Black Box
TimeLimit: 1000ms MemoryLimit:10000KB
64-bit integer IO format:%lld
Problem 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
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.
SampleInput
7 4 3 1 -4 2 8 -1000 2 1 2 6 6
SampleOutput
3 3 1 2 搞两个优先队列, 分别为 最大堆 和 最小堆, 目的是 在 n 个 数里, 获得第几大数。code:
#include <cstdio> #include <algorithm> #include <queue> #include <vector> using namespace std; void solve( int, int ); int main(void) { //freopen( "d://test.txt", "rw+", stdin ); int n, t; while( scanf( "%d%d", &n, &t ) != EOF ){ solve( n, t ); } return 0; } void solve( int n, int t ) { int *_m = new int [ n+1 ]; int num; priority_queue < int, vector< int >, greater <int> > pri_min; priority_queue < int, vector< int >, less <int> > pri_max; for( int i=0; i < n; ++ i ){ scanf( "%d", _m+i ); } for( int i=1, j=0; t --; ++ i ){ scanf( "%d", &num ); // 快速 填充到指定数目的数 while( pri_max.size()+pri_min.size() < num ){ pri_min.push( _m[ j ++ ] ); } // 快速 填充 到最大堆, 使最大堆数目为 i while( pri_max.size() < i ){ pri_max.push( pri_min.top() ); pri_min.pop(); } // 交换 最大堆 和 最小堆 数据, 直到符合情况 while( pri_min.size() && pri_max.top() > pri_min.top() ){ num = pri_max.top(); pri_max.pop(); pri_max.push( pri_min.top() ); pri_min.pop(); pri_min.push( num ); } printf( "%d\n", pri_max.top() ); } delete [] _m; }