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1 比较器与堆

1.1 堆结构

1.1.1 完全二叉树结构

完全二叉树结构:要么本层是满的,要么先满左边的,以下都是完全二叉树

graph TD
A-->B
A-->C
  1. graph TD
    A-->B
    A-->C
    B-->D
    B-->E
    C-->F
    

1.1.2 数组实现堆

用数组实现完全二叉树结构,从数组下标0开始,当成依次补齐二叉树结构的数据

graph TD
0--> 1
0--> 2
1--> 3
1-->4
2-->5
2-->6

某位置i的左孩子下标为:

lchild = 2*i + 1

某位置i的右孩子的下标为:

rchild = 2*i + 2

某位置i的父节点位置为:

parent = (i-1) / 2

当我们不使用数组的0下标,从1位置开始构建完全二叉树时,方便使用位操作:

某位置i的左孩子下标为:

lchild = 2*i <==> i << 1

某位置i的右孩子的下标为:

rchild = 2*i + 1 <==> (i << 1) | 1

某位置i的父节点位置为:

parent = i / 2 <==> i >> 1

1.1.3 大根堆与小根堆

==我们认为堆就是大根堆或者小根堆,既不是大根堆也不是小根堆的完全二叉树只是完全二叉树,不能称之为堆==

1.1.4 构建堆

heapInsert

思路:例如我们要构建一个大根堆,我们把所有的数依次添加到一个数组(下标从0开始)中去,每次添加一个数的时候,要去用找父亲节点的公式parent = (i-1) / 2找到父节点区比较,如果比父节点大就和父节点交换向上移动,移动后再用自己当前位置和父亲节点比较…,小于等于父节点不做处理。这样用户每加一个数,我们都能保证该结构是大根堆,对应代码的push方法

我们的调整代价实际上就是这颗树的高度层数,logN

heapify

原堆结构,删除最大值,继续调整维持成大根堆

思路:我们删除了最大值,也就是arr[0]位置,之后我们把堆最末尾的位置调整到arr[0]位置,堆大小减一。让现在arr[0]位置的数找左右孩子比较…,进行hearify操作,让其沉下去。沉到合适的位置之后,仍然是大根堆。对应代码的pop方法

heapify的下沉操作,仍然是树的高度,logN

堆结构很重要很重要

package class04;

public class Code02_Heap01 {

	public static class MyMaxHeap {
	        // 我们的大根堆 
		private int[] heap;
		private final int limit;
		// 表示目前这个堆收集了多少个数,也表示添加的下一个数应该放在哪个位置
		private int heapSize;

		public MyMaxHeap(int limit) {
			heap = new int[limit];
			this.limit = limit;
			heapSize = 0;
		}

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

		public boolean isFull() {
			return heapSize == limit;
		}

                // 每加入一个数,需要动态维持堆结构
		public void push(int value) {
			if (heapSize == limit) {
				throw new RuntimeException("heap is full");
			}
			heap[heapSize] = value;
			// value  heapSize
			heapInsert(heap, heapSize++);
		}

		// 用户此时,让你返回最大值,并且在大根堆中,把最大值删掉
		// 剩下的数,依然保持大根堆组织
		public int pop() {
			int ans = heap[0];
			swap(heap, 0, --heapSize);
			heapify(heap, 0, heapSize);
			return ans;
		}

                // 往堆上添加数,需要用当前位置找父节点比较
		private void heapInsert(int[] arr, int index) {
			// arr[index]
			// arr[index] 不比 arr[index父]大了 , 停
			// index = 0时也停
			while (arr[index] > arr[(index - 1) / 2]) {
				swap(arr, index, (index - 1) / 2);
				index = (index - 1) / 2;
			}
		}

