bzoj 2141: 排队 树状数组套线段树

题目

传送门

分析

树状数组套线段树。

对于每一次交换x和y的操作，先减去在交换之前x和y分别与a[x+1..y-1]产生了多少逆序对，再加上交换后x和y分别与a[x+1..y-1]产生了多少逆序对，然后再进行交换操作就好了。

一开始的想法是线段树套线段树，但是很明显线段树各方面的指标都没有树状数组优秀，所以就果断改成了树状数组。

貌似分块+二分或分块套树状数组或线段树套平衡树也是可做的，懒得打了。

代码

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#define N 20005
using namespace std;

int a
,root
,n,m,tot;
struct Segtree{int l,r,size;}t[10000005];

int lowbit(int x)
{
return x&(-x);
}

void Segtree_ins(int &d,int l,int r,int x,int y)
{
if (!d) d=++tot;
t[d].size+=y;
if (l==r) return;
int mid=(l+r)/2;
if (x<=mid) Segtree_ins(t[d].l,l,mid,x,y);
else Segtree_ins(t[d].r,mid+1,r,x,y);
}

int Segtree_bigger(int &d,int l,int r,int x)
{
if (l==r||!d) return 0;
int mid=(l+r)/2;
if (x<=mid) return t[t[d].r].size+Segtree_bigger(t[d].l,l,mid,x);
else return Segtree_bigger(t[d].r,mid+1,r,x);
}

int Segtree_smaller(int &d,int l,int r,int x)
{
if (l==r||!d) return 0;
int mid=(l+r)/2;
if (x<=mid) return Segtree_smaller(t[d].l,l,mid,x);
else return t[t[d].l].size+Segtree_smaller(t[d].r,mid+1,r,x);
}

void Treearr_ins(int x,int y)
{
while (x<=n)
{
Segtree_ins(root[x],1,1000000000,y,1);
x+=lowbit(x);
}
}

void Treearr_del(int x,int y)
{
while (x<=n)
{
Segtree_ins(root[x],1,1000000000,y,-1);
x+=lowbit(x);
}
}

int Treearr_bigger(int x,int y)
{
int ans=0;
while (x)
{
ans+=Segtree_bigger(root[x],1,1000000000,y);
x-=lowbit(x);
}
return ans;
}

int Treearr_smaller(int x,int y)
{
int ans=0;
while (x)
{
ans+=Segtree_smaller(root[x],1,1000000000,y);
x-=lowbit(x);
}
return ans;
}

int main()
{
scanf("%d",&n);
int ans=0;
for (int i=1;i<=n;i++)
{
scanf("%d",&a[i]);
ans+=Treearr_bigger(i-1,a[i]);
Treearr_ins(i,a[i]);
}
printf("%d\n",ans);
scanf("%d",&m);
for (int i=1;i<=m;i++)
{
int x,y;
scanf("%d%d",&x,&y);
if (x>y) swap(x,y);
ans-=Treearr_smaller(y-1,a[x])-Treearr_smaller(x,a[x])+Treearr_bigger(y-1,a[y])-Treearr_bigger(x,a[y]);
ans+=Treearr_bigger(y-1,a[x])-Treearr_bigger(x,a[x])+Treearr_smaller(y-1,a[y])-Treearr_smaller(x,a[y]);
if (a[x]<a[y]) ans++;
else if (a[x]>a[y]) ans--;
printf("%d\n",ans);
Treearr_del(x,a[x]);Treearr_del(y,a[y]);
swap(a[x],a[y]);
Treearr_ins(x,a[x]);Treearr_ins(y,a[y]);
}
return 0;
}