找到无序数组的第K大的数，实现思路有很多种，我们这次尝试下使用堆来实现。
时间复杂度 O(nlogk)

image.png

public static void main(String[] args) {

        int[] nums = { 1 ,3 ,4 ,8 ,9 ,7};

        // 模拟新元素直接入堆顶，然后调整堆顶位置
        nums[0] = 5;
        adjustHeap(nums, 0, nums.length-1);

        for (int num : nums) {
            System.out.println(num);
        }

    }

    /**
     * @param nums
     * @param adjustIndex  需要调整的位置
     * @param maxIndex 堆最大的size
     */
    public static void adjustHeap(int[] nums ,int adjustIndex ,int maxIndex) {

        int index = adjustIndex * 2 + 1;
        while (index <= maxIndex) {
            if ((index + 1) < maxIndex && nums[index] > nums[index + 1]) {
                index++;
            }
            if (nums[adjustIndex] > nums[index]) {

                int temp = nums[index];
                nums[index] = nums[adjustIndex];
                nums[adjustIndex] = temp;

                adjustIndex = index;
                index = adjustIndex * 2 + 1;
            } else {
                break;
            }
        }
    }

Heap的一般操作

package com.baidu.adu.common.benchmark;

import java.util.Arrays;
import java.util.List;

public class Heap {

    private Node[] heapArray;
    private int maxSize;
    private int currentSize;
    public int i1 = 0;
    public int i2 = 0;

    public Heap(int mx) {
        maxSize = mx;
        heapArray = new Node[maxSize];
        currentSize = 0;
    }

    public boolean isEmpty() {
        return currentSize == 0;
    }

    public boolean insert(int key) {
        if (currentSize == maxSize)
            return false;
        Node thenode = new Node(key);
        heapArray[currentSize] = thenode;
        trickleUp(currentSize++);
        return true;
    }

    public void trickleUp(int index) {
        int parent = (index - 1) / 2;
        Node bottom = heapArray[index];
        while (index > 0 && heapArray[parent].getkey() < bottom.getkey()) {

            i1++;
            heapArray[index] = heapArray[parent];
            index = parent;
            parent = (parent - 1) / 2;
        }
        heapArray[index] = bottom;
    }

    public Node remove() {
        Node root = heapArray[0];
        heapArray[0] = heapArray[--currentSize];
        trickleDown(0);
        return root;
    }

    public void trickleDown(int index) {
        int largeChild;
        Node top = heapArray[index];
        while (index < currentSize / 2) {
            i2++;
            int leftChild = 2 * index + 1;
            int rightChild = 2 * index + 2;
            if (rightChild < currentSize && heapArray[leftChild].getkey() < heapArray[rightChild].getkey())
                largeChild = rightChild;
            else
                largeChild = leftChild;
            if (top.getkey() >= heapArray[largeChild].getkey())
                break;
            heapArray[index] = heapArray[largeChild];
            index = largeChild;
        }
        heapArray[index] = top;
    }

    public boolean change(int index, int newvalue) {
        if (index < 0 || index >= currentSize)
            return false;
        int oldvalue = heapArray[index].getkey();
        heapArray[index].setkey(newvalue);
        if (oldvalue < newvalue)
            trickleUp(index);
        else
            trickleDown(index);
        return true;
    }

    public void displayHeap() {
        System.out.print("heapArray:");
        for (int i = 0; i < currentSize; i++) {
            if (heapArray[i] != null)
                System.out.print(heapArray[i].getkey() + "  ");
            else
                System.out.print("--");
        }
        System.out.println("");
        int nBlanks = 32;
        int itemsPerrow = 1;
        int column = 0;
        int j = 0;
        String dots = "........................";
        System.out.println(dots + dots);
        while (currentSize > 0) {
            if (column == 0)
                for (int i = 0; i < nBlanks; i++) {
                    System.out.print(" ");
                }
            System.out.print(heapArray[j].getkey());
            if (++j == currentSize)
                break;
            if (++column == itemsPerrow) {
                nBlanks /= 2;
                itemsPerrow *= 2;
                column = 0;
                System.out.println();
            } else
                for (int i = 0; i < nBlanks * 2 - 2; i++)
                    System.out.print(' ');

        }
        System.out.println("\n" + dots + dots);

    }

    public int getRoot() {

        return heapArray[0].getkey();
    }

    public static void main(String[] args) {

        Heap h = new Heap(10);

        List<Integer> list = Arrays.asList(44, 67, 33, 87, 15, 6, 24, 98, 65, 23, 45, 34, 4, 7, 9, 56, 35, 65, 12, 98);

        h.insert(list.get(0));
        h.insert(list.get(1));
        h.insert(list.get(2));
        h.insert(list.get(3));
        h.insert(list.get(4));
        h.insert(list.get(5));
        h.insert(list.get(6));
        h.insert(list.get(7));

        h.displayHeap();
        h.remove();
        h.displayHeap();

    }
}

package com.baidu.adu.common.benchmark;

public class Node {

    private int iData;

    public Node(int id) {
        iData = id;
    }

    public int getkey() {
        return iData;
    }

    public void setkey(int id) {
        iData = id;
    }

}