSuchElementException if 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 the priority queue.
* @param x the key to add to the 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 the priority queue.
* @return a smallest key on the priority queue
* @throws java.util.NoSuchElementException if the 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, 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);
}
/***********************************************************************
* Iterators
**********************************************************************/
/**
* Returns an iterator that iterates over the keys on the priority queue
* in ascending order.
* The iterator doesn't implement <tt>remove()</tt> 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 <tt>MinPQ</tt> data type.
*/
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 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.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-package.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-package.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-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/