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package algs24; import stdlib.*; import java.util.Comparator; import java.util.Iterator; import java.util.NoSuchElementException; /* *********************************************************************** * 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, * but the generic key type must still be Comparable. * * % java MinPQ < tinyPQ.txt * E A E (6 left on pq) * * We use a one-based array to simplify parent and child calculations. * *************************************************************************/ /** * 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 maximum key, * testing if the priority queue is empty, and iterating through * the keys. * <p> * 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> * 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 MinPQ<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 MinPQ(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 MinPQ(int initCapacity) { this(initCapacity, null); } /** Create an empty priority queue using the given comparator. */ public MinPQ(Comparator<? super K> comparator) { this(1, comparator); } /** Create an empty priority queue. */ public MinPQ() { 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 MinPQ(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 isMinHeap(); } /** 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 smallest key on the priority queue. * @throws java.util.NoSuchElementException if the priority queue is empty. */ public K min() { 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 isMinHeap(); } /** * Delete and return the smallest key on the priority queue. * @throws java.util.NoSuchElementException if the priority queue is empty. */ public K delMin() { if (isEmpty()) throw new NoSuchElementException("Priority queue underflow"); exch(1, N); K 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 pq[i].compareTo(pq[j]) > 0; } else { return comparator.compare(pq[i], pq[j]) > 0; } } private void exch(int i, int j) { K 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); } /* ********************************************************************* * Iterator **********************************************************************/ /** * Return an iterator that iterates over all of the keys on the priority queue * in ascending order. * <p> * The iterator doesn't implement <tt>remove()</tt> since it's optional. */ public Iterator<K> iterator() { return new HeapIterator(); } private class HeapIterator implements Iterator<K> { // create a new pq private MinPQ<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 MinPQ<K>(size()); else copy = new MinPQ<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.delMin(); } } void showHeap() { for (int i = 1; i <= N; i++) StdOut.print (pq[i] + " "); StdOut.println (); } /** * A test client. */ public static void main(String[] args) { MinPQ<String> pq = new MinPQ<>(100); StdIn.fromString ("10 20 30 40 50 - - - 05 25 35 - - - 70 80 05 - - - - "); while (!StdIn.isEmpty()) { StdOut.print ("pq: "); pq.showHeap(); String item = StdIn.readString(); if (item.equals("-")) StdOut.println("min: " + pq.delMin()); else pq.insert(item); GraphvizBuilder.binaryHeapToFile (pq.pq, pq.N); } StdOut.println("(" + pq.size() + " left on pq)"); } }