BZOJ 3295 CQOI 2011 动态逆序对 线段树套Treap

题目大意：给出一个数列，每次从这个序列中删掉一个数字，问每次删之前逆序对的数量是多少。

思路：这个题用CDQ分治是飞快的，然而我不知道怎么写。。于是就朴素的写了树套树。然后就朴素的被卡常了

内层用一个线段树。这个线段树不修改，一开始就要建好，然后线段树的每一个节点维护一个平衡树，存的是线段树存的区间中所有的值。

一开始先算一下逆序对数，然后每次删点的时候，先查询在这个点之前有多少大于他的，后面有多少小于他的，总的逆序对中将这些减掉。这个过程通过树套树不难实现。

CODE（交了这个代码T掉的，请选择在人多的时候先交一发糖果公园再交一次本题即可。。。因为多人测的时候会放宽一点时限。。。

你们感受一下

）：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAX 100010
using namespace std;
#define LEFT (pos << 1)
#define RIGHT (pos << 1|1)
#define SIZE(a) ((a) == NULL ? 0:a->size)

namespace IStream{
    const int L=1<<15;
    char buffer[L],*S,*T;
    inline char Get_Char()
    {
        if(S==T)
        {
            T=(S=buffer)+fread(buffer,1,L,stdin);
            if(S==T) return EOF;
        }
        return *S++;
    }
    inline int GetInt()
    {
        char c;
        int re=0;
        for(c=Get_Char();c<'0'||c>'9';c=Get_Char());
        while(c>='0'&&c<='9')
            re=(re<<1)+(re<<3)+(c-'0'),c=Get_Char();
        return re;
    }
}  

/*class OStream{
    private:
        static const int L=1<<15;
        char stack[20];int top;
        char buffer[L],*S;
    public:
        OStream()
        {
            S=buffer;
        }
        void PutLongLong(long long x)
        {
            stack[++top]='\n';
            if(!x) stack[++top]='0';
            else while(x)
                stack[++top]=x%10+'0',x/=10;
            while(top)
            {
                if(S==buffer+L-1)
                {
                    printf("%s",buffer);
                    S=buffer;
                }
                *S++=stack[top--];
            }
        }
        ~OStream()
        {
            *S=0;
            puts(buffer);
        }
}os;*/

int cnt,asks;
int src[MAX],pos[MAX];
int fenwick[MAX];
long long inv;

struct Treap{
	int random,val,size;
	Treap *son[2];

	Treap(int _) {
		val = _;
		random = rand();
		size = 1;
		son[0] = son[1] = NULL;
	}
	int Compare(int x) {
		if(x == val)	return -1;
		return x > val;
	}
	void Maintain() {
		size = 1;
		if(son[0] != NULL)	size += son[0]->size;
		if(son[1] != NULL)	size += son[1]->size;
	}
}*tree[MAX << 2];

inline int GetSum(int x)
{
	int re = 0;
	for(; x < MAX; x += x&-x)
		re += fenwick[x];
	return re;
}

inline void Fix(int x,int c)
{
	for(; x; x -= x&-x)
		fenwick[x] += c;
}

inline void Rotate(Treap *&a,bool dir)
{
	Treap *k = a->son[!dir];
	a->son[!dir] = k->son[dir];
	k->son[dir] = a;
	a->Maintain(),k->Maintain();
	a = k;
}

void Insert(Treap *&a,int x)
{
	if(a == NULL) {
		a = new Treap(x);
		return ;
	}
	int dir = a->Compare(x);
	Insert(a->son[dir],x);
	if(a->son[dir]->random > a->random)
		Rotate(a,!dir);
	a->Maintain();
}

void Delete(Treap *&a,int x)
{
	int dir = a->Compare(x);
	if(dir != -1)
		Delete(a->son[dir],x);
	else {
		if(a->son[0] == NULL)	a = a->son[1];
		else if(a->son[1] == NULL)	a = a->son[0];
		else {
			int _ = (a->son[0]->random > a->son[1]->random);
			Rotate(a,_);
			Delete(a->son[_],x);
		}
	}
	if(a != NULL)	a->Maintain();
}

int Ask(Treap *a,int x)
{
	if(a == NULL)	return 0;
	if(a->val > x)	return Ask(a->son[0],x);
	if(a->val == x)	return SIZE(a->son[0]);
	return SIZE(a->son[0]) + 1 + Ask(a->son[1],x);
}

void BuildTree(int l,int r,int pos)
{
	for(int i = l; i <= r; ++i)
		Insert(tree[pos],src[i]);
	if(l == r)	return ;
	int mid = (l + r) >> 1;
	BuildTree(l,mid,LEFT);
	BuildTree(mid + 1,r,RIGHT);
}

void Delete(int l,int r,int x,int pos,int c)
{
	Delete(tree[pos],c);
	if(l == r)	return ;
	int mid = (l + r) >> 1;
	if(x <= mid)	Delete(l,mid,x,LEFT,c);
	else	Delete(mid + 1,r,x,RIGHT,c);
}

int Ask(int l,int r,int x,int y,int pos,int c)
{
	if(l == x && y == r)
		return Ask(tree[pos],c);
	int mid = (l + r) >> 1;
	if(y <= mid)	return Ask(l,mid,x,y,LEFT,c);
	if(x > mid)	return Ask(mid + 1,r,x,y,RIGHT,c);
	int left = Ask(l,mid,x,mid,LEFT,c);
	int right = Ask(mid + 1,r,mid + 1,y,RIGHT,c);
	return left + right;
}

int main()
{
	srand(19970815);
	cin >> cnt >> asks;
	for(int i = 1; i <= cnt; ++i) {
		src[i] = IStream::GetInt();
		//scanf("%d",&src[i]);
		pos[src[i]] = i;
		inv += GetSum(src[i]);
		Fix(src[i],1);
	}
	BuildTree(1,cnt,1);

	memset(fenwick,0,sizeof(fenwick));
	for(int i = 1; i <= cnt; ++i)
		Fix(i,1);
	for(int x,i = 1; i <= asks; ++i) {
		printf("%lld\n",inv);
		//os.PutLongLong(inv);
		x = IStream::GetInt();
		//scanf("%d",&x);
		Delete(1,cnt,pos[x],1,x);
		Fix(pos[x],-1);
		if(pos[x] != 1)
			inv -= (GetSum(1) - GetSum(pos[x]) - Ask(1,cnt,1,pos[x] - 1,1,x));
		if(pos[x] != cnt)
			inv -= Ask(1,cnt,pos[x] + 1,cnt,1,x);
	}
	return 0;
}