		// 从index位置,往下看,不断的下沉,
		// 停的条件:我的孩子都不再比我大;已经没孩子了
		private void heapify(int[] arr, int index, int heapSize) {
			int left = index * 2 + 1;
			// 左孩子没越界,如果左孩子越界有孩子一定也越界
			while (left < heapSize) {
				// 左右两个孩子中,谁大,谁把自己的下标给largest
				// 什么请款下选择右  ->  (1) 有右孩子   && (2)右孩子的值比左孩子大才行
				// 否则,左
				int largest = left + 1 < heapSize && arr[left + 1] > arr[left] ? left + 1 : left;
				// 左右孩子中最大值,和当前值比较,谁大谁把下标给largest(当前,左,右的最大值下标)
				largest = arr[largest] > arr[index] ? largest : index;
				// index位置上的数比左右孩子的数都大,已经无需下沉
				if (largest == index) {
					break;
				}
				// 交换后,继续找左右孩子进行比较,周而复始
				swap(arr, largest, index);
				index = largest;
				left = index * 2 + 1;
			}
		}

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

	}

        // 暴力,O(N)复杂度实现的大根堆。用来做对数器
	public static class RightMaxHeap {
		private int[] arr;
		private final int limit;
		private int size;

		public RightMaxHeap(int limit) {
			arr = new int[limit];
			this.limit = limit;
			size = 0;
		}

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

		public boolean isFull() {
			return size == limit;
		}

		public void push(int value) {
			if (size == limit) {
				throw new RuntimeException("heap is full");
			}
			arr[size++] = value;
		}

		public int pop() {
			int maxIndex = 0;
			for (int i = 1; i < size; i++) {
				if (arr[i] > arr[maxIndex]) {
					maxIndex = i;
				}
			}
			int ans = arr[maxIndex];
			arr[maxIndex] = arr[--size];
			return ans;
		}

	}

	public static void main(String[] args) {
		int value = 1000;
		int limit = 100;
		int testTimes = 1000000;
		for (int i = 0; i < testTimes; i++) {
			int curLimit = (int) (Math.random() * limit) + 1;
			MyMaxHeap my = new MyMaxHeap(curLimit);
			RightMaxHeap test = new RightMaxHeap(curLimit);
			int curOpTimes = (int) (Math.random() * limit);
			for (int j = 0; j < curOpTimes; j++) {
				if (my.isEmpty() != test.isEmpty()) {
					System.out.println("Oops!");
				}
				if (my.isFull() != test.isFull()) {
					System.out.println("Oops!");
				}
				if (my.isEmpty()) {
					int curValue = (int) (Math.random() * value);
					my.push(curValue);
					test.push(curValue);
				} else if (my.isFull()) {
					if (my.pop() != test.pop()) {
						System.out.println("Oops!");
					}
				} else {
					if (Math.random() < 0.5) {
						int curValue = (int) (Math.random() * value);
						my.push(curValue);
						test.push(curValue);
					} else {
						if (my.pop() != test.pop()) {
							System.out.println("Oops!");
						}
					}
				}
			}
		}
		System.out.println("finish!");

	}

}

1.1.5 堆排序

  1. 对于用户给的所有数据,我们先让其构建成为大根堆
  2. 对于0到N-1位置的数,我们依次让N-1位置的数和0位置的数(全局最大值)交换,此时全局最大值来到了数组最大位置,堆大小减一,再heapify调整成大根堆。再用N-2位置的数和调整后的0位置的数交换,相同操作。直至0位置和0位置交换。每次heapify为logN,交换调整了N次
  3. 所以堆排序的时间复杂度为O(NlogN)
  4. 堆排序额为空间复杂度为O(1),且不存在递归行为
package class04;

import java.util.Arrays;
import java.util.PriorityQueue;

public class Code04_HeapSort {

	// 堆排序额外空间复杂度O(1)
	public static void heapSort(int[] arr) {
		if (arr == null || arr.length < 2) {
			return;
		}
		// O(N*logN),原始版本
//		for (int i = 0; i < arr.length; i++) { // O(N)
//			heapInsert(arr, i); // O(logN)
//		}

