K-th Number
Time Limit: 20000MS   Memory Limit: 65536K
Total Submissions: 36045   Accepted: 11522
Case Time Limit: 2000MS

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

field=source&key=Northeastern+Europe+2004">Northeastern Europe 2004, Northern Subregion



这道题貌似有非常多种解法



我是用归并树做的



所谓归并树就是将 归并排序过程组成一个树



树上的每一个节点就是非递减的。



以1 5 2 6 3 7为例:

把归并排序递归过程记录下来即是一棵归并树:

        [1 2 3 5 6 7]

    [1 2 5]      [3 6 7]

   [1 5] [2]    [3 6] [7]

  [1][5]         [6][3]

用相应的下标区间建线段树:(这里下标区间相应的是原数列)

            [1 6]

     [1 3]      [4 6]

  [1 2] [3]   [4 5][6]

  [1][2]      [4][5]



做法就是在归并树的根节点二分查找答案,然后用线段树查询rank值,由于线段树的每一个节点与归并树的节点是一一相应的,而归并树的的节点元素是非递减的,因此能够用二分算出rank值。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <string>
#include <algorithm>
#include <queue>
using namespace std;
const int maxn = 100000+10; struct node{
int lson,rson;
int mid(){
return (lson+rson)>>1;
}
}tree[maxn*4]; int seg[25][maxn];
int n,m;
int num[maxn];
int sta,ed; void build(int L,int R,int rt,int deep){
tree[rt].lson = L;
tree[rt].rson = R;
if(L==R){
seg[deep][L] = num[L];
return;
}
int mid = tree[rt].mid();
build(L,mid,rt<<1,deep+1);
build(mid+1,R,rt<<1|1,deep+1);
int i = L,j = mid+1,k = L;
while(i <= mid && j <= R){
if(seg[deep+1][i] < seg[deep+1][j]){
seg[deep][k] = seg[deep+1][i];
i++;
}else{
seg[deep][k] = seg[deep+1][j];
j++;
}
k++;
}
while(i <= mid){
seg[deep][k] = seg[deep+1][i];
i++;
k++;
}
while(j <= R){
seg[deep][k] = seg[deep+1][j];
j++;
k++;
}
return;
} int query(int rt,int dep,int key){
if(tree[rt].lson >= sta && tree[rt].rson <= ed){
int t = lower_bound(&seg[dep][tree[rt].lson],&seg[dep][tree[rt].rson]+1,key)-&seg[dep][tree[rt].lson];
return t;
}
int mid = tree[rt].mid();
int res = 0;
if(mid >= sta){
res += query(rt<<1,dep+1,key);
}
if(mid < ed){
res += query(rt<<1|1,dep+1,key);
}
return res;
} int binary(int tk){
int L = 1,R = n;
while(L <= R){
int mid = (L+R) >> 1;
if(query(1,0,seg[0][mid]) > tk){
R = mid-1;
}else{
L = mid+1;
}
}
if(query(1,0,seg[0][R])==tk){
return seg[0][R];
}else{
return seg[0][L];
}
} int main(){ cin >> n >> m;
for(int i = 1; i <= n; i++){
scanf("%d",&num[i]);
}
build(1,n,1,0);
while(m--){
int k;
scanf("%d%d%d",&sta,&ed,&k);
printf("%d\n",binary(k-1));
}
return 0;
}

PKU-2104-K-th Number的更多相关文章

  1. POJ 2104:K-th Number(主席树静态区间k大)

    题目大意:对于一个序列,每次询问区间[l,r]的第k大树. 分析: 主席树模板题 program kthtree; type point=record l,r,s:longint; end; var ...

  2. POJ 2104:K-th Number(整体二分)

    http://poj.org/problem?id=2104 题意:给出n个数和m个询问求区间第K小. 思路:以前用主席树做过,这次学整体二分来做.整体二分在yr大佬的指点下,终于大概懂了点了.对于二 ...

  3. 【POJ 2104】 K-th Number 主席树模板题

    达神主席树讲解传送门:http://blog.csdn.net/dad3zz/article/details/50638026 2016-02-23:真的是模板题诶,主席树模板水过.今天新校网不好,没 ...

  4. ACM-ICPC 2018 沈阳赛区网络预赛 K. Supreme Number

    A prime number (or a prime) is a natural number greater than 11 that cannot be formed by multiplying ...

