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IntervalHeap.java
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package gkimfl.util;
import static java.lang.Math.log;
import static java.util.Collections.swap;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Comparator;
import java.util.Iterator;
import java.util.List;
/**
* Double ended priority queue implemented as an interval heap.
*
* This collection provides efficient access to the minimum and maximum elements
* that it contains. The minimum and maximum elements can be queried in constant
* O(1) time, and removed in O(log(N)) time. Elements can be added in O(log(N))
* time.
*
* A textbook implementation will describe an array of intervals, where each
* interval has a large and small value. This implementation takes care to avoid
* allocating many small objects to record the intervals. Instead, this
* implementation maintains a min heap in the even array indices, and a max heap
* in the odd array indices. Intervals can be reconstructed from the even odd
* pairs.
*
* @author Allen Hubbe
*
* @param <E>
* - the type of elements held in this collection
*/
public class IntervalHeap<E> extends AbstractDequeue<E> {
private final Comparator<E> cmp;
List<E> queue;
public IntervalHeap() {
cmp = new NaturalComparator<E>();
queue = new ArrayList<E>();
}
public IntervalHeap(IntervalHeap<E> other) {
cmp = other.cmp;
queue = new ArrayList<E>(other.queue);
}
public IntervalHeap(Comparator<E> comparator) {
cmp = comparator;
queue = new ArrayList<E>();
}
public IntervalHeap(Collection<? extends E> c) {
cmp = new NaturalComparator<E>();
queue = new ArrayList<E>(c);
heapify();
}
public IntervalHeap(Collection<? extends E> c, Comparator<E> comparator) {
cmp = comparator;
queue = new ArrayList<E>(c);
heapify();
}
public IntervalHeap(int initialCapacity) {
cmp = new NaturalComparator<E>();
queue = new ArrayList<E>(initialCapacity);
}
public IntervalHeap(int initialCapacity, Comparator<E> comparator) {
cmp = comparator;
queue = new ArrayList<E>(initialCapacity);
}
/**
* Remove all elements from the heap.
*/
@Override
public void clear() {
queue.clear();
}
/**
* Return true if the heap is empty.
*/
@Override
public boolean isEmpty() {
return queue.isEmpty();
}
/**
* Return an iterator for the elements. This iterator does not yield
* elements in sorted order.
*/
@Override
public Iterator<E> iterator() {
return queue.iterator();
}
/**
* Insert several elements into the heap. If the number of elements to be
* added is large, this may call heapify for efficiency instead of adding
* the elements one at a time.
*/
@Override
public boolean addAll(Collection<? extends E> c) {
int cSize = c.size();
int nSize = cSize + queue.size();
if (nSize <= cSize * log(nSize) / log(2)) {
queue.addAll(c);
heapify();
return true;
}
else {
return super.addAll(c);
}
}
/**
* Insert an element into the heap.
*/
@Override
public boolean offer(E e) {
queue.add(e);
int iBound = queue.size();
int i = iBound - 1;
if ((i & 1) == 0) {
pullUpMax(i);
pullUpMin(i);
}
else {
pullUpMax(i);
if (lessAt(i, i - 1)) {
swap(queue, i, i - 1);
pullUpMin(i - 1);
pullUpMax(i);
}
}
return true;
}
/**
* Return the minimum element.
*/
@Override
public E peekFirst() {
return queue.get(0);
}
/**
* Return the maximum element.
*/
@Override
public E peekLast() {
if (queue.size() < 2) {
return queue.get(0);
}
return queue.get(1);
}
/**
* Return and remove the minimum element.
*/
@Override
public E pollFirst() {
int iBound = queue.size() - 1;
if (iBound < 1) {
return queue.remove(0);
}
else {
E e = queue.get(0);
if (iBound > 0) {
queue.set(0, queue.remove(iBound));
int i = pushDownMin(0);
if (i + 1 == iBound) {
pullUpMax(i);
}
else if (i + 1 < iBound && lessAt(i + 1, i)) {
// i is a leaf of the min heap
assert ((i << 1) + 2 > iBound);
swap(queue, i + 1, i);
pullUpMax(i + 1);
}
}
return e;
}
}
/**
* Return and remove the maximum element.
*/
@Override
public E pollLast() {
int iBound = queue.size() - 1;
if (iBound < 1) {
return queue.remove(0);
}
else {
E e = queue.get(1);
if (iBound < 2) {
queue.remove(1);
}
else {
queue.set(1, queue.remove(iBound));
int i = pushDownMax(1);
if ((i & 1) == 0) {
assert (i + 1 == iBound);
pullUpMin(i);
}
else if (lessAt(i, i - 1)) {
// i is a leaf of the max heap
assert ((i << 1) + 1 > iBound);
swap(queue, i, i - 1);
pullUpMin(i - 1);
}
}
return e;
}
}
/**
* Removing arbitrary elements is not supported.
*/
@Override
public boolean removeElem(E e) {
throw new UnsupportedOperationException();
}
/**
* Return the number of elements in the heap.
*/
@Override
public int size() {
return queue.size();
}
/**
* Return true if vA should should be ordered prior to vB.
