堆排序算法 java 实现

堆排序算法 java 实现

白话经典算法系列之七 堆与堆排序

Java排序算法（三）：堆排序

算法概念

堆排序(HeapSort)是指利用堆积树（堆）这种数据结构所设计的一种排序算法，可以利用数组的特点快速定位指定索引的元素。堆排序是不稳定的排序方法，辅助空间为O(1)， 最坏时间复杂度为O(nlog2n) ，堆排序的堆序的平均性能较接近于最坏性能。

算法思想

1. 建立最小堆；

2. 取出堆顶元素，顺序放到待排序数组中；将堆底元素放到堆顶，并重新调整堆；

3. 重复步骤 2 ，直至堆中所有元素全部取完；

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参考的两篇文章都是将堆顶元素和堆底元素互换，最后存放堆的数组就变成了有序数组。

1. 建立最大堆；
2. 将堆顶元素和堆底元素互换；重新调整除堆底有序元素外的堆；
3. 重复步骤 2 ，直至堆中全部元素都变有序；

算法实现

package com.lygedi.sort;

import org.apache.commons.lang.ArrayUtils;
import org.apache.commons.lang.StringUtils;

public class HeapSort {
	public static void main(String[] args) {
		int a[] = { 49, 38, 65, 9, 76, 13, 27, 49, 8, 34, 12, 64, 49, 56, 2, 51, 13, 5, 4, 62, 99, 98, 54, 56, 17, 17,
				18, 23, 34, 56, 15, 35, 25, 53, 51 };

		int[] b = a.clone();
		
		HeapSort hs = new HeapSort();
		hs.sortByMinHeapClass(a);
		hs.sortByOneMothed(b);
		
		System.out.println(a.length);
		for (int i = 0; i < a.length; i++)
			System.out.println(Integer.toString(i) + "-" + a[i] + "--" + b[i]);
	}
	
	public void sortByMinHeapClass(int[] list) {
		MinHeap mh = new MinHeap(list);
		System.out.println(mh);
		for (int i = 0; i < list.length; i++) {
			list[i] = mh.pushTop();
		}
	}
	
	public void sortByOneMothed(int[] list){
		for(int i = list.length-1; i>=0; i--){
			initMaxHeap(list,0,i);
			swap(list,0,i);
		}
	}

	private void initMaxHeap(int[] list,int startIndex,int stopIndex){
		int leftChild, rightChild;
		boolean isChanged = false;
		
		for(int i=startIndex;i<=stopIndex;i++){
			leftChild = i*2 + 1;
			rightChild = i*2 + 2;
			
			if(leftChild<=stopIndex && list[i]<list[leftChild]){
				swap(list,i,leftChild);				
				isChanged = true;
			}
			
			if(rightChild<=stopIndex && list[i]<list[rightChild]){
				swap(list,i,rightChild);	
				isChanged = true;
			}
			
			if(i>startIndex && isChanged){
				i = (i - 1)/2 - 1;
				isChanged = false;
			}
		}
	}
	
	private void swap(int[] list,int i,int j){
		int temp = list[i];
		list[i] = list[j];
		list[j] = temp;
	}
}

class MinHeap {
	private int[] heap;

	public MinHeap(int[] list) {
		heap = list;
		fixHeap();
	}

	public int pushTop() {
		int top = heap[0];
		int tail = heap[heap.length - 1];

		if (heap.length > 1) {
			int[] newheap = ArrayUtils.subarray(heap, 0, heap.length - 1);
			newheap[0] = tail;

			heap = newheap;
			fixHeap();
		}

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

	private void fixHeap() {
		int leftChild, rightChild;
		boolean isChanged = false;

		for (int i = 0; i < heap.length; i++) {
			leftChild = i * 2 + 1;
			rightChild = i * 2 + 2;

			if (leftChild <= heap.length - 1 && heap[i] > heap[leftChild]) {
				swap(heap,i,leftChild);	
				isChanged = true;
			}

			if (rightChild <= heap.length - 1 && heap[i] > heap[rightChild]) {
				swap(heap,i,rightChild);

				isChanged = true;
			}
            //如果子节点进行了调整，则要对父节点重新进行调整
			if (isChanged && i > 0) {
				i = (i - 1) / 2 - 1;
				isChanged = false;
			}
		}
	}

	public String toString() {
		StringBuilder sb = new StringBuilder();
		int count = heap.length;
		int grade = (int) Math.ceil(java.lang.StrictMath.pow(count, 1.0 / 2));
		
		String padding = "**";

		int index = 0;
		for (int i = 1; i <= grade; i++) {
			int padNum = (int)Math.pow(2, grade-i+1)-1;
			String gradePadding = StringUtils.repeat(padding, padNum);
			
			for (int j = 1; j <= Math.pow(2, i - 1); j++) {
				if (index < count) {
					sb.append(gradePadding);
					String paddingInt = StringUtils.leftPad(Integer.toString(heap[index]), padding.length(), "*");
					sb.append(paddingInt);
					index++;
					sb.append(gradePadding);
					sb.append(padding);
				}
			}
			sb.append("\r\n\r\n\r\n");
		}

		return sb.toString();
	}
}