堆

STL里面的堆操作一般用到的只有4个:make_heap();、pop_heap();、push_heap();、sort_heap();

他们的头文件函数是#include <algorithm>

首先是make_heap();

他的函数原型是：void make_heap(first_pointer,end_pointer,compare_function);

一个参数是数组或向量的头指针，第二个向量是尾指针。第三个参数是比较函数的名字。在缺省的时候，默认是大跟堆。（下面的参数都一样就不解释了）

作用：把这一段的数组或向量做成一个堆的结构。范围是(first,last)

然后是pop_heap();

它的函数原型是：void pop_heap(first_pointer,end_pointer,compare_function);

作用：pop_heap()不是真的把最大（最小）的元素从堆中弹出来。而是重新排序堆。它
把first和last交换，然后将[first,last-1)的数据再做成一个堆。

接着是push_heap()

void pushheap(first_pointer,end_pointer,compare_function);

作用：push_heap()假设由[first,last-1)是一个有效的堆，然后，再把堆中的新元素加
进来，做成一个堆。

最后是sort_heap()

void sort_heap(first_pointer,end_pointer,compare_function);
作用是sort_heap对[first,last)中的序列进行排序。它假设这个序列是有效堆。（当然
，经过排序之后就不是一个有效堆了）

下面是例程：

#include<algorithm>

#include<cstdio>

using namespace std;

bool cmp(int a,int b)

{
return a>b;
}
int main()
{
int i,number[20]={29,23,20,22,17,15,26,51,19,12,35,40};

make_heap(&number[0],&number[12]);

//结果是:51 35 40 23 29 20 26 22 19 12 17 15

for(i=0;i<12;i++)

printf("%d ",number[i]);

printf("\n");

make_heap(&number[0],&number[12],cmp);

//结果：12 17 15 19 23 20 26 51 22 29 35 40

for(i=0;i<12;i++)

printf("%d ",number[i]);

printf("\n");

//加入元素8

number[12]=8;

//加入后调整

push_heap(&number[0],&number[13],cmp);

//结果：8 17 12 19 23 15 26 51 22 35 40 20

for(i=0;i<13;i++)

printf("%d ",number[i]);

printf("\n");

//弹出元素8

pop_heap(&number[0],&number[13],cmp);

//结果：12 17 15 19 23 20 26 51 22 29 35 40

for(i=0;i<13;i++)

printf("%d ",number[i]);

printf("\n");

sort_heap(&number[0],&number[12],cmp);

//结果不用说都知道是有序的了！

for(i=0;i<12;i++)

printf("%d ",number[i]);

return 0;

}
Compile options needed: /GX
//
// heap_functions.cpp : Illustrates how to use the
// make_heap, sort_heap, push_heap
// and pop_heap functions.
//
// Functions:
//
// make_heap : convert a sequence to a heap
// sort_heap : sort a heap
// push_heap : insert an element in a heap
// pop_heap : remove the top element from a heap
//
// Written by Kalindi Sanghrajka
// of Microsoft Product Support Services,
// Software Core Developer Support.
// Copyright (c) 1996 Microsoft Corporation. All rights reserved.
//////////////////////////////////////////////////////////////////////

// disable warning C4786: symbol greater than 255 character,
// okay to ignore
#pragma warning(disable: 4786)

#include <iostream>
#include <algorithm>
#include <functional>
#include <vector>
using namespace std;
void main()
{
const int VECTOR_SIZE = 8 ;

// Define a template class vector of int
typedef vector<int, allocator<int> > IntVector ;

//Define an iterator for template class vector of strings
typedef IntVector::iterator IntVectorIt ;

IntVector Numbers(VECTOR_SIZE) ;

IntVectorIt it ;

// Initialize vector Numbers
Numbers[0] = 4 ;
Numbers[1] = 10;
Numbers[2] = 70 ;
Numbers[3] = 10 ;
Numbers[4] = 30 ;
Numbers[5] = 69 ;
Numbers[6] = 96 ;
Numbers[7] = 100;