                // 优化版本,heapInsert改为heapify。从末尾开始看是否需要heapify=》O(N)复杂度。
                // 但是这只是优化了原有都是构建堆(O(NlogN)),最终的堆排序仍然是O(NlogN)
		for (int i = arr.length - 1; i >= 0; i--) {
			heapify(arr, i, arr.length);
		}
		int heapSize = arr.length;
		swap(arr, 0, --heapSize);
		// O(N*logN)
		while (heapSize > 0) { // O(N)
			heapify(arr, 0, heapSize); // O(logN)
			swap(arr, 0, --heapSize); // O(1)
		}
	}

	// arr[index]刚来的数,往上
	public static void heapInsert(int[] arr, int index) {
		while (arr[index] > arr[(index - 1) / 2]) {
			swap(arr, index, (index - 1) / 2);
			index = (index - 1) / 2;
		}
	}

	// arr[index]位置的数,能否往下移动
	public static void heapify(int[] arr, int index, int heapSize) {
                // 左孩子的下标
		int left = index * 2 + 1; 
                // 下方还有孩子的时候
		while (left < heapSize) { 
			// 两个孩子中,谁的值大,把下标给largest
			// 1)只有左孩子,left -> largest
			// 2) 同时有左孩子和右孩子,右孩子的值<= 左孩子的值,left -> largest
			// 3) 同时有左孩子和右孩子并且右孩子的值> 左孩子的值, right -> largest
			int largest = left + 1 < heapSize && arr[left + 1] > arr[left] ? left + 1 : left;
			// 父和较大的孩子之间,谁的值大,把下标给largest
			largest = arr[largest] > arr[index] ? largest : index;
			if (largest == index) {
				break;
			}
			swap(arr, largest, index);
			index = largest;
			left = index * 2 + 1;
		}
	}

	public static void swap(int[] arr, int i, int j) {
		int tmp = arr[i];
		arr[i] = arr[j];
		arr[j] = tmp;
	}

	// for test
	public static void comparator(int[] arr) {
		Arrays.sort(arr);
	}

	// for test
	public static int[] generateRandomArray(int maxSize, int maxValue) {
		int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
		for (int i = 0; i < arr.length; i++) {
			arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
		}
		return arr;
	}

	// for test
	public static int[] copyArray(int[] arr) {
		if (arr == null) {
			return null;
		}
		int[] res = new int[arr.length];
		for (int i = 0; i < arr.length; i++) {
			res[i] = arr[i];
		}
		return res;
	}

	// for test
	public static boolean isEqual(int[] arr1, int[] arr2) {
		if ((arr1 == null && arr2 != null) || (arr1 != null && arr2 == null)) {
			return false;
		}
		if (arr1 == null && arr2 == null) {
			return true;
		}
		if (arr1.length != arr2.length) {
			return false;
		}
		for (int i = 0; i < arr1.length; i++) {
			if (arr1[i] != arr2[i]) {
				return false;
			}
		}
		return true;
	}

	// for test
	public static void printArray(int[] arr) {
		if (arr == null) {
			return;
		}
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
	}

	// for test
	public static void main(String[] args) {

		// 默认小根堆
		PriorityQueue<Integer> heap = new PriorityQueue<>();
		heap.add(6);
		heap.add(8);
		heap.add(0);
		heap.add(2);
		heap.add(9);
		heap.add(1);

		while (!heap.isEmpty()) {
			System.out.println(heap.poll());
		}

		int testTime = 500000;
		int maxSize = 100;
		int maxValue = 100;
		boolean succeed = true;
		for (int i = 0; i < testTime; i++) {
			int[] arr1 = generateRandomArray(maxSize, maxValue);
			int[] arr2 = copyArray(arr1);
			heapSort(arr1);
			comparator(arr2);
			if (!isEqual(arr1, arr2)) {
				succeed = false;
				break;
			}
		}
		System.out.println(succeed ? "Nice!" : "Fucking fucked!");

		int[] arr = generateRandomArray(maxSize, maxValue);
		printArray(arr);
		heapSort(arr);
		printArray(arr);
	}

}

关于上述heapInsert改为heapIfy的优化:

在我们从0到N-1进行heapInsert的时候,是O(NlogN)不做解释,当我们从N-1到0上依次heapify的时候,整体来看,整棵树的跟节点的heapify层数N/2,第二层为N/4且有两个节点。那么实质是N个不同的层数相加:

T(N) = (\frac{N}{2} * 1) + (\frac{N}{4} * 2) + (\frac{N}{8} * 3) + (\frac{N}{16} * 4) + ... 

