堆排序、最大堆、最小堆（精简代码）

直接拿了维基百科的代码，这个是比较精简也比较清晰得：https://zh.wikipedia.org/zh/堆排序

import java.util.Arrays;

public class HeapSort {
    private int[] arr;  //索引0存放第一个元素，不是常见的0不存放东西，由1开始
    public HeapSort(int[] arr) {
        this.arr = arr;
    }

    /**
     * 堆排序的主要入口方法，共两步。
     */
    public void sort() {
        /*
         *  第一步：将数组堆化====这里就是怎么去转化数组为最大堆
         *  beginIndex = 第一个非叶子节点。
         *  从第一个非叶子节点开始即可。无需从最后一个叶子节点开始。
         *  叶子节点可以看作已符合堆要求的节点，根节点就是它自己且自己以下值为最大。
         */
        int len = arr.length - 1;
        int beginIndex = (len - 1) >> 1;  
        //找到第一个非叶子节点，2*n+1=左孩子索引，2*n+2=右孩子索引   n为非叶子节点索引。(len - 1) >> 1整除肯定为n
        for (int i = beginIndex; i >= 0; i--)
            maxHeapify(i, len);  //从第一个非叶子节点开始，保证下面是最大堆
        /*
         * 第二步：对堆化数据排序
         * 每次都是移出最顶层的根节点A[0]，与最尾部节点位置调换，同时遍历长度 - 1。
         * 然后从新整理被换到根节点的末尾元素，使其符合堆的特性。
         * 直至未排序的堆长度为 0。
         */
        for (int i = len; i > 0; i--) {
            swap(0, i);
            maxHeapify(0, i - 1);
        }
    }

    private void swap(int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    /**
     * 调整索引为 index 处的数据，使其符合堆的特性。
     *
     * @param index 需要堆化处理的数据的索引
     * @param len 未排序的堆（数组）的长度
     */
    private void maxHeapify(int index, int len) {
        int li = (index << 1) + 1; // 左子节点索引
        int ri = li + 1;           // 右子节点索引
        int cMax = li;             // 子节点值最大索引，默认左子节点。
        if (li > len) return;      // 左子节点索引超出计算范围，直接返回。
        if (ri <= len && arr[ri] > arr[li]) // 先判断左右子节点，哪个较大。
            cMax = ri;
        if (arr[cMax] > arr[index]) {
            swap(cMax, index);      // 如果父节点被子节点调换，
            maxHeapify(cMax, len);  // 则需要继续判断换下后的父节点是否符合堆的特性。
        }
    }

    /**
     * 测试用例
     *
     * 输出：
     * [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9]
     */
    public static void main(String[] args) {
        int[] arr = new int[] {3, 5, 3, 0, 8, 6, 1, 5, 8, 6, 2, 4, 9, 4, 7, 0, 1, 8, 9, 7, 3, 1, 2, 5, 9, 7, 4, 0, 2, 6};
        new HeapSort(arr).sort();
        System.out.println(Arrays.toString(arr));
    }
}

看一下java.util.PriorityQueue#heapify(最小堆化，如何将一个数组初始化为最小堆，queue为相应的数组)

	/**
     * Establishes the heap invariant (described above) in the entire tree,
     * assuming nothing about the order of the elements prior to the call.
     */
    @SuppressWarnings("unchecked")
    private void heapify() {
    //(size >>> 1) - 1 这个也是找第一个非叶子节点，计算方式有点不一样，size = length
        for (int i = (size >>> 1) - 1; i >= 0; i--)
            siftDown(i, (E) queue[i]);
    }

 	/**
     * Inserts item x at position k, maintaining heap invariant by
     * demoting x down the tree repeatedly until it is less than or
     * equal to its children or is a leaf.可见是构造最小堆
     *
     * @param k the position to fill
     * @param x the item to insert
     */
    private void siftDown(int k, E x) {
        if (comparator != null)
            siftDownUsingComparator(k, x);
        else
            siftDownComparable(k, x);
    }
	private void siftDownComparable(int k, E x) {
        Comparable<? super E> key = (Comparable<? super E>)x;
        int half = size >>> 1;        // loop while a non-leaf
        while (k < half) {
            int child = (k << 1) + 1; // assume left child is least
            Object c = queue[child];
            int right = child + 1;
            if (right < size &&
                ((Comparable<? super E>) c).compareTo((E) queue[right]) > 0)
                c = queue[child = right];
            if (key.compareTo((E) c) <= 0)
                break;
            queue[k] = c;
            k = child;
        }
        queue[k] = key;
    }

PriorityQueue如何向最小堆中插入一个元素

	/**
     * Inserts the specified element into this priority queue.
     *
     * @return {@code true} (as specified by {@link Queue#offer})
     * @throws ClassCastException if the specified element cannot be
     *         compared with elements currently in this priority queue
     *         according to the priority queue's ordering
     * @throws NullPointerException if the specified element is null
     */
    public boolean offer(E e) {
        if (e == null)
            throw new NullPointerException();
        modCount++;
        int i = size;
        if (i >= queue.length)
            grow(i + 1);  //扩容
        size = i + 1; //元素的实际数量加1
        if (i == 0)
            queue[0] = e;
        else
            siftUp(i, e); //因为最下堆是完全二叉树，先直接把元素放在新数组的最后一位，然后向上回溯
        return true;
    }
	/**
     * Inserts item x at position k, maintaining heap invariant by
     * promoting x up the tree until it is greater than or equal to
     * its parent, or is the root.
     *
     * To simplify and speed up coercions and comparisons. the
     * Comparable and Comparator versions are separated into different
     * methods that are otherwise identical. (Similarly for siftDown.)
     *
     * @param k the position to fill
     * @param x the item to insert
     */
    private void siftUp(int k, E x) {
        if (comparator != null)
            siftUpUsingComparator(k, x);
        else
            siftUpComparable(k, x);
    }

    @SuppressWarnings("unchecked")
    private void siftUpComparable(int k, E x) {
        Comparable<? super E> key = (Comparable<? super E>) x;
        while (k > 0) {
            int parent = (k - 1) >>> 1;
            Object e = queue[parent];
            if (key.compareTo((E) e) >= 0)
                break;
            queue[k] = e;
            k = parent;
        }
        queue[k] = key;
    }

    @SuppressWarnings("unchecked")
    private void siftUpUsingComparator(int k, E x) {
        while (k > 0) {
            int parent = (k - 1) >>> 1;
            Object e = queue[parent];
            if (comparator.compare(x, (E) e) >= 0)
                break;
            queue[k] = e;
            k = parent;
        }
        queue[k] = x;
    }