zoukankan      html  css  js  c++  java
  • POJ-2104-K-th Number(区间第K大+主席树模板题)

    Description

    You are working for Macrohard company in data structures department. After failing your previous task about key insertion you were asked to write a new data structure that would be able to return quickly k-th order statistics in the array segment. 
    That is, given an array a[1...n] of different integer numbers, your program must answer a series of questions Q(i, j, k) in the form: "What would be the k-th number in a[i...j] segment, if this segment was sorted?" 
    For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question be Q(2, 5, 3). The segment a[2...5] is (5, 2, 6, 3). If we sort this segment, we get (2, 3, 5, 6), the third number is 5, and therefore the answer to the question is 5.

    Input

    The first line of the input file contains n --- the size of the array, and m --- the number of questions to answer (1 <= n <= 100 000, 1 <= m <= 5 000). 
    The second line contains n different integer numbers not exceeding 109 by their absolute values --- the array for which the answers should be given. 
    The following m lines contain question descriptions, each description consists of three numbers: i, j, and k (1 <= i <= j <= n, 1 <= k <= j - i + 1) and represents the question Q(i, j, k).

    Output

    For each question output the answer to it --- the k-th number in sorted a[i...j] segment.

    Sample Input

    7 3
    1 5 2 6 3 7 4
    2 5 3
    4 4 1
    1 7 3

    Sample Output

    5
    6
    3

    Hint

    This problem has huge input,so please use c-style input(scanf,printf),or you may got time limit exceed.

    Source

    Northeastern Europe 2004, Northern Subregion
    #include<cstdio>
    #include<iostream>
    #include<cstring>
    #include<algorithm>
    #include<queue>
    #include<stack>
    #include<set>
    #include<map>
    #include<vector>
    #include<cmath>
    
    
    const int maxn=1e5+5;
    typedef long long ll;
    using namespace std;
    vector<int>vec;
    struct node
    {
        int  l,r;
        int  sum;
    }tree[maxn*40];
    
    int a[maxn];
    
    int getid(int  x)
    {
        return lower_bound(vec.begin(),vec.end(),x)-vec.begin()+1;
    }
    int cnt=0,root[maxn];
    void update(int l,int r,int pre,int &now,int p)
    {
       tree[++cnt]=tree[pre];
       now=cnt;
       tree[now].sum++;
       if(l==r)
       {
           return ;
       }
       int mid=(l+r)>>1;
       if(mid>=p)
       {
           update(l,mid,tree[pre].l,tree[now].l,p);
       }
       else
       {
           update(mid+1,r,tree[pre].r,tree[now].r,p);
       }
    }
    
    int query(int l,int r,int L,int R,int k)
    {
        if(l==r)
        {
            return l;
        }
        int mid=(l+r)>>1;
        int tmp=tree[tree[R].l].sum-tree[tree[L].l].sum;
        if(tmp>=k)
        {
         return  query(l,mid,tree[L].l,tree[R].l,k);
        } 
        else
        {
            return query(mid+1,r,tree[L].r,tree[R].r,k-tmp);
        }
    }
    int main()
    {
        int n,m;
        scanf("%d%d",&n,&m);
        for(int t=1;t<=n;t++)
        {
            scanf("%d,",&a[t]);
            vec.push_back(a[t]);
        }
        sort(vec.begin(),vec.end());
        vec.erase(unique(vec.begin(),vec.end()),vec.end());
        for(int t=1;t<=n;t++)
        {
            update(1,n,root[t-1],root[t],getid(a[t]));
        }
        int l,r,k;
        while(m--)
        {
            scanf("%d%d%d",&l,&r,&k);
            printf("%d
    ",vec[query(1,n,root[l-1],root[r],k)-1]);
        }
        
        return 0;
    } 
  • 相关阅读:
    你可见过一种基于状压的二进制筛法?
    dp
    tricks
    csp2020 游记
    洛谷P2982 [USACO10FEB]慢下来Slowing down
    NOIP 2018 大翻车记
    2019 ICPC 南京网络赛
    POJ2778 AC自动机 + 快速矩阵幂
    2019 CCPC网络赛
    2018ICPC 北京
  • 原文地址:https://www.cnblogs.com/Staceyacm/p/11306980.html
Copyright © 2011-2022 走看看