hdu 4251 划分树

The Famous ICPC Team Again

Time Limit: 30000/15000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1155    Accepted Submission(s): 561

Problem Description

When Mr. B, Mr. G and Mr. M were preparing for the 2012 ACM-ICPC World Final Contest, Mr. B had collected a large set of contest problems for their daily training. When they decided to take training, Mr. B would choose one of them from the problem set. All the problems in the problem set had been sorted by their time of publish. Each time Prof. S, their coach, would tell them to choose one problem published within a particular time interval. That is to say, if problems had been sorted in a line, each time they would choose one of them from a specified segment of the line.

Moreover, when collecting the problems, Mr. B had also known an estimation of each problem’s difficultness. When he was asked to choose a problem, if he chose the easiest one, Mr. G would complain that “Hey, what a trivial problem!”; if he chose the hardest one, Mr. M would grumble that it took too much time to finish it. To address this dilemma, Mr. B decided to take the one with the medium difficulty. Therefore, he needed a way to know the median number in the given interval of the sequence.

 

Input

For each test case, the first line contains a single integer n (1 <= n <= 100,000) indicating the total number of problems. The second line contains n integers xi (0 <= xi <= 1,000,000,000), separated by single space, denoting the difficultness of each problem, already sorted by publish time. The next line contains a single integer m (1 <= m <= 100,000), specifying number of queries. Then m lines follow, each line contains a pair of integers, A and B (1 <= A <= B <= n), denoting that Mr. B needed to choose a problem between positions A and B (inclusively, positions are counted from 1). It is guaranteed that the number of items between A and B is odd.

 

Output

For each query, output a single line containing an integer that denotes the difficultness of the problem that Mr. B should choose.

 

Sample Input

   
   
   
   

    
    
    
    5
5 3 2 4 1
3
1 3
2 4
3 5
5
10 6 4 8 2
3
1 3
2 4
3 5
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    Case 1:
3
3
2
Case 2:
6
6
4
   
   
   
   

题意：

给你一串数字表示题目的难度，题目已经按时间顺序排好，每次找出时间在[s,t]之间，
且难度为中间值的题目，而且保证了给的查找范围是奇数，所以变成了每次查找[s,t]中，
第（t-s）/2+1大的难度为多少

#include <functional>
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <Map>
using namespace std;
typedef long long ll;
typedef long double ld;

using namespace std;

const int maxn = 100010;

int tree[20][maxn];
int sorted[maxn];
int toleft[20][maxn];


void build(int l,int r,int dep)
{
    if(l == r)
        return;
    int mid = (l+r)>>1;
    int same = mid-l+1;
    for(int i = l;i <= r;i++)
    {
        if(tree[dep][i] < sorted[mid])
            same--;
    }
    int lpos = l;
    int rpos = mid+1;
    for(int i = l;i <= r;i++)
    {
        if(tree[dep][i] < sorted[mid])
            tree[dep+1][lpos++] = tree[dep][i];
        else if(tree[dep][i] == sorted[mid] && same > 0)
        {
            tree[dep+1][lpos++] = tree[dep][i];
            same --;
        }
        else
            tree[dep+1][rpos++] = tree[dep][i];
        toleft[dep][i] = toleft[dep][l-1] + lpos -l;
    }
    build(l,mid,dep+1);
    build(mid+1,r,dep+1);
 }


 int query(int L,int R,int l,int r,int dep,int k)
 {
     if(l == r)
        return tree[dep][l];
     int mid = (L+R)>>1;

     int cnt = toleft[dep][r]-toleft[dep][l-1]; 
     if(cnt >= k)
     {   
         int lpos = L+toleft[dep][l-1]-toleft[dep][L-1];
         int rpos = lpos+cnt-1;
         return query(L,mid,lpos,rpos,dep+1,k);
     }
     else
     {  
         int rpos = r+toleft[dep][R]-toleft[dep][r];
         int lpos = rpos-(r-l-cnt);
         return query(mid+1,R,lpos,rpos,dep+1,k-cnt);
     }
 }


 int main()
 {
     int n,m;
     int cas = 1;
     while(scanf("%d",&n) != EOF)
     {
         memset(tree,0,sizeof(tree));
         for(int i = 1;i <= n;i++)
         {
             scanf("%d",&sorted[i]);
             tree[0][i] = sorted[i];
         }
         sort(sorted+1,sorted+n+1);
         build(1,n,0);
         scanf("%d",&m);
         int l,r;
         printf("Case %d:\n",cas++);
         while(m--)
         {
             scanf("%d%d",&l,&r);
             int k =(r-l)/2+1;
             printf("%d\n",query(1,n,l,r,0,k));
         }
     }
     return 0;
 }