  5. [POJ2104] K – th Number (可持久化线段树 主席树)

    题目背景 这是个非常经典的主席树入门题--静态区间第K小 数据已经过加强,请使用主席树.同时请注意常数优化 题目描述 如题,给定N个正整数构成的序列,将对于指定的闭区间查询其区间内的第K小值. 输入输 ...

  6. POJ 2104:K-th Number 整体二分

    感觉整体二分是个很有趣的东西. 在别人的博客上看到一句话 对于二分能够解决的询问,如果有多个,那么如果支持离线处理的话,那么就可以使用整体二分了 树套树写了一天还是WA着,调得焦头烂额,所以决定学cd ...

  7. ACM-ICPC 2018 沈阳赛区网络预赛 K Supreme Number(规律)

    https://nanti.jisuanke.com/t/31452 题意 给出一个n (2 ≤ N ≤ 10100 ),找到最接近且小于n的一个数,这个数需要满足每位上的数字构成的集合的每个非空子集 ...

  8. Count the number of possible triangles

    From: http://www.geeksforgeeks.org/find-number-of-triangles-possible/ Given an unsorted array of pos ...

  9. 大数据热点问题TOP K

    1单节点上的topK (1)批量数据 数据结构:HashMap, PriorityQueue 步骤:(1)数据预处理:遍历整个数据集,hash表记录词频 (2)构建最小堆:最小堆只存k个数据. 时间复 ...

  10. Codeforces Round #350 (Div. 2) F. Restore a Number 模拟构造题

    F. Restore a Number   Vasya decided to pass a very large integer n to Kate. First, he wrote that num ...

随机推荐

  1. PS小技巧之完美抠图

    具体详细步骤如下01.打开图片,ctrl+j复制一层得到图层1,点击红圈处新建图层2,放于图层1与背景层之间,填充你喜欢的颜色,作为检查效果和新的背景图层. 02.点击图层1,用“快速选择工具”大致做 ...

  2. 使用CefSharp在.Net程序中嵌入Chrome浏览器(三)——基本操作

    CefSharp本身提供了WPF和WinForm两个版本的控件,这两个版本的控件使用方法大同小异,由于我WPF的版本用的较多,这里就简单的介绍下WPF版的CEFSharp控件的用法. 加载页面: Ch ...

  3. HDU 4734 F(x) (2013成都网络赛,数位DP)

    F(x) Time Limit: 1000/500 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submiss ...

  4. VMware Workstation Pro 12 桥接联网(物理主机:Windows 7,虚拟机:CentOS 6.8)

    物理主机:Windows 7,虚拟机:CentOS 6.8 1.设置虚拟机的 默认路径:编辑 -> 首选项 -> 设置“虚拟机的默认位置” 2.设置 虚拟网络:编辑 -> 虚拟网络编 ...

  5. Xamarin.Forms.Xaml.XamlParseException: MarkupExtension not found for trans:Translate using a PCL in Release Mode

    I'm pretty desperate finding the solution for the problem stated below. I have a cross platform solu ...

  6. ES6的一些基本用法

    ● let ● variable hoisting ● arrow Function, Lambda表达式 ● Destructuring Assignments 解构赋值 ● 默认参数值 Defau ...

  7. 使用EF Code First搭建一个简易ASP.NET MVC网站,允许数据库迁移

    本篇使用EF Code First搭建一个简易ASP.NET MVC 4网站,并允许数据库迁移. 创建一个ASP.NET MVC 4 网站. 在Models文件夹内创建Person类. public ...

  8. Delphi数学运算当中四舍五入的问题

    在最近版本的Delphi Pascal 编译器中,Round 函数是以 CPU 的 FPU (浮点部件) 处理器为基础的.这种处理器采用了所谓的 "银行家舍入法",即对中间值 (如 ...

  9. 无线通信中FEC 编码原理及评价

    转自:http://blog.csdn.net/wiznet2012/article/details/7492146 大家好,前面我们给大家介绍了无线通信中FEC编码原理(1)和(2),今天继续献上F ...

  10. 《ASP.NET Web API 2框架揭秘》

    <ASP.NET Web API 2框架揭秘> 基本信息 作者: 蒋金楠 出版社:电子工业出版社 ISBN:9787121235368 上架时间:2014-7-5 出版日期:2014 年7 ...