北京北大青鳥通州校區學術部老師講解：什么是堆排序？
北京北大青鳥專家解答：堆排序是另一種選擇排序方法,它是樹型選擇排序的改進,優勢是使用的輔助空間較少,僅需要一個元素用于空間交換。（北京北大青鳥）
堆排序包括兩個步驟 (1)初始堆(堆的定義：(1)堆是一個完全二叉樹(2)根結點的值或者大于左右子樹的值或者小于左右子樹的值(3)左右子樹也是一個堆)（北京北大青鳥）
(2)調整堆(當初始小頂堆之后，堆頂元素是最小的元素，取出最小的元素與最后一個元素相交換，再把剩下n-1個元素調整成堆,依次調整直到1為止)（北京北大青鳥）
public abstract class PriorityQueue {
private Object[] heap;
private int size;
private int maxSize;
/** Determines the ordering of objects in this priority queue. Subclasses
must define this one method. */
protected abstract boolean lessThan(Object a, Object b);
/** Subclass constructors must call this. */
protected final void initialize(int maxSize) {
size = 0;
int heapSize = maxSize + 1;
heap = new Object[heapSize];
this.maxSize = maxSize;
}
/**
* Adds an Object to a PriorityQueue in log(size) time.
* If one tries to add more objects than maxSize from initialize
* a RuntimeException (ArrayIndexOutOfBound) is thrown.
*/
public final void put(Object element) {
size++;
heap[size] = element;
upHeap();
}
/**
* Adds element to the PriorityQueue in log(size) time if either
* the PriorityQueue is not full, or not lessThan(element, top()).
* @param element
* @return true if element is added, false otherwise.
*/
public boolean insert(Object element){
if(size < maxSize){
put(element);
return true;
}
else if(size > 0 && !lessThan(element, top())){
heap[1] = element;
adjustTop();
return true;
}
else
return false;
}
/** Returns the least element of the PriorityQueue in constant time. */
public final Object top() {
if (size > 0)
return heap[1];
else
return null;
}
/** Removes and returns the least element of the PriorityQueue in log(size)
time. */
public final Object pop() {
if (size > 0) {
Object result = heap[1]; // save first value
heap[1] = heap[size]; // move last to first
heap[size] = null; // permit GC of objects
size--;
downHeap(); // adjust heap
return result;
} else
return null;
}
/** Should be called when the Object at top changes values. Still log(n)
* worst case, but it's at least twice as fast to
instead of
* { pq.top().change(); pq.adjustTop(); }
*
* { o = pq.pop(); o.change(); pq.push(o); }
*
/** Returns the number of elements currently stored in the PriorityQueue. */
public final int size() {
return size;
}
/** Removes all entries from the PriorityQueue. */
public final void clear() {
for (int i = 0; i <= size; i++)
heap[i] = null;
size = 0;
}
private final void upHeap() {
int i = size;
Object node = heap[i]; // save bottom node
int j = i >>> 1;
while (j > 0 && lessThan(node, heap[j])) {
heap[i] = heap[j]; // shift parents down
i = j;
j = j >>> 1;
}
heap[i] = node; // install saved node
}
private final void downHeap() {
int i = 1;
Object node = heap[i]; // save top node
int j = i << 1; // find smaller child
int k = j + 1;
if (k <= size && lessThan(heap[k], heap[j])) {
j = k;
}
while (j <= size && lessThan(heap[j], node)) {
heap[i] = heap[j]; // shift up child
i = j;
j = i << 1;
k = j + 1;
if (k <= size && lessThan(heap[k], heap[j])) {
j = k;
}
}
heap[i] = node; // install saved node
}
}
結束（北京北大青鳥）
相關鏈接：Java的排序之“快速排序”