=>

2T(N) = (\frac{N}{2} * 2) + (\frac{N}{2} * 2) + (\frac{N}{4} * 3) + (\frac{N}{8} * 4) + ... 

=>

T(N) = N + \frac{N}{2} + \frac{N}{4} + \frac{N}{8} + ...

=> O(N)

1.1.6 语言、系统提供的堆和手写堆的选择

1.1.6.1 系统实现的堆

系统实现的堆实质上就是优先级队列,虽然名称叫优先级队列,底层就是堆实现的。默认是小根堆,我们可以自定义比较器把它改为大根堆

package class04;

import java.util.Comparator;
import java.util.PriorityQueue;


public class Test {

	//  负数,o1 放在上面的情况
	public static class MyComp implements Comparator<Integer>{

		@Override
		public int compare(Integer o1, Integer o2) {
			return o2 - o1;
		}
		
	}
	
	
	
	public static void main(String[] args) {
		System.out.println("hello");
		// 大根堆
		PriorityQueue<Integer> heap = new PriorityQueue<>(new MyComp());
		
		heap.add(5);
		heap.add(7);
		heap.add(3);
		heap.add(0);
		heap.add(2);
		heap.add(5);
		
		while(!heap.isEmpty()) {
			System.out.println(heap.poll());
		}
    
	}
}

堆的相关面试题:

题目一:已知一个几乎有序的数组。几乎有序是指,如果把数组排好序的话,每个元素移动的距离一定不超过k,并且k相对于数组长度来说是比较小的。请选择一个合适的排序策略,对这个数组进行排序

思路:例如给定一个数组,k=5,那么我们从0开始,前K+1个数也就是0到5位置的数放到小根堆,排序之后把最小的放到0位置,接下来把6位置放小根堆(此时小根堆里面有0到6位置的数),由于0位置的数有距离限制只能从0到5上选择,所以此时弹出最小值放到1位置,此时1位置被固定…

package class04;

import java.util.Arrays;
import java.util.PriorityQueue;

public class Code05_SortArrayDistanceLessK {

	public static void sortedArrDistanceLessK(int[] arr, int k) {
		if (k == 0) {
			return;
		}
		// 默认小根堆
		PriorityQueue<Integer> heap = new PriorityQueue<>();
		int index = 0;
		// 0...K-1
		for (; index <= Math.min(arr.length - 1, k - 1); index++) {
			heap.add(arr[index]);
		}
		int i = 0;
		for (; index < arr.length; i++, index++) {
			heap.add(arr[index]);
			arr[i] = heap.poll();
		}
		while (!heap.isEmpty()) {
			arr[i++] = heap.poll();
		}
	}

	// for test
	public static void comparator(int[] arr, int k) {
		Arrays.sort(arr);
	}

	// for test
	public static int[] randomArrayNoMoveMoreK(int maxSize, int maxValue, int K) {
		int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
		for (int i = 0; i < arr.length; i++) {
			arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
		}
		// 先排个序
		Arrays.sort(arr);
		// 然后开始随意交换,但是保证每个数距离不超过K
		// swap[i] == true, 表示i位置已经参与过交换
		// swap[i] == false, 表示i位置没有参与过交换
		boolean[] isSwap = new boolean[arr.length];
		for (int i = 0; i < arr.length; i++) {
			int j = Math.min(i + (int) (Math.random() * (K + 1)), arr.length - 1);
			if (!isSwap[i] && !isSwap[j]) {
				isSwap[i] = true;
				isSwap[j] = true;
				int tmp = arr[i];
				arr[i] = arr[j];
				arr[j] = tmp;
			}
		}
		return arr;
	}

