public class MaxPQ<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 this priority queue
*/
public MaxPQ(int initCapacity) {
pq = (Key[]) new Object[initCapacity + 1];
n = 0;
}
/**
* Initializes an empty priority queue.
*/
public MaxPQ() {
this(1);
}
}
private boolean less(int i, int j) {
if (comparator == null) {
return ((Comparable<Key>) pq).compareTo(pq[j]) < 0;
}
else {
return comparator.compare(pq, pq[j]) < 0;
}
}
private void exch(int i, int j) {
Key swap = pq;
pq = pq[j];
pq[j] = swap;
}
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;
}
}
/**
* 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 a maximum key and returns its associated index.
*
* @return an index associated with a maximum key
* @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);
n--;
sink(1);
pq[n+1] = null; // to avoid loiterig and help with garbage collection
if ((n > 0) && (n == (pq.length - 1) / 4)) resize(pq.length / 2);
assert isMaxHeap();
return max;
}
// 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 = pq;
}
pq = temp;
}
public boolean isEmpty() {
return n == 0;
}
// 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);
}
/**
* Returns an iterator that iterates over the keys on this priority queue
* in descending order.
* The iterator doesn't implement remove() since it's optional.
*
* @return an iterator that iterates over the keys in descending order
*/
public Iterator<Key> iterator() {
return new HeapIterator();
}
private class HeapIterator implements Iterator<Key> {
// create a new pq
private MaxPQ<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 MaxPQ<Key>(size());
else copy = new MaxPQ<Key>(size(), comparator);
for (int i = 1; i <= n; i++)
copy.insert(pq);
}
public boolean hasNext() { return !copy.isEmpty(); }
public void remove() { throw new UnsupportedOperationException(); }
public Key next() {
if (!hasNext()) throw new NoSuchElementException();
return copy.delMax();
}
}
/**
* 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;
for (int k = n/2; k >= 1; k--)
sink(pq, k, n);
while (n > 1) {
exch(pq, 1, n--);
sink(pq, 1, n);
}
}
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