Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
- Heap sort is an in-place algorithm.
- Its typical implementation is not stable, but can be made stable.
- Typically 2-3 times slower than well-implemented QuickSort.
A solution from algs4:
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/******************************************************************************
* Compilation: javac Heap.java
* Execution: java Heap < input.txt
* Dependencies: StdOut.java StdIn.java
* Data files: https://algs4.cs.princeton.edu/24pq/tiny.txt
* https://algs4.cs.princeton.edu/24pq/words3.txt
*
* Sorts a sequence of strings from standard input using heapsort.
*
* % more tiny.txt
* S O R T E X A M P L E
*
* % java Heap < tiny.txt
* A E E L M O P R S T X [ one string per line ]
*
* % more words3.txt
* bed bug dad yes zoo ... all bad yet
*
* % java Heap < words3.txt
* all bad bed bug dad ... yes yet zoo [ one string per line ]
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code Heap} class provides a static method to sort an array
* using <em>heapsort</em>.
* <p>
* This implementation takes Θ(<em>n</em> log <em>n</em>) time
* to sort any array of length <em>n</em> (assuming comparisons
* take constant time). It makes at most
* 2 <em>n</em> log<sub>2</sub> <em>n</em> compares.
* <p>
* This sorting algorithm is not stable.
* It uses Θ(1) extra memory (not including the input array).
* <p>
* For additional documentation, see
* <a href="https://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 Heap {
// This class should not be instantiated.
private Heap() { }
/**
* Rearranges the array in ascending order, using the natural order.
* @param pq the array to be sorted
*/
public static void sort(Comparable[] pq) {
int n = pq.length;
// heapify phase
for (int k = n/2; k >= 1; k--)
sink(pq, k, n);
// sortdown phase
int k = n;
while (k > 1) {
exch(pq, 1, k--);
sink(pq, 1, k);
}
}
/***************************************************************************
* Helper functions to restore the heap invariant.
***************************************************************************/
private static void sink(Comparable[] pq, int k, int n) {
while (2*k <= n) {
int j = 2*k;
if (j < n && less(pq, j, j+1)) j++;
if (!less(pq, k, j)) break;
exch(pq, k, j);
k = j;
}
}
/***************************************************************************
* Helper functions for comparisons and swaps.
* Indices are "off-by-one" to support 1-based indexing.
***************************************************************************/
private static boolean less(Comparable[] pq, int i, int j) {
return pq[i-1].compareTo(pq[j-1]) < 0;
}
private static void exch(Object[] pq, int i, int j) {
Object swap = pq[i-1];
pq[i-1] = pq[j-1];
pq[j-1] = swap;
}
// print array to standard output
private static void show(Comparable[] a) {
for (int i = 0; i < a.length; i++) {
StdOut.println(a[i]);
}
}
/**
* Reads in a sequence of strings from standard input; heapsorts them;
* and prints them to standard output in ascending order.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
String[] a = StdIn.readAllStrings();
Heap.sort(a);
show(a);
}
}
/******************************************************************************
* Copyright 2002-2022, 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.
******************************************************************************/