	// for test
	public static int[] copyArray(int[] arr) {
		if (arr == null) {
			return null;
		}
		int[] res = new int[arr.length];
		for (int i = 0; i < arr.length; i++) {
			res[i] = arr[i];
		}
		return res;
	}

	// for test
	public static boolean isEqual(int[] arr1, int[] arr2) {
		if ((arr1 == null && arr2 != null) || (arr1 != null && arr2 == null)) {
			return false;
		}
		if (arr1 == null && arr2 == null) {
			return true;
		}
		if (arr1.length != arr2.length) {
			return false;
		}
		for (int i = 0; i < arr1.length; i++) {
			if (arr1[i] != arr2[i]) {
				return false;
			}
		}
		return true;
	}

	// for test
	public static void printArray(int[] arr) {
		if (arr == null) {
			return;
		}
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
	}

	// for test
	public static void main(String[] args) {
		System.out.println("test begin");
		int testTime = 500000;
		int maxSize = 100;
		int maxValue = 100;
		boolean succeed = true;
		for (int i = 0; i < testTime; i++) {
			int k = (int) (Math.random() * maxSize) + 1;
			int[] arr = randomArrayNoMoveMoreK(maxSize, maxValue, k);
			int[] arr1 = copyArray(arr);
			int[] arr2 = copyArray(arr);
			sortedArrDistanceLessK(arr1, k);
			comparator(arr2, k);
			if (!isEqual(arr1, arr2)) {
				succeed = false;
				System.out.println("K : " + k);
				printArray(arr);
				printArray(arr1);
				printArray(arr2);
				break;
			}
		}
		System.out.println(succeed ? "Nice!" : "Fucking fucked!");
	}

}

时间复杂度O(NlogK)

1.1.6.2 系统堆和手写堆选择

使用系统提供的堆:如果我们只是要依次拿最大值,那么做成大根堆,如果我们要最小值我们把堆结构做成小根堆。就是简单的我们添加值,拿值,我们就选择系统提供的堆

选择手写堆:如果已经放到系统堆中的元素,加入我们根据需求会在放入堆之后要改动这些元素的值,系统堆并不保证弹出来的东西是正确的,这个时候需要我们手动写一个我们自定义的堆。虽然存在那种排好堆改某些元素让其重新有序的堆结构,但是实质上它是重新扫每个元素去heapinsert,代价太高。手动改写堆的例子例如Dijkstra算法就存在改写堆的优化

package class04;

import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.PriorityQueue;

public class Code03_Heap02 {

	// 堆
	public static class MyHeap<T> {
	        // 堆结构,数组实现
		private ArrayList<T> heap;
		// 任意一个元素,我们记录它在我们堆上的位置信息(反向表),此时我们找到我们要改的元素的位置就O(1)
		private HashMap<T, Integer> indexMap;
		// 堆大小
		private int heapSize;
		// 比较规则
		private Comparator<? super T> comparator;

                // 构造
		public MyHeap(Comparator<? super T> com) {
			heap = new ArrayList<>();
			indexMap = new HashMap<>();
			heapSize = 0;
			comparator = com;
		}

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

		public int size() {
			return heapSize;
		}

		public boolean contains(T key) {
			return indexMap.containsKey(key);
		}

		public void push(T value) {
			heap.add(value);
			// 由于依次添加元素,添加进来的元素位置就是heapSize
			indexMap.put(value, heapSize);
			heapInsert(heapSize++);
		}

                // 弹出0号位置的元素,要同步堆和字典的操作
		public T pop() {
			T ans = heap.get(0);
			int end = heapSize - 1;
			swap(0, end);
			heap.remove(end);
			indexMap.remove(ans);
			heapify(0, --heapSize);
			return ans;
		}


