POJ 2104: K-th Number

K-th Number

Time Limit: 20000MS		Memory Limit: 65536K
Total Submissions: 52878		Accepted: 18188
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

Northeastern Europe 2004, Northern Subregion

题意：

给出n个数，询问区间第k大...

分析：

这题解法有很多...

之前写了整体二分...然后还可以用静态主席树水过...

感觉时间空间复杂度还是差很多的...

Run ID	User	Problem	Result	Memory	Time	Language	Code Length	Submit Time
16573738	NEIGHTHORN	2104	Accepted	22644K	1735MS	G++	1196B	2017-02-12 11:25:34
16456326	NEIGHTHORN	2104	Accepted	7672K	2829MS	G++	1492B	2017-01-07 11:10:22

代码：

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
//by NeighThorn
using namespace std;

const int maxn=100000+5,maxm=10000000+5;

int n,m,len,tot,a[maxn],mp[maxn],ls[maxm],rs[maxm],sum[maxm],root[maxn];

inline int find(int x){
	int l=1,r=len,ans;
	while(l<=r){
		int mid=(l+r)>>1;
		if(mp[mid]>=x)
			ans=mid,r=mid-1;
		else
			l=mid+1;
	}
	return ans;
}

inline void change(int l,int r,int x,int &y,int val){
	y=++tot,sum[y]=sum[x]+1;
	if(l==r)
		return;
	int mid=(l+r)>>1;ls[y]=ls[x],rs[y]=rs[x];
	if(val<=mid)
		change(l,mid,ls[x],ls[y],val);
	else
		change(mid+1,r,rs[x],rs[y],val);
}

inline int query(int l,int r,int x,int y,int num){
	if(l==r)
		return l;
	int mid=(l+r)>>1;
	if(sum[ls[y]]-sum[ls[x]]>=num)
		return query(l,mid,ls[x],ls[y],num);
	else
		return query(mid+1,r,rs[x],rs[y],num-(sum[ls[y]]-sum[ls[x]]));
}

signed main(void){
	scanf("%d%d",&n,&m);
	for(int i=1,x;i<=n;i++)
		scanf("%d",&a[i]),mp[i]=a[i];
	sort(mp+1,mp+n+1);
	len=unique(mp+1,mp+n+1)-mp-1;
	for(int i=1;i<=n;i++)
		change(1,n,root[i-1],root[i],find(a[i]));
	for(int i=1,s,x,y;i<=m;i++)
		scanf("%d%d%d",&x,&y,&s),printf("%d\n",mp[query(1,len,root[x-1],root[y],s)]);
	return 0;
}
//1234

　　

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By NeighThorn