数据结构源码

实现类

import java.util.Random;

public class MaxHeap<E extends Comparable<E>> {

    private Array<E> data;

    public MaxHeap(int capacity) {
        data = new Array<>(capacity);
    }

    public MaxHeap() {
        data = new Array<>();
    }

    public MaxHeap(E[] arr) {

        data = new Array<>(arr);
        for (int i = parent(arr.length - 1); i >= 0; i--) {
            siftDown(i);
        }
    }

    /**
     * 返回堆中的元素个数
     * @return
     */
    public int size() {
        return data.getSize();
    }

    /**
     * 返回一个布尔值，表示堆中是否为空
     */
    public boolean isEmpty() {
        return data.isEmpty();
    }

    /**
     * 返回完全二叉树的数组表示中，一个索引所表示的元素的父亲节点的索引
     * @param index
     * @return
     */
    private int parent(int index) {
        if (index == 0)
            throw new IllegalArgumentException("index-0 doesn't have parent.");
        return (index - 1) / 2;
    }

    /**
     * 返回完全二叉树的数组表示中，一个索引所表示的元素的左孩子节点的索引
     * @param index
     * @return
     */
    private int leftChild(int index) {
        return index * 2 + 1;
    }


    private int rightChild(int index) {
        return index * 2 + 2;
    }

    /**
     * 像堆中添加元素
     * @param e
     */
    public void add(E e) {
        data.addLast(e);
        siftUp(data.getSize() - 1);
    }

    private void siftUp(int k) {
        while (k > 0 && data.get(parent(k)).compareTo(data.get(k)) < 0) {
            data.swap(k, parent(k));
            k = parent(k);
        }
    }

    public E findMax() {
        if (data.getSize() == 0) {
            throw new IllegalArgumentException("Can not findMax when heap is empty.");
        }
        return data.get(0);
    }

    /**
     * 取出堆中最大元素
     * @return
     */
    public E extractMax() {
        E ret = findMax();
        data.swap(0, data.getSize() - 1);
        data.removeLast();
        siftDown(0);

        return ret;
    }

    private void siftDown(int k) {
        while (leftChild(k) < data.getSize()) {
            int j = leftChild(k);
            if (j + 1 < data.getSize() && data.get(j + 1).compareTo(data.get(j)) > 0) {
                j++;
            }
            // data[j] 是leftChild和rightChild中的最大值
            if (data.get(k).compareTo(data.get(j)) >= 0)
                break;

            data.swap(k, j);
            k = j;
        }
    }

    public E replace(E e) {

        E ret = findMax();
        data.set(0, e);
        siftDown(0);
        return ret;
    }


    public static void main(String[] args) {

        int n = 1000000;

        Random random = new Random();
        Integer[] testData = new Integer[n];
        for (int i = 0; i < n; i++) {
            testData[i] = random.nextInt(Integer.MAX_VALUE);
        }

        double time1 = testHeap(testData, false);
        System.out.println("Without heapify: " + time1 + " s");

        double time2 = testHeap(testData, true);
        System.out.println("With heapify: " + time2 + " s");
    }

    private static double testHeap(Integer[] testData, boolean isHeapify) {
        long startTime = System.nanoTime();

        MaxHeap<Integer> maxHeap;
        if (isHeapify) {
            maxHeap = new MaxHeap<>(testData);
        }
        else {
            maxHeap = new MaxHeap<>();
            for (int num: testData)
                maxHeap.add(num);
        }

        int[] arr = new int[testData.length];
        for (int i = 0; i < testData.length; i++) {
            arr[i] = maxHeap.extractMax();
        }

        for (int i = 1; i < testData.length; i++) {
            if (arr[i - 1] < arr[i])
                throw new IllegalArgumentException("Error");
        }
        System.out.println("Test maxHeap completed.");

        long endTime = System.nanoTime();
        return (endTime - startTime) * 1000000000.0;
    }
}