                // 用来满足自定义的需求,用户要改某个元素的值,我们需要改过之后继续维持堆结构
		public void resign(T value) {
			int valueIndex = indexMap.get(value);
			// 改变值之后,我们不确定是值变大了还是变小了,即不确定是需要heapInsert还是heapify,但是两个操作只会命中一个
			heapInsert(valueIndex);
			heapify(valueIndex, heapSize);
		}

                // heapInsert时,需要用我们自己的比较器进行比较
		private void heapInsert(int index) {
			while (comparator.compare(heap.get(index), heap.get((index - 1) / 2)) < 0) {
				swap(index, (index - 1) / 2);
				index = (index - 1) / 2;
			}
		}

		private void heapify(int index, int heapSize) {
			int left = index * 2 + 1;
			while (left < heapSize) {
				int largest = left + 1 < heapSize && (comparator.compare(heap.get(left + 1), heap.get(left)) < 0)
						? left + 1
						: left;
				largest = comparator.compare(heap.get(largest), heap.get(index)) < 0 ? largest : index;
				if (largest == index) {
					break;
				}
				swap(largest, index);
				index = largest;
				left = index * 2 + 1;
			}
		}

                // 每次交换,不经要交换堆中两个位置的元素,在我们的字典中也要要换位置
		private void swap(int i, int j) {
			T o1 = heap.get(i);
			T o2 = heap.get(j);
			heap.set(i, o2);
			heap.set(j, o1);
			indexMap.put(o1, j);
			indexMap.put(o2, i);
		}

	}

	public static class Student {
		public int classNo;
		public int age;
		public int id;

		public Student(int c, int a, int i) {
			classNo = c;
			age = a;
			id = i;
		}

	}

	public static class StudentComparator implements Comparator<Student> {

		@Override
		public int compare(Student o1, Student o2) {
			return o1.age - o2.age;
		}

	}

	public static void main(String[] args) {
		Student s1 = null;
		Student s2 = null;
		Student s3 = null;
		Student s4 = null;
		Student s5 = null;
		Student s6 = null;

		s1 = new Student(2, 50, 11111);
		s2 = new Student(1, 60, 22222);
		s3 = new Student(6, 10, 33333);
		s4 = new Student(3, 20, 44444);
		s5 = new Student(7, 72, 55555);
		s6 = new Student(1, 14, 66666);

		PriorityQueue<Student> heap = new PriorityQueue<>(new StudentComparator());
		heap.add(s1);
		heap.add(s2);
		heap.add(s3);
		heap.add(s4);
		heap.add(s5);
		heap.add(s6);
		while (!heap.isEmpty()) {
			Student cur = heap.poll();
			System.out.println(cur.classNo + "," + cur.age + "," + cur.id);
		}

		System.out.println("===============");

		MyHeap<Student> myHeap = new MyHeap<>(new StudentComparator());
		myHeap.push(s1);
		myHeap.push(s2);
		myHeap.push(s3);
		myHeap.push(s4);
		myHeap.push(s5);
		myHeap.push(s6);
		while (!myHeap.isEmpty()) {
			Student cur = myHeap.pop();
			System.out.println(cur.classNo + "," + cur.age + "," + cur.id);
		}

		System.out.println("===============");

		s1 = new Student(2, 50, 11111);
		s2 = new Student(1, 60, 22222);
		s3 = new Student(6, 10, 33333);
		s4 = new Student(3, 20, 44444);
		s5 = new Student(7, 72, 55555);
		s6 = new Student(1, 14, 66666);

		heap = new PriorityQueue<>(new StudentComparator());

		heap.add(s1);
		heap.add(s2);
		heap.add(s3);
		heap.add(s4);
		heap.add(s5);
		heap.add(s6);

		s2.age = 6;
		s4.age = 12;
		s5.age = 10;
		s6.age = 84;

		while (!heap.isEmpty()) {
			Student cur = heap.poll();
			System.out.println(cur.classNo + "," + cur.age + "," + cur.id);
		}

