Java用数组实现堆

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堆：

堆是有如下特点的二叉树：

1、它是完全二叉树，即树的最后一层不要求是满的，第一个空结点开始的结点，左边所有的兄弟结点必须全部不为空，右边所有结点必须全部为空。

2、常常用一个数组来实现。

3、堆中每个结点的关键字都大于等于它的孩子结点的关键字。而左右孩子结点间没有强制规定大小关系。

所以根据3，我们可以知道，堆是一种弱有序的数据结构。

下面用Java实现堆的操作，包括向堆插入结点到堆尾，并进行向上调整，移除堆顶的元素，把堆尾元素移到堆顶并进行调整，更改堆元素的值并进行调整，输出堆中元素等方法。

package test2;class HeapNode{private int key;public HeapNode(int key){this.key = key;}public void setKey(int key){this.key = key;}public int getKey(){return key;}}public class Heap {private HeapNode[] heapArray;private int maxSize;private int currentSize;public Heap(int maxSize){this.maxSize = maxSize;heapArray = new HeapNode[maxSize];currentSize = 0;}public boolean insertNode(int key){if(maxSize == currentSize){return false;}HeapNode newNode = new HeapNode(key);heapArray[currentSize] = newNode;trickleUp(currentSize);//插入在尾端，向上调整，比起插入在根结点向下调整要方便，因为前者只需跟父结点比较，后者要跟两个子结点比较。++currentSize;return true;}public void trickleUp(int index){//插入到堆最末的结点进行向上调整int parentIndex = (index-1)/2;while(parentIndex >= 0){if(heapArray[index].getKey() > heapArray[parentIndex].getKey()){HeapNode temp = heapArray[index];heapArray[index] = heapArray[parentIndex];heapArray[parentIndex] = temp;index = parentIndex;parentIndex = (index-1)/2;//记得对当前值的下标和其父结点的下标更新}else{return;}}return;}public void trickleDown(int index){int leftChild ;int rightChild ;HeapNode  temp;while(index < currentSize && index >= 0){leftChild = 2*index + 1;rightChild = 2*index + 2;if(leftChild >= currentSize){//如果左孩子不存在return;}else if(rightChild >= currentSize){//如果左孩子存在，右孩子不存在if(heapArray[leftChild].getKey() > heapArray[index].getKey()){temp = heapArray[index];heapArray[index] = heapArray[leftChild];heapArray[leftChild] = temp;index = leftChild;}}else{//如果左右孩子都存在if(heapArray[leftChild].getKey() > heapArray[rightChild].getKey()){temp = heapArray[index];heapArray[index] = heapArray[leftChild];heapArray[leftChild] = temp;index = leftChild;}else{temp = heapArray[index];heapArray[index] = heapArray[rightChild];heapArray[rightChild] = temp;index = rightChild;}}//end of if-else}//while}//end of methodpublic boolean deleteRootNode(){if(currentSize == 0){return false;}HeapNode root = heapArray[0];//需要时可将其返回heapArray[0] = heapArray[--currentSize];trickleDown(0);//删除根结点后，将最后一个结点放到堆顶，对其向下进行调整；return true;}public boolean changeNodeKey(int index, int newKey){if(index < currentSize && index >= 0){if(heapArray[index].getKey() > newKey){//若新值比当前值小，说明要把新值结点下沉heapArray[index].setKey(newKey);trickleDown(index);}else{//若新值比当前值大，说明要把新值结点上升heapArray[index].setKey(newKey);trickleUp(index);}return true;}return false;}public void displayHeap(){for(int i=0; i<this.currentSize;i++){System.out.print(" "+heapArray[i].getKey());}System.out.println(" ");}}class HeapApp{public static void main(String args[]){Heap heap = new Heap(20);heap.insertNode(1);heap.insertNode(2);heap.insertNode(3);heap.insertNode(9);heap.deleteRootNode();heap.displayHeap();heap.changeNodeKey(2, 8);heap.displayHeap();}}

测试结果：

 3 1 2  8 1 3

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