// print content of Numbers
cout << "Numbers { " ;
for(it = Numbers.begin(); it != Numbers.end(); it++)
cout << *it << " " ;
cout << " }\n" << endl ;

// convert Numbers into a heap
make_heap(Numbers.begin(), Numbers.end()) ;

cout << "After calling make_heap\n" << endl ;

// print content of Numbers
cout << "Numbers { " ;
for(it = Numbers.begin(); it != Numbers.end(); it++)
cout << *it << " " ;
cout << " }\n" << endl ;

// sort the heapified sequence Numbers
sort_heap(Numbers.begin(), Numbers.end()) ;

cout << "After calling sort_heap\n" << endl ;

// print content of Numbers
cout << "Numbers { " ;
for(it = Numbers.begin(); it != Numbers.end(); it++)
cout << *it << " " ;
cout << " }\n" << endl ;

//insert an element in the heap
Numbers.push_back(7) ;
push_heap(Numbers.begin(), Numbers.end()) ;

// you need to call make_heap to re-assert the
// heap property
make_heap(Numbers.begin(), Numbers.end()) ;

cout << "After calling push_heap and make_heap\n" << endl ;

// print content of Numbers
cout << "Numbers { " ;
for(it = Numbers.begin(); it != Numbers.end(); it++)
cout << *it << " " ;
cout << " }\n" << endl ;

// remove the root element from the heap Numbers
pop_heap(Numbers.begin(), Numbers.end()) ;

cout << "After calling pop_heap\n" << endl ;

// print content of Numbers
cout << "Numbers { " ;
for(it = Numbers.begin(); it != Numbers.end(); it++)
cout << *it << " " ;
cout << " }\n" << endl ;
}
程序输出为：
Numbers { 4 10 70 10 30 69 96 100 }
之后调用 make_heap
Numbers { 100 30 96 10 4 69 70 10 }
之后调用 sort_heap
Numbers { 4 10 10 30 69 70 96 100 }
之后调用 push_heap 和 make_heap
Numbers { 100 69 96 30 4 70 10 10 7 }
之后调用 pop_heap
Numbers { 96 69 70 30 4 7 10 10 100 }

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//用堆实现k个有序序列的排序，即给出k个有序序列，每个序列n个元素，得到总的有序序列

#include<iostream>
#include<algorithm>
#include<cstring>
#include<vector>
#define maxint 0x3f3f3f3f
using namespace std;


struct point
{
int x;  //第几个序列 
int y;  //值 
};
bool cmp(point a,point b)
{
return a.y>b.y;
}
vector<int> sort(vector< vector<int> > arr,int k,int n)
{
//建堆,数组 
point h[k];
vector<int> ans; 
int flag[k];              //记录每个序列当前所指的下标 
memset(flag,0,sizeof(flag));
for(int i=0;i<k;i++)
{
h[i].x=i;
h[i].y=arr[i][0];
}
make_heap(h,h+k,cmp);
//对堆操作 
for(int i=0;i<n*k;i++)
{
   pop_heap(h,h+k,cmp);
   ans.push_back(h[k-1].y);
   h[k-1].y=arr[ h[k-1].x ][ ++flag[ h[k-1].x ] ];
   push_heap(h,h+k,cmp);
}
return ans;

}
int main()
{
int n,k;
cout<<"请输入序列数k=";
cin>>k;
cout<<"请输入每个序列的数字个数n=";
cin>>n; 
vector<int> a(2*n,maxint);        //取完该数组后，放入maxint 
vector< vector<int> > arr(k,a);
cout<<"请输入各个序列的具体数值："<<endl; 
for(int i=0;i<k;i++)
{
for(int j=0;j<n;j++)
{
cin>>arr[i][j];
}
}
vector<int> ans;
ans=sort(arr,k,n);
cout<<"排序结果为："; 
for(int i=0;i<n*k;i++)
{
cout<<ans[i]<<' ';
}
}