poj 2442 Sequence

http://poj.org/problem?id=2442

题意：给出m个序列，每个序列有n个数，从每个序列中选择一个数相加，总共有n^m个数，输出这些数中最小的n个数；

思路：用的是stl中的heap(堆)从上到下层层维护堆，堆的复杂度为nlogn；

代码：

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
int a[2010] = {0};
int b[2010] = {0};
int heap[2010] = {0};
int main()
{
    int w = 0;
    scanf("%d",&w);
    int n = 0;
    int m = 0;
    while(w--)
    {
     scanf("%d%d",&m,&n);
     for(int i = 0;i < n; ++i)
     scanf("%d",&a[i]);
     sort(a,a+n);
     while(--m)
     {
         for(int i = 0;i < n; ++i)
         scanf("%d",&b[i]);
         sort(b,b+n);
         for(int i = 0;i < n; ++i)
         heap[i] = a[i] + b[0];
         make_heap(heap,heap+n);
         for(int i = 1;i < n; ++i)
         {
             int biao = 0;
            for(int j = 0;j < n; ++j)
            {
                int temp = b[i] + a[j];
                if(temp < heap[0])
                {
                    pop_heap(heap,heap+n);
                    heap[n-1] = temp;
                    push_heap(heap,heap+n);
                    biao = 0;
                }
                else
                    break;
            }
            if(biao)
            break;
         }
         sort_heap(heap,heap+n);
         for(int i = 0;i < n; ++i)
         a[i] = heap[i];

     }
     for(int i = 0;i < n - 1; ++i)
      printf("%d ",a[i]);
      printf("%d\n",a[n-1]);
    }
    return 0;
}

堆的讲解：

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 }

来自: http://hi.baidu.com/solofancy/blog/item/1ab517384c1147f93a87cee0.html