zoukankan      html  css  js  c++  java
  • poj-2104-K-th number

    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 10 9 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.

    主席树

    AC 代码为:

     1 #include<iostream>
     2 #include<cstdio>
     3 #include<cstring>
     4 #include<vector>
     5 #include<algorithm>
     6 using namespace std;
     7 const int maxn=1e5+10;
     8 int a[maxn],root[maxn],n,m,x,y,k,cnt;
     9 vector<int> v;
    10 int getid(int x) {return lower_bound(v.begin(),v.end(),x)-v.begin()+1;}
    11 struct node{
    12     int l,r,sum;
    13 } tree[maxn*40];
    14 void update(int l,int r,int &x,int y,int pos)
    15 {
    16     tree[++cnt]=tree[y],tree[cnt].sum++,x=cnt;
    17     if(l==r) return ;
    18     int mid=(l+r)>>1;
    19     if(pos<=mid) update(l,mid,tree[x].l,tree[y].l,pos);
    20     else update(mid+1,r,tree[x].r,tree[y].r,pos);
    21 }
    22 
    23 int query(int l,int r,int x,int y,int k)
    24 {
    25     if(l==r) return l;
    26     int mid=(l+r)>>1;
    27     int sum=tree[tree[y].l].sum-tree[tree[x].l].sum;
    28     if(k>sum) return query(mid+1,r,tree[x].r,tree[y].r,k-sum);
    29     else return query(l,mid,tree[x].l,tree[y].l,k);
    30 }
    31 int main()
    32 {
    33     scanf("%d%d",&n,&m),cnt=0;
    34     for(int i=1;i<=n;i++) scanf("%d",&a[i]),v.push_back(a[i]);
    35     sort(v.begin(),v.end()),v.erase(unique(v.begin(),v.end()),v.end());
    36     for(int i=1;i<=n;i++) update(1,n,root[i],root[i-1],getid(a[i]));
    37     for(int i=1;i<=m;i++)
    38     {
    39         scanf("%d%d%d",&x,&y,&k);
    40         printf("%d
    ",v[query(1,n,root[x-1],root[y],k)-1]);
    41     }
    42     
    43     return 0;
    44 }
    View Code
  • 相关阅读:
    【OS_Windows】用微pe制作启动盘安装操作系统
    技术列表
    RPC 的概念模型与实现解析
    asp.net站点阻止某个文件夹或者文件被浏览器访问
    常用插件
    安全相关
    asp.net mvc 请求处理流程,记录一下。
    接口的显示实现和隐式实现
    值类型与引用类型的简单测试,没有太多的理论,一目了然。
    IEnumerable、GetEnumerator、IEnumerator之间的关系。
  • 原文地址:https://www.cnblogs.com/csushl/p/9386567.html
Copyright © 2011-2022 走看看