		System.out.println("===============");

		s1 = new Student(2, 50, 11111);
		s2 = new Student(1, 60, 22222);
		s3 = new Student(6, 10, 33333);
		s4 = new Student(3, 20, 44444);
		s5 = new Student(7, 72, 55555);
		s6 = new Student(1, 14, 66666);

		myHeap = new MyHeap<>(new StudentComparator());

		myHeap.push(s1);
		myHeap.push(s2);
		myHeap.push(s3);
		myHeap.push(s4);
		myHeap.push(s5);
		myHeap.push(s6);

		s2.age = 6;
		myHeap.resign(s2);
		s4.age = 12;
		myHeap.resign(s4);
		s5.age = 10;
		myHeap.resign(s5);
		s6.age = 84;
		myHeap.resign(s6);

		while (!myHeap.isEmpty()) {
			Student cur = myHeap.pop();
			System.out.println(cur.classNo + "," + cur.age + "," + cur.id);
		}
		
		// 对数器
		System.out.println("test begin");
		int maxValue = 100000;
		int pushTime = 1000000;
		int resignTime = 100;
		MyHeap<Student> test = new MyHeap<>(new StudentComparator());
		ArrayList<Student> list = new ArrayList<>();
		for(int i = 0 ; i < pushTime; i++) {
			Student cur = new Student(1,(int) (Math.random() * maxValue), 1000);
			list.add(cur);
			test.push(cur);
		}
		for(int i = 0 ; i < resignTime; i++) {
			int index = (int)(Math.random() * pushTime);
			list.get(index).age = (int) (Math.random() * maxValue);
			test.resign(list.get(index));
		}
		int preAge = Integer.MIN_VALUE;
		while(test.isEmpty()) {
			Student cur = test.pop();
			if(cur.age < preAge) {
				System.out.println("Oops!");
			}
			preAge = cur.age;
		}
		System.out.println("test finish");
	}

}

1.2 比较器

1、比较器的实质就是重载比较运算符

2、比较器可以很好的应用在特殊标准的排序上

3、比较器可以很好的应用在根据特殊标准排序的结构上

任何有序结构,我们可以传入我们的比较器,自定义我们自己的排序规则,不传它会按自己默认的规则排序

4、写代码变得异常容易,还用于泛型编程

比较规则中o1,o2,比较器返回负数表示o1要排在前面,返回正数表示o1要排在后面,返回0表示o1和o1相等无需排序。在java中自定义的比较器(MyComparator)实现Comparator接口,实现该接口中的compare方法,自定义我们的比较规则。

使用示例:Arrays.sort(student, new MyComparator())

package class04;

import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.TreeSet;

public class Code01_Comparator {

        // 自定义我们的排序对象
	public static class Student {
		public String name;
		public int id;
		public int age;

		public Student(String name, int id, int age) {
			this.name = name;
			this.id = id;
			this.age = age;
		}
	}

	public static class IdAscendingComparator 
	
	implements Comparator<Student> {

		// 返回负数的时候,第一个参数排在前面
		// 返回正数的时候,第二个参数排在前面
		// 返回0的时候,谁在前面无所谓
		@Override
		public int compare(Student o1, Student o2) {
			return o1.id - o2.id;
		}

	}

	public static class IdDescendingComparator implements Comparator<Student> {

		@Override
		public int compare(Student o1, Student o2) {
			return o2.id - o1.id;
		}

	}

	public static class AgeAscendingComparator implements Comparator<Student> {

		@Override
		public int compare(Student o1, Student o2) {
			return o1.age - o2.age;
		}

	}

	public static class AgeDescendingComparator implements Comparator<Student> {

		@Override
		public int compare(Student o1, Student o2) {
			return o2.age - o1.age;
		}

	}
	
	
	public static class AgeShengIdSheng implements Comparator<Student> {

		@Override
		public int compare(Student o1, Student o2) {
			return o1.age != o2.age ? (o1.age - o2.age) 
					: (o1.id - o2.id);
		}

	}
	
	
	// 先按照id排序,id小的,放前面;
	// id一样,age大的,前面;
	public static class IdInAgeDe implements Comparator<Student> {

