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Treap [POJ 1442] Black Box

2024-07-28 20:17:52   219人阅读

Black Box
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 7770 Accepted: 3178

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.

Sample Input

7 43 1 -4 2 8 -1000 21 2 6 6

Sample Output

3312

Source

Northeastern Europe 1996
 
#include <iostream>#include <stdio.h>#include <time.h>using namespace std;#define N 30100#define INF 0x7fffffffint val[N];struct Treap{    int ch[N][2],fix[N],size[N];    int top,root;        inline void PushUp(int rt)    {        size[rt]=size[ch[rt][0]]+size[ch[rt][1]]+1;    }    void Newnode(int &rt,int v)    {        rt=++top;        val[rt]=v;        size[rt]=1;        fix[rt]=rand();        ch[rt][0]=ch[rt][1]=0;    }    void Init()    {        top=root=0;        ch[0][0]=ch[0][1]=0;        size[0]=val[0]=0;        memset(size,0,sizeof(size));    }    void Rotate(int &x,int kind)    {        int y=ch[x][kind^1];        ch[x][kind^1]=ch[y][kind];        ch[y][kind]=x;        PushUp(x);        PushUp(y);        x=y;    }    void Insert(int &rt,int v)    {        if(!rt)            Newnode(rt,v);        else        {            int kind=(v>=val[rt]);            size[rt]++;            Insert(ch[rt][kind],v);            if(fix[ch[rt][kind]]<fix[rt])                Rotate(rt,kind^1);        }    }    int Find(int rt,int k)    {        int cnt=size[ch[rt][0]];        if(k==cnt+1) return val[rt];        else if(k<=cnt) return Find(ch[rt][0],k);        else return Find(ch[rt][1],k-cnt-1);    }}t;int main(){    int n,i,m;    srand((int)time(0));    while(scanf("%d%d",&n,&m)!=EOF)    {        t.Init();        for(i=1;i<=n;i++)        {            scanf("%d",&val[i]);        }        int last=1,x;        for(i=1;i<=m;i++)        {            scanf("%d",&x);            while(last<=x)            {                t.Insert(t.root,val[last]);                last++;            }            printf("%d\n",t.Find(t.root,i));        }    }    return 0;}

 

Treap [POJ 1442] Black Box


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