堆排序

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堆排序基本概念

堆是一种数据结构，它是将一些数据放在物理数据结构：数组或者vector中；逻辑数据结构是完全二叉树。

如果根节点的值大于两个子节点值，就是大根堆；

如果根节点的值小于两个子节点值，就是小根堆。

用堆这种数据结构来实现排序，就是堆排序。


该算法的操作主要有
minheapify：最小堆处理，复杂度是O(logN)

find_min：找到最小值，复杂度是O(1)

delete_min：删除最小值节点，及根节点，复杂度是O(logN)

build_minheap：建立最小堆，复杂度是O(N)

minheap_sort：最小堆排序，复杂度是O(NlogN)


算法导论中该算法在minheapify时用的是递归，如下程序用的是迭代处理，效率会更高一些；


如下程序实现的是小根堆
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#include<iostream>
#include<cstdio>
#include<stdlib.h>
#include<assert.h>
#include<map>
#include<vector>
using namespace std;
 
void minheapify(vector<double>& minheap,int pos){
    if(pos==(minheap.size()-1))//insert new node and minheapify this node
    {
        while(pos!=1 && minheap[pos]<minheap[pos/2]){
            //swap
            double temp=minheap[pos/2];
            minheap[pos/2]=minheap[pos];
            minheap[pos]=temp;
            //next compare
            pos=pos/2;
        }
    }
    else if(pos==1){//delete root node and swap this node with last node and minheapify root node
        while(1)
        {
            //leave node
            if((pos*2 > minheap.size()-1) && (pos*2+1 > minheap.size()-1))
                break;
                 
            double temp=minheap[pos];
            int loc=pos;
            if((pos*2 <= minheap.size()-1) && minheap[pos]>minheap[pos*2]){
                loc=pos*2;
                temp=minheap[pos*2];
            }
            if((pos*2+1 <= minheap.size()-1) && temp>minheap[pos*2+1]){
                loc=pos*2+1;
                temp=minheap[pos*2+1];
            }
            if(loc!=pos){
                minheap[loc]=minheap[pos];
                minheap[pos]=temp;
                pos=loc;
                continue;
            }
            else if(loc==pos)
                break;
        }
    }
     
}
 
void build_minheap(vector<double>& minheap, double* a, int n){
    for(int i=0;i<n;i++){
        minheap.push_back(a[i]);
        minheapify(minheap,minheap.size()-1);
    }
}
 
double find_min(vector<double>& minheap){
    return minheap[1];
}
 
void delete_min(vector<double>& minheap){
    minheap[1]=minheap[minheap.size()-1];
    minheap.erase(minheap.end()-1);
    minheapify(minheap,1);
}
 
vector<double> minheap_sort(vector<double>& minheap){
    vector<double> result;
    while(minheap.size()>1){
        result.push_back(find_min(minheap));
        delete_min(minheap);       
    }
    return result;
}
 
int main()
{
    vector<double> minheap;
    minheap.push_back(-1);
    int n=5;
    double a[5]={100.1,20,3,5,2};
    build_minheap(minheap,a,n);
    for(int i=0;i<minheap.size();i++)
        cout<<minheap[i]<<" ";
    cout<<endl<<"build complete"<<endl;
     
    vector<double> result;
    result=minheap_sort(minheap);
    for(int i=0;i<result.size();i++)
        cout<<result[i]<<" ";
     
    getchar();
    return 0;
}





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