268 lines
8.5 KiB
Java
268 lines
8.5 KiB
Java
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/*************************************************************************
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* Compilation: javac MinPQ.java
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* Execution: java MinPQ < input.txt
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*
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* Generic min priority queue implementation with a binary heap.
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* Can be used with a comparator instead of the natural order.
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*
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* % java MinPQ < tinyPQ.txt
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* E A E (6 left on pq)
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*
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* We use a one-based array to simplify parent and child calculations.
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*
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* Can be optimized by replacing full exchanges with half exchanges
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* (ala insertion sort).
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*
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*************************************************************************/
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import java.util.Comparator;
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import java.util.Iterator;
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import java.util.NoSuchElementException;
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import edu.princeton.cs.introcs.StdIn;
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import edu.princeton.cs.introcs.StdOut;
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/**
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* The MinPQ class represents a priority queue of generic keys.
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* It supports the usual insert and delete-the-minimum
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* operations, along with methods for peeking at the minimum key,
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* testing if the priority queue is empty, and iterating through
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* the keys.
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*
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* This implementation uses a binary heap.
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* The insert and delete-the-minimum operations take
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* logarithmic amortized time.
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* The min , size , and is-empty operations take constant time.
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* Construction takes time proportional to the specified capacity or the number of
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* items used to initialize the data structure.
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*
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* For additional documentation, see <a href="http://algs4.cs.princeton.edu/24pq">Section 2.4</a> of
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* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
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*
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* @author Robert Sedgewick
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* @author Kevin Wayne
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*/
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public class MinPQ<Key> implements Iterable<Key> {
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private Key[] pq; // store items at indices 1 to N
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private int N; // number of items on priority queue
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private Comparator<Key> comparator; // optional comparator
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/**
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* Initializes an empty priority queue with the given initial capacity.
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* @param initCapacity the initial capacity of the priority queue
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*/
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public MinPQ(int initCapacity) {
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pq = (Key[]) new Object[initCapacity + 1];
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N = 0;
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}
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/**
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* Initializes an empty priority queue.
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*/
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public MinPQ() {
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this(1);
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}
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/**
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* Initializes an empty priority queue with the given initial capacity,
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* using the given comparator.
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* @param initCapacity the initial capacity of the priority queue
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* @param comparator the order to use when comparing keys
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*/
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public MinPQ(int initCapacity, Comparator<Key> comparator) {
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this.comparator = comparator;
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pq = (Key[]) new Object[initCapacity + 1];
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N = 0;
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}
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/**
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* Initializes an empty priority queue using the given comparator.
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* @param comparator the order to use when comparing keys
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*/
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public MinPQ(Comparator<Key> comparator) { this(1, comparator); }
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/**
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* Initializes a priority queue from the array of keys.
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* Takes time proportional to the number of keys, using sink-based heap construction.
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* @param keys the array of keys
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*/
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public MinPQ(Key[] keys) {
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N = keys.length;
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pq = (Key[]) new Object[keys.length + 1];
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for (int i = 0; i < N; i++)
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pq[i+1] = keys[i];
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for (int k = N/2; k >= 1; k--)
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sink(k);
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assert isMinHeap();
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}
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/**
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* Is the priority queue empty?
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* @return true if the priority queue is empty; false otherwise
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*/
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public boolean isEmpty() {
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return N == 0;
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}
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/**
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* Returns the number of keys on the priority queue.
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* @return the number of keys on the priority queue
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*/
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public int size() {
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return N;
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}
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/**
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* Returns a smallest key on the priority queue.
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* @return a smallest key on the priority queue
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* @throws java.util.NoSuchElementException if priority queue is empty
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*/
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public Key min() {
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if (isEmpty()) throw new NoSuchElementException("Priority queue underflow");
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return pq[1];
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}
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// helper function to double the size of the heap array
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private void resize(int capacity) {
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assert capacity > N;
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Key[] temp = (Key[]) new Object[capacity];
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for (int i = 1; i <= N; i++) temp[i] = pq[i];
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pq = temp;
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}
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/**
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* Adds a new key to the priority queue.
