洛谷P1975【国家集训队】排队

题目大意

给出(n)个数,每次交换两个数(l,r)之后维护逆序对数量。

题解

初始答案用归并排序求即可。

我们考虑交换的影响，

显然对于区间([1,l))与((r,n]),本次交换并不会对其贡献有什么影响。

对于(l)向右移之后，在区间([l,r])中比(l)小的数的贡献消失了，新增了比(l)大的数的个数的贡献

(r)同理。

对于(l,r)本身，如果(l)的值大于(r)，--(ans),否则++(ans)

于是我们需要一个数据结构，支持以下操作

区间查询比(val)小的数，

区间查询比(val)大的数，

单点修改。

老规矩，线段树套平衡树即可

献上丑陋的代码

/*
@Date    : 2019-07-21 10:03:17
@Author  : Adscn (adscn@qq.com)
@Link    : https://www.cnblogs.com/LLCSBlog
*/
#ifdef FASTER
#pragma GCC diagnostic error "-std=c++11"
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-fwhole-program")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-fstrict-overflow")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-skip-blocks")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("-funsafe-loop-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")
#endif
#include<bits/stdc++.h>
using namespace std;
#define IL inline
#define RG register
#define gi getint()
#define gc getchar()
#define File(a) freopen(a".in","r",stdin);freopen(a".out","w",stdout)
IL int getint()
{
	RG int xi=0;
	RG char ch=gc;
	bool f=0;
	while(ch<'0'||ch>'9')ch=='-'?f=1:f,ch=gc;
	while(ch>='0'&&ch<='9')xi=(xi<<1)+(xi<<3)+ch-48,ch=gc;
	return f?-xi:xi;
}
template<typename T>
IL void pi(T k,char ch=0)
{
	if(k<0)k=-k,putchar('-');
	if(k>=10)pi(k/10,0);
	putchar(k%10+'0');
	if(ch)putchar(ch);
}
const int N=2e4+10;
class SplayTree{
private:
	struct node;
	typedef node* tree;
	struct node{
		tree ch[2],par;
		int siz,val,cnt;
		node(void){ch[0]=ch[1]=par=NULL,cnt=val=siz=0;}
		node(int v,tree p):par(p),val(v){ch[0]=ch[1]=NULL,cnt=siz=1;}
	}*root;
public:
	SplayTree(){root=NULL;}
	~SplayTree(){entire_free(root);}
protected:
	inline void entire_free(tree x)
	{
		if(!x)return;
		entire_free(x->ch[0]),entire_free(x->ch[1]);
		delete x;
	}
	inline bool ws(tree x,tree p){return p?p->ch[1]==x:0;}
	inline int siz(tree x){return x?x->siz:0;}
	inline void connect(tree x,tree p,bool which)
	{
		x?(x->par=p):0,
		(p?p->ch[which]:root)=x;
	}
	inline void pushup(tree x){if(x)x->siz=siz(x->ch[0])+siz(x->ch[1])+x->cnt;}
	inline void rotate(tree x)
	{
		tree p=x->par,g=p->par;
		bool r=ws(x,p);
		connect(x,g,ws(p,g)),
		connect(x->ch[!r],p,r),
		connect(p,x,!r);
		pushup(p);
	}
	inline void Splay(tree x,tree y)
	{
		if(!x)return;
		register tree p,g;
		while(x->par!=y)
		{
		 	p=x->par,g=p->par;
		 	if(g!=y)rotate(ws(x,p)^ws(p,g)?x:p);
		 	rotate(x);
		}
		pushup(x);
	}
	inline void find(int val)
	{
		tree x=root;
		while(x&&x->ch[val>x->val]&&val!=x->val)x=x->ch[val>x->val];
//		if(x->val!=val){
//			cerr<<"Error : FIND : val:"<<val<<" does not exist!"<<endl;
//			return;
//		}
		Splay(x,NULL);
	}
public:
	inline void insert(int val)
	{
		if(!root){
			root=new node(val,NULL);
			return;
		}
		#define nxt (val>x->val)
		for(tree x=root;x;x=x->ch[nxt])
		{
			if(x->val==val)
			{
