hdu 6601 区间条件极值 - 区间 最大 三角形周长

题目传送门//res tp hdu

目的

对长度为n的区间，给定q个子区间，求其元素能构成三角形的最大周长。有多组测试。

n 1e5

q 1e5

a_i [1,1e9] (i∈[1,n]);

数据结构

划分树

分析

需在不超过O（logn）的时间内完成一次查询

若一个数列不能构成三角形，则其为斐波那契数列。斐列不超过50项即可达到1e9，故每次只需查询区间的前k大即可，不超过50次询问，即可得到该数列是否能构成三角形

划分树的单次询问第k小/大为logn

#include<iostream>
#include<algorithm>
#include<cmath>
typedef long long ll;
using namespace std;
const int MAXN = 100000+50;
const int DEEP = 20;
ll tree[DEEP][MAXN];
int cnt[DEEP][MAXN];
ll sorted[MAXN];
void build(int deep,int lft,int rht)
{
	if(lft == rht) return;
	int mid = (lft + rht)>>1;
	int scnt = mid - lft + 1;
	ll M = sorted[mid];
	for(int i = lft;i<=rht;++i){
		if(tree[deep][i] < M) scnt--;
	}
	int p = lft, r = mid + 1;
	for(int i = lft,cnt_in_left = 0;i<=rht;++i){
		ll num = tree[deep][i];
		if(num < M || (num == M && scnt)){
			if(num == M) scnt--;
			cnt_in_left++;
			tree[deep + 1][p++] = num;
		}
		else tree[deep + 1][r++] = num;
		cnt[deep][i] = cnt_in_left;
	}
	build(deep + 1,lft,mid);
	build(deep + 1,mid + 1,rht);
}
ll query(int deep, int lft, int rht, int qlft, int qrht, int k){
	if(lft == rht) return tree[deep][lft];
	int mid = (lft + rht)>>1;
	int left = 0,sum_in_left = cnt[deep][qrht];
	if(qlft != lft){
		left = cnt[deep][qlft-1];
		sum_in_left-=left;
	}
	if(sum_in_left >= k){
		int new_qlft = lft + left;
		int new_qrht = new_qlft + sum_in_left - 1;
		return query(deep + 1,lft,mid,new_qlft,new_qrht,k);
	}
	else{
		int a = qlft - lft - left;
		int b = qrht - qlft - sum_in_left;
		int new_qlft = (mid + 1) + a;
		int new_qrht = new_qlft + b;
		return query(deep+1,mid+1,rht,new_qlft,new_qrht,k - sum_in_left);
	}
}
int main()
{
	int n,q,l,r;
	while(scanf(" %d %d",&n,&q)!=EOF){
		for(int i = 1;i<=n;++i) {
			scanf(" %lld",&sorted[i]);
			tree[0][i] = sorted[i];
		}
		sort(sorted+1,sorted+1+n);
		build(0,1,n);
		while(q--){
			scanf(" %d %d",&l,&r);
			if(r - l + 1 < 3) printf("-1\n");
			else{
				int len = r - l + 1;
				long long a,b,c,ans = -1;
				a = query(0,1,n,l,r,len);
				b = query(0,1,n,l,r,len-1);
				for(int i = len-2;i>=1;--i){
					c = query(0,1,n,l,r,i);
					if(b + c > a){
						ans = a + b + c;break;
					}
					a= b;b = c;
				}
				printf("%lld\n",ans);
			}
		}
	}
}