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* @param x the key to add to the priority queue
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*/
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public void insert(Key x) {
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// double size of array if necessary
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if (N == pq.length - 1) resize(2 * pq.length);
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// add x, and percolate it up to maintain heap invariant
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pq[++N] = x;
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swim(N);
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assert isMinHeap();
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}
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/**
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* Removes and returns a smallest key on the priority queue.
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* @return a smallest key on the priority queue
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* @throws java.util.NoSuchElementException if the priority queue is empty
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*/
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public Key delMin() {
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if (isEmpty()) throw new NoSuchElementException("Priority queue underflow");
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exch(1, N);
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Key min = pq[N--];
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sink(1);
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pq[N+1] = null; // avoid loitering and help with garbage collection
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if ((N > 0) && (N == (pq.length - 1) / 4)) resize(pq.length / 2);
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assert isMinHeap();
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return min;
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}
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/***********************************************************************
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* Helper functions to restore the heap invariant.
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**********************************************************************/
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private void swim(int k) {
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while (k > 1 && greater(k/2, k)) {
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exch(k, k/2);
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k = k/2;
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}
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}
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private void sink(int k) {
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while (2*k <= N) {
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int j = 2*k;
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if (j < N && greater(j, j+1)) j++;
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if (!greater(k, j)) break;
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exch(k, j);
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k = j;
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}
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}
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/***********************************************************************
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* Helper functions for compares and swaps.
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**********************************************************************/
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private boolean greater(int i, int j) {
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if (comparator == null) {
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return ((Comparable<Key>) pq[i]).compareTo(pq[j]) > 0;
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}
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else {
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return comparator.compare(pq[i], pq[j]) > 0;
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}
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}
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private void exch(int i, int j) {
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Key swap = pq[i];
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pq[i] = pq[j];
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pq[j] = swap;
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}
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// is pq[1..N] a min heap?
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private boolean isMinHeap() {
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return isMinHeap(1);
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}
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// is subtree of pq[1..N] rooted at k a min heap?
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private boolean isMinHeap(int k) {
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if (k > N) return true;
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int left = 2*k, right = 2*k + 1;
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if (left <= N && greater(k, left)) return false;
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if (right <= N && greater(k, right)) return false;
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return isMinHeap(left) && isMinHeap(right);
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}
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/***********************************************************************
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* Iterators
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**********************************************************************/
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/**
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* Returns an iterator that iterates over the keys on the priority queue
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* in ascending order.
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* The iterator doesn't implement remove() since it's optional.
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* @return an iterator that iterates over the keys in ascending order
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*/
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public Iterator<Key> iterator() { return new HeapIterator(); }
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private class HeapIterator implements Iterator<Key> {
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// create a new pq
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private MinPQ<Key> copy;
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// add all items to copy of heap
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// takes linear time since already in heap order so no keys move
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public HeapIterator() {
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if (comparator == null) copy = new MinPQ<Key>(size());
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else copy = new MinPQ<Key>(size(), comparator);
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for (int i = 1; i <= N; i++)
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copy.insert(pq[i]);
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}
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public boolean hasNext() { return !copy.isEmpty(); }
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public void remove() { throw new UnsupportedOperationException(); }
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public Key next() {
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if (!hasNext()) throw new NoSuchElementException();
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return copy.delMin();
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}
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}
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/**
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* Unit tests the MinPQ data type.
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*/
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public static void main(String[] args) {
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MinPQ<String> pq = new MinPQ<String>();
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while (!StdIn.isEmpty()) {
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String item = StdIn.readString();
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if (!item.equals("-")) pq.insert(item);
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else if (!pq.isEmpty()) StdOut.print(pq.delMin() + " ");
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}
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StdOut.println("(" + pq.size() + " left on pq)");
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}
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}
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