堆排序和优先队列【最大堆】

来源：互联网发布：core java第十版中文编辑：程序博客网时间：2024/05/19 16:21
最大堆性质： A[PARENT(i)]>=A[i]
最大堆排序后是升序哦！
#include <iostream>
using namespace std;
#define N 10
void HEAP_SORT(int a[], int n);
void BUILD_MAX_HEAP(int a[], int n);
void MAX_HEAPIFY(int a[], int n, int i);
int HEAP_EXTRACT_MAX(int a[], int n);
void MAX_HEAP_INSERT(int a[], int n, int key);
int HEAP_INCREASE_KEY(int a[], int n, int i, int key);
int PARENT(int a[], int i);
void exchange(int a[], int i, int j);
int LEFT(int a[], int i);
int RIGHT(int a[], int i);
void PRINT(int a[], int n);
int heap_size=N;
int main()
{
      //数组第一个元素是占据下标为0的空间的。以便让正式的数据从下标1开始。。这样left(i)=2i  rigth(i)=2i+1　
//    int a[N+1]={-12,4,1,3,2,16,9,10,14,8,7};
 //   int heap_size=N;
    int a[N+1]={-12,16,4,10,14,7,9,3,2,8,1};
     MAX_HEAPIFY(a,N+1,2);
     PRINT(a,N+1);
//    BUILD_MAX_HEAP(a,N+1);
/*
    cout<<"begin:        ";
    PRINT(a,N+1);
    HEAP_SORT(a,N+1);
    cout<<"after:        ";
    PRINT(a,N+1);
    */
/*
    int a[N+1]={-12,1,9,10,2,7,5,6,4,13,3,18,11,100};
    cout<<"数组初始化："<<endl;
    PRINT(a,N+1);
    cout<<"建立最大堆："<<endl;
    BUILD_MAX_HEAP(a,N+1);
    PRINT(a,N+1);
    cout<<"删除最大堆的当前最大元素："<<endl;
    HEAP_EXTRACT_MAX(a,N+1);
    cout<<"数组长度： "<<sizeof(a)/sizeof(a[0])<<endl;
    PRINT(a,N);
    cout<<"最大堆第9位的数增加到15："<<endl;
    HEAP_INCREASE_KEY(a,N+1,9,15);
    PRINT(a,N);
    cout<<"最大堆插入一个元素56："<<endl;
    MAX_HEAP_INSERT(a,N+1,56);
    PRINT(a,N+1);
    cout<<"最大堆排序后的数组为："<<endl;
    HEAP_SORT(a,N+1);
    PRINT(a,N+1);
*/
    return 0;
}
int HEAP_MAXIMUM(int a[], int n){
    return a[n-1];
}
int HEAP_EXTRACT_MAX(int a[], int n){
    if(heap_size<1)
        return -12;
    int max1=a[1];
    a[1]=a[heap_size];
    heap_size--;
    MAX_HEAPIFY(a,n,1);
    return max1;
}
int HEAP_INCREASE_KEY(int a[], int n, int i, int key){
    if(key<a[i])
        return -12;
    a[i]=key;
  //  cout<<i<<": "<<a[i]<<" "<<key<<endl;
    while(i>1&&a[PARENT(a,i)]<a[i]){
 //           cout<<i<<":"<<a[i]<<" "<<PARENT(a,i)<<":"<<a[PARENT(a,i)]<<endl;
        exchange(a,i,PARENT(a,i));
        i=PARENT(a,i);
    }
    cout<<"i: "<<i<<endl;
    return 0;
}
void MAX_HEAP_INSERT(int a[], int n, int key){
    heap_size++;
    cout<<"heap_size: "<<heap_size<<endl;
    a[heap_size]=-999;
    HEAP_INCREASE_KEY(a,n,heap_size,key);
}
void HEAP_SORT(int a[], int n){
//    cout<<"after build:  ";
//    PRINT(a,n);
    for(int i=n-1;i>=2;i--){
        exchange(a,1,i);
        heap_size-=1;
        MAX_HEAPIFY(a,n,1);
    }
}
void BUILD_MAX_HEAP(int a[], int n){
    
    //在建堆中 HEAP_SIZE始终不变，初始时就根据输入的数据设定好了！！！
    for(int i=(n-1)/2;i>=1;i--){
        MAX_HEAPIFY(a,n,i);
    }
    cout<<"after build:  ";
    cout<<endl;
    PRINT(a,n);
}
/*
void MAX_HEAPIFY(int a[], int n, int i){
    int l,r;
    l=LEFT(a,i);
    r=RIGHT(a,i);
    int largest=-12;
    if(l<=heap_size&&a[l]>a[i])
        largest=l;
    else
        largest=i;
    if(r<=heap_size&&a[r]>a[largest])
        largest=r;
    if(largest!=i&&largest!=-12){
        exchange(a,i ,largest);
        MAX_HEAPIFY(a,n,largest);
    }
}
*/
void MAX_HEAPIFY(int a[], int n, int i){
    while(i<=heap_size/2){
        int l,r;
        l=LEFT(a,i);
        r=RIGHT(a,i);
        int largest=-12;
        if(l<=heap_size&&a[l]>a[i]){
            largest=l;
        }
        else{
            largest=i;
        }
        if(r<=heap_size&&a[r]>a[largest]){
            largest=r;
        }
        cout<<"largest: "<<largest<<"  a[largest]: "<<a[largest]<<"  i: "<<i<<"  a[i] "<<a[i]<<endl;
        if(largest!=i){
            exchange(a,i ,largest);
            i=largest;   //为什么不能放在这里！！！
         }else{          //错误写法if(largest==i)  因为经过上面if语句后largest必然等于 i 啦！！！
            return;
         }
       //  i=largest;
       cout<<"i "<<i<<" largest "<<largest<<endl;
     }
}
int LEFT(int a[], int i){
        return 2*i;
}
int RIGHT(int a[], int i){
        return 2*i+1;
}
int PARENT(int a[], int i){
    return i/2;
}
void exchange(int a[], int i, int j){
    int temp=a[i];
    a[i]=a[j];
    a[j]=temp;
}
void PRINT(int a[], int n){
    for(int i=1;i<n;i++){
        cout<<a[i]<<" ";
    }
    cout<<endl;
}
参考： http://blog.csdn.net/z84616995z/article/details/17797393#reply
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