STL--H - Black Box（两个优先队列，求第k小的值）
H - Black Box
Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u
Description
Our Black Box represents a primitive database. It can save an integer array and has a special i variable. At the initial moment Black Box is empty and i equals 0. This Black Box processes a sequence of commands (transactions). There are two types of transactions:
ADD (x): put element x into Black Box;
GET: increase i by 1 and give an i-minimum out of all integers containing in the Black Box. Keep in mind that i-minimum is a number located at i-th place after Black Box elements sorting by non- descending.
Let us examine a possible sequence of 11 transactions:
Example 1
It is required to work out an efficient algorithm which treats a given sequence of transactions. The maximum number of ADD and GET transactions: 30000 of each type.
Let us describe the sequence of transactions by two integer arrays:
1. A(1), A(2), ..., A(M): a sequence of elements which are being included into Black Box. A values are integers not exceeding 2 000 000 000 by their absolute value, M <= 30000. For the Example we have A=(3, 1, -4, 2, 8, -1000, 2).
2. u(1), u(2), ..., u(N): a sequence setting a number of elements which are being included into Black Box at the moment of first, second, ... and N-transaction GET. For the Example we have u=(1, 2, 6, 6).
The Black Box algorithm supposes that natural number sequence u(1), u(2), ..., u(N) is sorted in non-descending order, N <= M and for each p (1 <= p <= N) an inequality p <= u(p) <= M is valid. It follows from the fact that for the p-element of our u sequence we perform a GET transaction giving p-minimum number from our A(1), A(2), ..., A(u(p)) sequence.
ADD (x): put element x into Black Box;
GET: increase i by 1 and give an i-minimum out of all integers containing in the Black Box. Keep in mind that i-minimum is a number located at i-th place after Black Box elements sorting by non- descending.
Let us examine a possible sequence of 11 transactions:
Example 1
N Transaction i Black Box contents after transaction Answer
(elements are arranged by non-descending)
1 ADD(3) 0 3
2 GET 1 3 3
3 ADD(1) 1 1, 3
4 GET 2 1, 3 3
5 ADD(-4) 2 -4, 1, 3
6 ADD(2) 2 -4, 1, 2, 3
7 ADD(8) 2 -4, 1, 2, 3, 8
8 ADD(-1000) 2 -1000, -4, 1, 2, 3, 8
9 GET 3 -1000, -4, 1, 2, 3, 8 1
10 GET 4 -1000, -4, 1, 2, 3, 8 2
11 ADD(2) 4 -1000, -4, 1, 2, 2, 3, 8
It is required to work out an efficient algorithm which treats a given sequence of transactions. The maximum number of ADD and GET transactions: 30000 of each type.
Let us describe the sequence of transactions by two integer arrays:
1. A(1), A(2), ..., A(M): a sequence of elements which are being included into Black Box. A values are integers not exceeding 2 000 000 000 by their absolute value, M <= 30000. For the Example we have A=(3, 1, -4, 2, 8, -1000, 2).
2. u(1), u(2), ..., u(N): a sequence setting a number of elements which are being included into Black Box at the moment of first, second, ... and N-transaction GET. For the Example we have u=(1, 2, 6, 6).
The Black Box algorithm supposes that natural number sequence u(1), u(2), ..., u(N) is sorted in non-descending order, N <= M and for each p (1 <= p <= N) an inequality p <= u(p) <= M is valid. It follows from the fact that for the p-element of our u sequence we perform a GET transaction giving p-minimum number from our A(1), A(2), ..., A(u(p)) sequence.
Input
Input contains (in given order): M, N, A(1), A(2), ..., A(M), u(1), u(2), ..., u(N). All numbers are divided by spaces and (or) carriage return characters.
Output
Write to the output Black Box answers sequence for a given sequence of transactions, one number each line.
Sample Input
7 4 3 1 -4 2 8 -1000 2 1 2 6 6
Sample Output
3 3 1 2
做法，定义两个优先队列，以大优先的p1，以小优先的p2，如果要求的是第x小的值，p1中存下(x-1)个小值，那么第x个就是p2的队首，在求第一个小的值，p1为空，求完第一个小的值后，将p2的队首放入p1，再来求第二小的值，读取给出的数（a）时，如果a大于p1的队首，那么a放入p2，否则，将a放入p1，p1的队首放入p2，保证p1的个数均比p2小，且为（x-1）个，读取完数后p2的队首就是第x小的数，输出，再把p2的队首放入p1，执行之前的操作，得到下一个要求的最小值。
用两个优先队列，分开整体的数组，得到第x小值
#include <cstdio>
#include <cstring>
#include <queue>
#include <vector>
#include <algorithm>
using namespace std;
#define LL __int64
priority_queue <LL> p1 ;
priority_queue <LL,vector<LL>,greater<LL> > p2 ;
LL a[6000000] ;
int main()
{
int i , j , n , m , x ;
LL temp ;
while(scanf("%d %d", &n, &m)!=EOF)
{
while( !p1.empty() )
p1.pop();
while( !p2.empty() )
p2.pop() ;
for(i = 1 ; i <= n ; i++)
scanf("%I64d", &a[i]);
i = 1 ;
while(m--)
{
scanf("%d", &x);
for( ; i <= x ; i++)
{
if( p1.empty() || p1.top() < a[i] )
p2.push(a[i]);
else
{
p1.push(a[i]);
temp = p1.top() ;
p1.pop() ;
p2.push(temp);
}
}
temp = p2.top();
p2.pop() ;
printf("%d\n", temp);
p1.push(temp);
}
}
return 0;
}