				++x->cnt;
				Splay(x,NULL);
				return;
			}
			if(!x->ch[nxt])
			{
				x->ch[nxt]=new node(val,x);
				Splay(x->ch[nxt],NULL);
				return;
			}
		}
		#undef nxt
		return;
	}
	inline void remove(int val)
	{
		find(val);
		tree x=root;
		if(!x||x->val!=val)return;
//		cerr<<val<<endl;
/*		try{
			if(x==NULL)throw "empty";
			if(x->val!=val)throw "non-existent";
		}catch(const char *s){
			if(s=="empty")cerr<<"Error: REMOVE : Tree is empty"<<endl;
			if(s=="non-existent")cerr<<"Error: REMOVE : val doesn't exist"<<endl;
			return;
		}*/
		if(x->cnt>1)--x->cnt;
		else if(!x->ch[0])
		{
			connect(x->ch[1],NULL,0);
			delete x;
		}
		else{
			tree k=x->ch[0];
			while(k->ch[1])k=k->ch[1];
			Splay(k,x);
			connect(x->ch[1],k,1);
			connect(k,NULL,0);
			delete x;
		}
	}
	inline int rank_min(int x)
	{
		insert(x);
		assert(x==root->val);
		int ans=siz(root->ch[0]);
		remove(x);
		return ans;
	}
	inline int rank_max(int x)
	{
		insert(x);
		assert(x==root->val);
		int ans=siz(root->ch[1]);
		remove(x);
		return ans;
	}
}bt[N<<2];
void Insert(int rt,int l,int r,int pos,int val)
{
	bt[rt].insert(val);
	if(l==r)return;
	int mid=(l+r)>>1;
	if(pos<=mid)Insert(rt<<1,l,mid,pos,val);
	else Insert(rt<<1|1,mid+1,r,pos,val);
}
void Remove(int rt,int l,int r,int pos,int val)
{
	bt[rt].remove(val);
	if(l==r)return;
	int mid=(l+r)>>1;
	if(pos<=mid)Remove(rt<<1,l,mid,pos,val);
	else Remove(rt<<1|1,mid+1,r,pos,val);
}
inline int Rank_min(int rt,int l,int r,int ql,int qr,int val)
{
	if(ql<=l&&r<=qr)return bt[rt].rank_min(val);
	int ans=0,mid=(l+r)>>1;
	if(ql<=mid)ans+=Rank_min(rt<<1,l,mid,ql,qr,val);
	if(qr>mid) ans+=Rank_min(rt<<1|1,mid+1,r,ql,qr,val);
	return ans;
}
inline int Rank_max(int rt,int l,int r,int ql,int qr,int val)
{
	if(ql<=l&&r<=qr)return bt[rt].rank_max(val);
	int ans=0,mid=(l+r)>>1;
	if(ql<=mid)ans+=Rank_max(rt<<1,l,mid,ql,qr,val);
	if(qr>mid) ans+=Rank_max(rt<<1|1,mid+1,r,ql,qr,val);
	return ans;
}
int c[N];
int tmp[N],n;
int a[N],ans;
inline void Merge_sort(int L,int R)
{
	if(L==R)return;
	int mid=(L+R)>>1;
	Merge_sort(L,mid),Merge_sort(mid+1,R);
	int l=L,r=mid+1,t=L;
	while(l<=mid&&r<=R)
	{
		if(c[l]>c[r])ans+=mid-l+1,tmp[t++]=c[r++];
		else tmp[t++]=c[l++];
	}
	while(l<=mid)tmp[t++]=c[l++];
	while(r<=R)tmp[t++]=c[r++];
	for(int i=L;i<=R;++i)c[i]=tmp[i];
}
int main(void)
{
	#ifndef ONLINE_JUDGE
	File("file");
	#endif
	n=gi;
	for(int i=1;i<=n;++i)c[i]=a[i]=gi,Insert(1,1,n,i,a[i]);
	Merge_sort(1,n);
	pi(ans,'
');
	int m=gi;
	while(m--)
	{
		int l=gi,r=gi;
		if(l>r)swap(l,r);
		ans+=Rank_max(1,1,n,l+1,r-1,a[l])-Rank_min(1,1,n,l+1,r-1,a[l]);
		ans+=Rank_min(1,1,n,l+1,r-1,a[r])-Rank_max(1,1,n,l+1,r-1,a[r]);
		if(a[l]>a[r])--ans;
		if(a[l]<a[r])++ans;
		pi(ans,'
');
		Insert(1,1,n,l,a[r]);
		Insert(1,1,n,r,a[l]);
		Remove(1,1,n,l,a[l]);
		Remove(1,1,n,r,a[r]);
		swap(a[l],a[r]);
	}
	return 0;
}