*/
private boolean less(E vA, E vB) {
return cmp.compare(vA, vB) < 0;
}
/**
* Return true if the value at iA should should be ordered prior to the
* value at iB.
*/
private boolean lessAt(int iA, int iB) {
return less(queue.get(iA), queue.get(iB));
}
/**
* Efficiently order elements into heap. This operation is guaranteed to run
* in O(N) time, N being the number of elements. Like a normal
* (non-interval) heap, elements are ordered starting from the leaves, and
* pushed down towards the leaves. Unlike a normal heap, elements must be
* pulled back up from the leaves. The pull up operation is bounded by the
* current position of progress of the heapify algorithm, to ensure
* correctness and guarantee efficiency.
*/
private void heapify() {
int iBound = queue.size();
for (int i = iBound - 1; 0 <= i; --i) {
if ((i & 1) == 0) {
int j = pushDownMin(i);
if (j + 1 == iBound) {
pullUpMax(j, i + 1);
}
else if (j + 1 < iBound && lessAt(j + 1, j)) {
swap(queue, j + 1, j);
pullUpMin(j, i);
pullUpMax(j + 1, i + 1);
}
}
else {
if (0 <= i - 1 && lessAt(i, i - 1)) {
swap(queue, i, i - 1);
}
int j = pushDownMax(i);
if ((j & 1) == 0) {
assert (i < j);
assert (j + 1 == iBound);
pullUpMin(j, i + 1);
}
else if (i < j && lessAt(j, j - 1)) {
swap(queue, j, j - 1);
pullUpMax(j, i);
pullUpMin(j - 1, i + 1);
}
}
}
}
/**
* Pull an element at position i up in the max heap until it satisfies the
* max heap invariant. The initial position i normally corresponds to a leaf
* in the max heap, but it may be a leaf in the min heap in case of a leaf
* representing an empty interval.
*/
private int pullUpMax(int i) {
E v = queue.get(i);
while (1 < i) {
int iUp = ((i >> 1) - 1) | 1;
E vUp = queue.get(iUp);
if (!less(vUp, v)) {
break;
}
queue.set(i, vUp);
i = iUp;
}
queue.set(i, v);
return i;
}
/**
* Pull an element at position i up in the min heap until it satisfies the
* min heap invariant. The initial position i should always be in the min
* heap.
*/
private int pullUpMin(int i) {
E v = queue.get(i);
while (0 < i) {
int iUp = ((i >> 1) - 1) & ~1;
E vUp = queue.get(iUp);
if (!less(v, vUp)) {
break;
}
queue.set(i, vUp);
i = iUp;
}
queue.set(i, v);
return i;
}
/**
* Pull an element at position i up in the max heap until it satisfies the
* max heap invariant, but do not consider ancestors before position base.
*/
private int pullUpMax(int i, int base) {
E v = queue.get(i);
while (base < i) {
int iUp = ((i >> 1) - 1) | 1;
E vUp = queue.get(iUp);
if (iUp < base || !less(vUp, v)) {
break;
}
queue.set(i, vUp);
i = iUp;
}
queue.set(i, v);
return i;
}
/**
* Pull an element at position i up in the min heap until it satisfies the
* min heap invariant, but do not consider ancestors before position base.
*/
private int pullUpMin(int i, int base) {
E v = queue.get(i);
while (base < i) {
int iUp = ((i >> 1) - 1) & ~1;
E vUp = queue.get(iUp);
if (iUp < base || !less(v, vUp)) {
break;
}
queue.set(i, vUp);
i = iUp;
}
queue.set(i, v);
return i;
}
/**
* Push an element at position i down in the max heap until it satisfies the
* max heap invariant. The resulting position is normally in the max heap,
* but may be in the min heap if it is a leaf representing an empty
* interval.
*/
private int pushDownMax(int i) {
int iBound = queue.size();
E v = queue.get(i);
while (true) {
int iDown = (i << 1) + 1;
E vDown;
if (iBound < iDown) {
break;
}
if (iDown == iBound) {
iDown = iBound - 1;
vDown = queue.get(iDown);
}
else {
vDown = queue.get(iDown);
int iRight = iDown + 2;
if (iRight <= iBound) {
if (iRight == iBound) {
iRight = iBound - 1;
}
E vRight = queue.get(iRight);
if (less(vDown, vRight)) {
vDown = vRight;
iDown = iRight;
}
}
}
if (!less(v, vDown)) {
break;
}
queue.set(i, vDown);
i = iDown;
}
queue.set(i, v);
return i;
}
/**
* Push an element at position i down in the min heap until it satisfies the
* min heap invariant. The resulting position will be in the min heap.
*/
private int pushDownMin(int i) {
int iBound = queue.size();
E v = queue.get(i);
while (true) {
int iDown = (i << 1) + 2;
if (iBound <= iDown) {
break;
}
E vDown = queue.get(iDown);
int iRight = iDown + 2;
if (iRight < iBound) {
E vRight = queue.get(iRight);
if (less(vRight, vDown)) {
vDown = vRight;
iDown = iRight;
}
}
if (!less(vDown, v)) {
break;
}
queue.set(i, vDown);
i = iDown;
}
queue.set(i, v);
return i;
}
}