BZOJ3224[Tyvj 1728 普通平衡树]题解--Treap

#include<cstdio>
#include<cstdlib>
using namespace std;
const int maxn=100005;
int n,rot,ans,tot;
struct Treap
{
int x,l,r,w,s,ran;
}a[maxn];
inline int Read()
{
int res=0,f=1;
char ch=getchar(),cc=ch;
while (ch<'0'||ch>'9') cc=ch,ch=getchar();
if (cc=='-') f=-1;
while (ch>='0'&&ch<='9') res=res*10+ch-48,ch=getchar();
return res*f;
}
void Updata(int k)
{
a[k].s=a[a[k].l].s+a[a[k].r].s+a[k].w;
}
void Rturn(int &k)
{
int t=a[k].l; a[k].l=a[t].r; a[t].r=k;
a[t].s=a[k].s; Updata(k); k=t;
}
void Lturn(int &k)
{
int t=a[k].r; a[k].r=a[t].l; a[t].l=k;
a[t].s=a[k].s; Updata(k); k=t;
}
void Insert(int &k,int x)
{
if (k==0) {k=++tot; a[k].x=x; a[k].w=a[k].s=1; a[k].ran=rand(); return;}
a[k].s++;
if (a[k].x==x) a[k].w++;
else if (x<a[k].x)
{
Insert(a[k].l,x);
if (a[a[k].l].ran<a[k].ran) Rturn(k);
}
else
{
Insert(a[k].r,x);
if (a[a[k].r].ran<a[k].ran) Lturn(k);
}
}
void Delete(int &k,int x)
{
if (k==0) return;
if (a[k].x==x)
{
if (a[k].w>1) {a[k].w--; a[k].s--; return;}
else if (!a[k].l||!a[k].r) k=a[k].l+a[k].r;
else if (a[a[k].l].ran<a[a[k].r].ran) {Rturn(k); Delete(k,x);} else {Lturn(k); Delete(k,x);}
}
else if (x<a[k].x) a[k].s--,Delete(a[k].l,x); else a[k].s--,Delete(a[k].r,x);
}
int Rank(int k,int x)
{
if (k==0) return 0;
if (x==a[k].x) return a[a[k].l].s+1;
if (x<a[k].x) return Rank(a[k].l,x); else return a[a[k].l].s+a[k].w+Rank(a[k].r,x);
}
int Num(int k,int x)
{
if (k==0) return 0;
if (x<=a[a[k].l].s) return Num(a[k].l,x);
else if (x>a[a[k].l].s+a[k].w) return Num(a[k].r,x-a[a[k].l].s-a[k].w);
else return a[k].x;
}
void Pre(int k,int x)
{
if (k==0) return;
if (x>a[k].x) {ans=a[k].x; Pre(a[k].r,x);} else Pre(a[k].l,x);
}
void Sub(int k,int x)
{
if (k==0) return;
if (x<a[k].x) {ans=a[k].x; Sub(a[k].l,x);} else Sub(a[k].r,x);
}
int main()
{
freopen("3224.in","r",stdin);
freopen("3224.out","w",stdout);
n=Read(); rot=tot=0;
while (n--)
{
int id=Read(),x=Read();
switch(id)
{
case 1:Insert(rot,x);break;
case 2:Delete(rot,x);break;
case 3:printf("%d\n",Rank(rot,x));break;
case 4:printf("%d\n",Num(rot,x));break;
case 5:ans=0,Pre(rot,x),printf("%d\n",ans);break;
case 6:ans=0,Sub(rot,x),printf("%d\n",ans);break;
}
}
return 0;
}

#include<cstdio>
#include<cstdlib>
using namespace std;
const int maxn=100005;
int n,tot,ans;
struct Treap
{
Treap* son[2];
int x,w,s,ran;
int Cmp(int k) {if (k<x) return 0; if (k>x) return 1; return -1;}
void Pushup() {s=son[0]->s+son[1]->s+w;};
}a[maxn],*Null=a,*rot=Null;
inline int Read()
{
int res=0,f=1;
char ch=getchar(),cc=ch;
while (ch<'0'||ch>'9') cc=ch,ch=getchar();
if (cc=='-') f=-1;
while (ch>='0'&&ch<='9') res=res*10+ch-48,ch=getchar();
return res*f;
}
Treap* New(int x,int p)
{
++tot; a[tot].w=a[tot].s=p; a[tot].x=x; a[tot].ran=rand();
a[tot].son[0]=a[tot].son[1]=Null;
return &a[tot];
}
void Turn(Treap* &k,int d)
{
Treap* t=k->son[d]; k->son[d]=t->son[d^1]; t->son[d^1]=k;
t->s=k->s; k->Pushup(); k=t;
}
void Insert(Treap* &k,int x,int p)
{
if (k==Null) {k=New(x,p); return;}
int d=k->Cmp(x); k->s+=p;
if (d<0) k->w+=p;
else
{
Insert(k->son[d],x,p);
if (k->son[d]->ran<k->ran) Turn(k,d);
}
}
void Delete(Treap* &k,int x)
{
if (k==Null) return;
int d=k->Cmp(x);
if (d<0)
{
if (k->w>1) {k->w--; k->s--; return;}
else if (k->son[0]==Null) k=k->son[1];
else if (k->son[1]==Null) k=k->son[0];
else if (k->son[0]->ran<k->son[1]->ran) {Turn(k,0); Delete(k,x);} else {Turn(k,1); Delete(k,x);}
}
else k->s--,Delete(k->son[d],x);
}
int Rank(Treap* k,int x)
{
if (k==Null) return -1;
int d=k->Cmp(x);
if (d<0) return k->son[0]->s+1;
else if (!d) return Rank(k->son[0],x);
else return k->son[0]->s+k->w+Rank(k->son[1],x);
}
int Num(Treap* k,int x)
{
if (k==Null) return 0;
if (x<=k->son[0]->s) return Num(k->son[0],x);
else if (x>k->son[0]->s+k->w) return Num(k->son[1],x-k->son[0]->s-k->w);
else return k->x;
}
int Pre(Treap* k,int x)
{
if (k==Null) return -1;
if (x>k->x) {ans=k->x; Pre(k->son[1],x);} else Pre(k->son[0],x);
}
int Sub(Treap* k,int x)
{
if (k==Null) return -1;
if (x<k->x) {ans=k->x; Sub(k->son[0],x);} else Sub(k->son[1],x);
}
int main()
{
freopen("3224.in","r",stdin);
freopen("3224.out","w",stdout);
n=Read(); tot=0; int i=0;
while (n--)
{
int id=Read(),x=Read(); ++i;
switch(id)
{
case 1:Insert(rot,x,1);break;
case 2:Delete(rot,x);break;
case 3:printf("%d\n",Rank(rot,x));break;
case 4:printf("%d\n",Num(rot,x));break;
case 5:ans=0,Pre(rot,x),printf("%d\n",ans);break;
case 6:ans=0,Sub(rot,x),printf("%d\n",ans);break;
}
}
return 0;
}