最大堆

二叉堆：

　　堆排序时间复杂度O(nlgn)

package com.bing;

import java.util.Arrays; 
//ywb
public class HeapSort {
    
    
    //首先假设 以left(i) ,right(i) 为根节点的子树满足最大堆性质
    public static  <T extends Comparable<? super T>> void  max_HeapIf_Y(T[] A,int i,int heapSize)
    {
        int l=left(i),r=right(i),largest;
        if(l<=heapSize && A[i].compareTo(A[l])<0)
        {
            largest = l;
        }else
        {
            largest = i;
        }
        if(r<=heapSize && A[largest].compareTo(A[r])<0)
        {
            largest = r;
        }
        if(largest!=i)
        {
            exchange(A,i,largest);
            max_HeapIf_Y(A,largest,heapSize);
        }
        
    }
    
    public static <T extends Comparable<? super T>> void build_max_heap(T[] A,int heapSize) 
    {
        
        for(int i=A.length/2;i>=0;i--)
        {
            max_HeapIf_Y(A,i,heapSize);
        }
    }
    
    public static <T extends Comparable<? super T>> void heapSort(T[] A) 
    {
        build_max_heap(A,A.length-1);
        int heapSize = A.length-1;
        for(int i=A.length-1;i>=1;i--)
        {
            exchange(A,0,i);
            heapSize--;
            max_HeapIf_Y(A,0,heapSize);
        }
    }
    public static void main(String[] args) {
        Integer[] a = {8,9,6,3,7,0,2,15,-1,8,8,28,4,0,45,78,22
                ,2000,3243,4,0,4,4,48,3,33,55,11,22,9};
        System.out.println(Arrays.toString(a));
        long start = System.nanoTime();
        heapSort(a);
        long end = System.nanoTime();
        System.out.println(Arrays.toString(a));
        System.out.println(end - start);
        
    }
    public static int left(int i)
    {
        return 2*i+1;    
    }
    public static int right(int i)
    {
        return 2*i+2;    
    }
    public static int parent(int i)
    {
        return i/2;    
    }
    public static <T> void exchange(T[] A,int i,int j){
        T temp = A[i];
        A[i] = A[j];
        A[j] = temp;
    }
    
}

　

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