		@Override
		public int compare(Student o1, Student o2) {
			return o1.id != o2.id ? o1.id - o2.id  : (  o2.age - o1.age  );
		}

	}
	

	public static void printStudents(Student[] students) {
		for (Student student : students) {
			System.out.println("Name : " + student.name + ", Id : " + student.id + ", Age : " + student.age);
		}
	}

	public static void printArray(Integer[] arr) {
		if (arr == null) {
			return;
		}
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
	}

	public static class MyComp implements Comparator<Integer> {

		@Override
		public int compare(Integer o1, Integer o2) {
			return o2 - o1;
		}

	}
	
	
	public static class AComp implements Comparator<Integer>{

		// 如果返回负数,认为第一个参数应该拍在前面
		// 如果返回正数,认为第二个参数应该拍在前面
		// 如果返回0,认为谁放前面都行
		@Override
		public int compare(Integer arg0, Integer arg1) {
			
			return arg1 - arg0;
			
			//	return 0;
		}
		
	}
	

	public static void main(String[] args) {
		
		Integer[] arr = {5,4,3,2,7,9,1,0};
		
		Arrays.sort(arr, new AComp());
		
		for(int i = 0 ;i < arr.length;i++) {
			System.out.println(arr[i]);
		}
		
		System.out.println("===========================");
		
		Student student1 = new Student("A", 2, 20);
		Student student2 = new Student("B", 3, 21);
		Student student3 = new Student("C", 1, 22);

		Student[] students = new Student[] { student1, student2, student3 };
		System.out.println("第一条打印");
		
		
		Arrays.sort(students, new IdAscendingComparator());
		
		
		printStudents(students);
		System.out.println("===========================");
		
		

		Arrays.sort(students, new IdDescendingComparator());
		printStudents(students);
		System.out.println("===========================");

		Arrays.sort(students, new AgeAscendingComparator());
		printStudents(students);
		System.out.println("===========================");
////
////		Arrays.sort(students, new AgeDescendingComparator());
////		printStudents(students);
////		System.out.println("===========================");
//		
//		Arrays.sort(students, new AgeShengIdSheng());
//		printStudents(students);
//		
//		System.out.println("===========================");
//		System.out.println("===========================");
//		System.out.println("===========================");
//
//		PriorityQueue<Student> maxHeapBasedAge = new PriorityQueue<>(new AgeDescendingComparator());
//		maxHeapBasedAge.add(student1);
//		maxHeapBasedAge.add(student2);
//		maxHeapBasedAge.add(student3);
//		while (!maxHeapBasedAge.isEmpty()) {
//			Student student = maxHeapBasedAge.poll();
//			System.out.println("Name : " + student.name + ", Id : " + student.id + ", Age : " + student.age);
//		}
//		System.out.println("===========================");

		PriorityQueue<Student> minHeapBasedId
		= new PriorityQueue<>(new AgeAscendingComparator());
		minHeapBasedId.add(student1);
		minHeapBasedId.add(student2);
		minHeapBasedId.add(student3);
		while (!minHeapBasedId.isEmpty()) {
			Student student = minHeapBasedId.poll();
			System.out.println("Name : " + student.name + ", Id : " + student.id + ", Age : " + student.age);
		}
		System.out.println("===========================");
		System.out.println("===========================");
		System.out.println("===========================");

		TreeSet<Student> treeAgeDescending = new TreeSet<>(new AgeAscendingComparator());
		treeAgeDescending.add(student1);
		treeAgeDescending.add(student2);
		treeAgeDescending.add(student3);

		Student studentFirst = treeAgeDescending.first();
		System.out.println("Name : " + studentFirst.name + ", Id : " + studentFirst.id + ", Age : " + studentFirst.age);

		Student studentLast = treeAgeDescending.last();
		System.out.println("Name : " + studentLast.name + ", Id : " + studentLast.id + ", Age : " + studentLast.age);
		System.out.println("===========================");

	}

}