edu.princeton.cs.algs4.MaxPQ Maven / Gradle / Ivy
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/******************************************************************************
* Compilation: javac MaxPQ.java
* Execution: java MaxPQ < input.txt
* Dependencies: StdIn.java StdOut.java
* Data files: https://algs4.cs.princeton.edu/24pq/tinyPQ.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.
*
* 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 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.
*
* This implementation uses a binary heap.
* 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.
*
* For additional documentation, see Section 2.4 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*
* @param the generic type of key on this priority queue
*/
public class MaxPQ implements Iterable {
private Key[] pq; // store items at indices 1 to n
private int n; // number of items on priority queue
private Comparator comparator; // optional comparator
/**
* Initializes an empty priority queue with the given initial capacity.
*
* @param initCapacity the initial capacity of this priority queue
*/
public MaxPQ(int initCapacity) {
pq = (Key[]) new Object[initCapacity + 1];
n = 0;
}
/**
* Initializes an empty priority queue.
*/
public MaxPQ() {
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 in which to compare the keys
*/
public MaxPQ(int initCapacity, Comparator 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 in which to compare the keys
*/
public MaxPQ(Comparator 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 MaxPQ(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 isMaxHeap();
}
/**
* 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 largest key on this priority queue.
*
* @return a largest key on this priority queue
* @throws NoSuchElementException if this priority queue is empty
*/
public Key max() {
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 new 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 isMaxHeap();
}
/**
* Removes and returns a largest key on this priority queue.
*
* @return a largest key on this priority queue
* @throws NoSuchElementException if this priority queue is empty
*/
public Key delMax() {
if (isEmpty()) throw new NoSuchElementException("Priority queue underflow");
Key max = pq[1];
exch(1, n--);
sink(1);
pq[n+1] = null; // to avoid loiteing 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 ((Comparable) 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 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;
int 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.
***************************************************************************/
/**
* Returns an iterator that iterates over the keys on this priority queue
* in descending order.
* The iterator doesn't implement {@code remove()} since it's optional.
*
* @return an iterator that iterates over the keys in descending order
*/
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 Key next() {
if (!hasNext()) throw new NoSuchElementException();
return copy.delMax();
}
}
/**
* Unit tests the {@code MaxPQ} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
MaxPQ pq = new MaxPQ();
while (!StdIn.isEmpty()) {
String item = StdIn.readString();
if (!item.equals("-")) pq.insert(item);
else if (!pq.isEmpty()) StdOut.print(pq.delMax() + " ");
}
StdOut.println("(" + pq.size() + " left on pq)");
}
}
/******************************************************************************
* Copyright 2002-2018, 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.
******************************************************************************/