PKU 2104（线段树+归并+二分）

K-th Number

Time Limit: 20000MS		Memory Limit: 65536K
Total Submissions: 20110		Accepted: 5251
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 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

此题是我做线段树专辑遇到的一题比较棘手的。。。

还是参考了其他人的思路才过了，之前一直TLE - -！

#include <iostream>
using namespace std;
#define N 100005

struct LineTree
{
	int l,r;
	int depth;
	LineTree *lchild,*rchild;
};

int pos,x,y,key;
LineTree mem[3*N];
int val[N];
int res[20][N];

LineTree *NewTree()
{
	LineTree *s=&mem[pos++];
	return s;
}

LineTree *CreateTree(int a,int b,int dep)
{
	LineTree *s=NewTree();
	s->l=a;
	s->r=b;
	s->depth=dep;
	int mid;
	if(a!=b)
	{
		mid=(a+b)/2;
		s->lchild=CreateTree(a,mid,dep+1);
		s->rchild=CreateTree(mid+1,b,dep+1);
		int i=s->l,j=mid+1,l=s->l;
		while ( i <= mid && j <= b ) 
		{
			if ( res [dep + 1] [i] < res [dep + 1] [j] )	
				res [dep] [l ++] = res [dep + 1] [i ++];
			else
				res [dep] [l ++] = res [dep + 1] [j ++];
        }
		
        while ( i <= mid ) res [dep] [l ++] = res [dep + 1] [i ++];
        while ( j <= s->r ) res [dep] [l ++] = res [dep + 1] [j ++];
		
		
	}
	else
	{
		res[dep][a]=val[a];
	}
	return s;
}

int search(LineTree *s)
{
	if ( x <= s->l && s->r <= y ) 
	{		
		if ( res [s->depth] [s->l] >= key ) return 0;		
		if ( res [s->depth] [s->r] < key ) return s->r - s->l + 1;		
		if ( res [s->depth] [s->r] == key ) return s->r - s->l;
		int     low = s->l , high = s->r , mid;		
		while ( low + 1 < high ) 
		{			
			mid = ( low + high )/2;			
			if ( res [s->depth] [mid] < key ) low = mid;			
			else high = mid;			
		}		
		return low - s->l + 1;		
	}	
	int     ret = 0;	
	if ( x <= s->lchild->r ) ret += search(s->lchild);
	if ( s->rchild->l <= y ) ret += search(s->rchild); 	
	return ret;	
}

int main()
{
	int n,m,i,c,low,high,mid;
	while(scanf("%d%d",&n,&m)!=EOF)
	{
		for(i=0;i<n;i++)
			scanf("%d",&val[i]);
		pos=1;
		LineTree *s;
		s=CreateTree(0,n-1,0);
		while(m--)
		{
			scanf("%d%d%d",&x,&y,&c);
			x --; y --;			
			low = 0; high = n;
			while ( low + 1 < high ) {
				mid = ( low + high ) / 2;				
				key = res [0] [mid];				
				if ( search(s) >= c ) high = mid;				
				else low = mid;				
			}
			printf("%d/n",res[0][low]);
		}
	}
	return 0;
}