数据结构拆解

维护字段和内部类

     private Array<E> data;

    

构造函数

    public MaxHeap(int capacity) {
        data = new Array<>(capacity);
    }

    public MaxHeap() {
        data = new Array<>();
    }

    public MaxHeap(E[] arr) {

        data = new Array<>(arr);
        for (int i = parent(arr.length - 1); i >= 0; i--) {
            siftDown(i);
        }
    }

增

    /**
     * 像堆中添加元素
     * @param e
     */
    public void add(E e) {
        data.addLast(e);
        siftUp(data.getSize() - 1);
    }

删

    /**
     * 取出堆中最大元素
     * @return
     */
    public E extractMax() {
        E ret = findMax();
        data.swap(0, data.getSize() - 1);
        data.removeLast();
        siftDown(0);

        return ret;
    }

改

    private void siftUp(int k) {
        while (k > 0 && data.get(parent(k)).compareTo(data.get(k)) < 0) {
            data.swap(k, parent(k));
            k = parent(k);
        }
    }

    private void siftDown(int k) {
        while (leftChild(k) < data.getSize()) {
            int j = leftChild(k);
            if (j + 1 < data.getSize() && data.get(j + 1).compareTo(data.get(j)) > 0) {
                j++;
            }
            // data[j] 是leftChild和rightChild中的最大值
            if (data.get(k).compareTo(data.get(j)) >= 0)
                break;

            data.swap(k, j);
            k = j;
        }
    }

    public E replace(E e) {

        E ret = findMax();
        data.set(0, e);
        siftDown(0);
        return ret;
    }

查

    /**
     * 返回堆中的元素个数
     * @return
     */
    public int size() {
        return data.getSize();
    }

    /**
     * 返回一个布尔值，表示堆中是否为空
     */
    public boolean isEmpty() {
        return data.isEmpty();
    }

    /**
     * 返回完全二叉树的数组表示中，一个索引所表示的元素的父亲节点的索引
     * @param index
     * @return
     */
    private int parent(int index) {
        if (index == 0)
            throw new IllegalArgumentException("index-0 doesn't have parent.");
        return (index - 1) / 2;
    }

    /**
     * 返回完全二叉树的数组表示中，一个索引所表示的元素的左孩子节点的索引
     * @param index
     * @return
     */
    private int leftChild(int index) {
        return index * 2 + 1;
    }


    private int rightChild(int index) {
        return index * 2 + 2;
    }

    

    public E findMax() {
        if (data.getSize() == 0) {
            throw new IllegalArgumentException("Can not findMax when heap is empty.");
        }
        return data.get(0);
    }

测试用例

    public static void main(String[] args) {

        int n = 1000000;

        Random random = new Random();
        Integer[] testData = new Integer[n];
        for (int i = 0; i < n; i++) {
            testData[i] = random.nextInt(Integer.MAX_VALUE);
        }

        double time1 = testHeap(testData, false);
        System.out.println("Without heapify: " + time1 + " s");

        double time2 = testHeap(testData, true);
        System.out.println("With heapify: " + time2 + " s");
    }

    private static double testHeap(Integer[] testData, boolean isHeapify) {
        long startTime = System.nanoTime();

        MaxHeap<Integer> maxHeap;
        if (isHeapify) {
            maxHeap = new MaxHeap<>(testData);
        }
        else {
            maxHeap = new MaxHeap<>();
            for (int num: testData)
                maxHeap.add(num);
        }

        int[] arr = new int[testData.length];
        for (int i = 0; i < testData.length; i++) {
            arr[i] = maxHeap.extractMax();
        }

        for (int i = 1; i < testData.length; i++) {
            if (arr[i - 1] < arr[i])
                throw new IllegalArgumentException("Error");
        }
        System.out.println("Test maxHeap completed.");

        long endTime = System.nanoTime();
        return (endTime - startTime) * 1000000000.0;
    }