Codeforces 961 E Tufurama

计数问题与主席树

最新推荐文章于 2020-04-07 19:41:00 发布

转载最新推荐文章于 2020-04-07 19:41:00 发布 · 79 阅读

0 ·

CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/JYYHH/p/8761843.html

本文探讨了一个关于计数特定配对的问题，并提供了一种使用主席树的数据结构解决方案。通过枚举并查找符合条件的配对数量，有效地解决了问题。

Discription

One day Polycarp decided to rewatch his absolute favourite episode of well-known TV series "Tufurama". He was pretty surprised when he got results only for season 7 episode 3 with his search query of "Watch Tufurama season 3 episode 7 online full hd free". This got Polycarp confused — what if he decides to rewatch the entire series someday and won't be able to find the right episodes to watch? Polycarp now wants to count the number of times he will be forced to search for an episode using some different method.

TV series have n seasons (numbered 1 through n), the i-th season has a_i episodes (numbered 1 through a_i). Polycarp thinks that if for some pair of integers x and y(x < y) exist both season x episode y and season y episode x then one of these search queries will include the wrong results. Help Polycarp to calculate the number of such pairs!

Input

The first line contains one integer n (1 ≤ n ≤ 2·10⁵) — the number of seasons.

The second line contains n integers separated by space a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹)— number of episodes in each season.

Output

Print one integer — the number of pairs x and y (x < y) such that there exist both season x episode y and season y episode x.

Examples

Input

5
1 2 3 4 5

Output

Input

3
8 12 7

Output

Input

3
3 2 1

Output

Note

Possible pairs in the second example:

x = 1, y = 2 (season 1 episode 2 $\text{[math]}$ season 2 episode 1);
x = 2, y = 3 (season 2 episode 3 $\text{[math]}$ season 3 episode 2);
x = 1, y = 3 (season 1 episode 3 $\text{[math]}$ season 3 episode 1).

In the third example:

x = 1, y = 2 (season 1 episode 2 $\text{[math]}$ season 2 episode 1);
x = 1, y = 3 (season 1 episode 3 $\text{[math]}$ season 3 episode 1).

建一个模型之后发现是主席树模板题23333

/*
    先枚举x，然后找出所有 x< y <=a[x] 中 a[y]>=x的个数
*/
#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int maxn=200005;
struct node{
	int s;
	node *lc,*rc;
}nil[maxn*33],*rot[maxn],*cnt;
int a[maxn],n,m,le;
ll ans=0;

node *update(node *u,int l,int r){
	node *ret=++cnt;
	*ret=*u,ret->s++;
	if(l==r) return ret;
	
	int mid=l+r>>1;
	if(le<=mid) ret->lc=update(ret->lc,l,mid);
	else ret->rc=update(ret->rc,mid+1,r);
	return ret;
}

int query(node *u,node *v,int l,int r){
	if(l>=le) return v->s-u->s;
	int mid=l+r>>1,an=query(u->rc,v->rc,mid+1,r);
	if(le<=mid) an+=query(u->lc,v->lc,l,mid);
	return an;
}

inline void prework(){
	rot[0]=nil->lc=nil->rc=cnt=nil;
	nil->s=0;
	for(int i=1;i<=n;i++) le=a[i],rot[i]=update(rot[i-1],1,n);
}

inline void solve(){
	for(int i=1;i<=n;i++) if(a[i]>i) le=i,ans+=(ll)query(rot[i],rot[a[i]],1,n);
}

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
	    scanf("%d",a+i);
	    if(a[i]>n) a[i]=n;
	}
	prework();
	solve();
	cout<<ans<<endl;
	
//	for(int i=1;i<n;i++)
//	    for(int j=i+1;j<=n;j++) if(a[i]>=j&&a[j]>=i) printf("%d %d\n",i,j);
	return 0;
}

转载于:https://www.cnblogs.com/JYYHH/p/8761843.html