小结-Splay
参照陈竞潇学长的模板写的BZOJ 3188：
#include<cstdio>
#include<cstring>
#include<algorithm>
#define for1(i,a,b) for(int i=(a);i<=(b);++i)
using namespace std;
typedef long long ll;
const int N=1E5+100;
int n,m,data[N];
struct node{
node();
node *ch[2],*fa;
ll d,sum,set,add[2]; int size; short vset;
short pl() {return this==fa->ch[1];}
void count(); void push();
void mark(ll,ll,short);
}*null;
node::node(){ch[0]=ch[1]=fa=null; size=vset=sum=add[0]=add[1]=0;}
void node::mark(ll val,ll dd,short t){
if(this==null) return;
if(!t){
set=val;
sum=size*set;
d=set;
vset=1;
add[0]=add[1]=0;
}else{
add[0]+=val;
add[1]+=dd;
sum+=val*size;
sum+=dd*size*(size-1)/2;
d+=val+dd*(ch[0]->size);
}
}
void node::push(){
if(this==null)return;
if(vset){
ch[0]->mark(set,0,0);
ch[1]->mark(set,0,0);
vset=0; set=0;
}
if(add[0]||add[1]){
ch[0]->mark(add[0],add[1],1);
ch[1]->mark(add[0]+add[1]*(ch[0]->size+1),add[1],1);
add[0]=add[1]=0;
}
}
void node::count(){
size=ch[0]->size+ch[1]->size+1;
sum=ch[0]->sum+ch[1]->sum+d;
}
namespace Splay{
node *ROOT;
node *build(int l=1,int r=n){
if (l>r) return null;
int mid=(l+r)>>1;
node *ro=new node;
ro->d=data[mid];
ro->ch[0]=build(l,mid-1);
ro->ch[1]=build(mid+1,r);
ro->ch[0]->fa=ro;
ro->ch[1]->fa=ro;
ro->count();
return ro;
}
void Build(){
null=new node;
*null=node();
ROOT=build();
}
void rotate(node *k){
node *r=k->fa; if (k==null||r==null) return;
r->push(); k->push();
int x=k->pl()^1;;
r->ch[x^1]=k->ch[x];
r->ch[x^1]->fa=r;
if (r->fa!=null) r->fa->ch[r->pl()]=k;
else ROOT=k;
k->fa=r->fa; r->fa=k;
k->ch[x]=r;
r->count(); k->count();
}
void splay(node *r,node *tar=null){
for (;r->fa!=tar;rotate(r))
if (r->fa->fa!=tar)rotate(r->pl()==r->fa->pl()?r->fa:r);
r->push();
}
void insert(int x,int val){
node *r=ROOT;
if (ROOT==null){
ROOT=new node;
ROOT->d=val;
ROOT->count();
return;
}
while (1)
{
r->push();
int c;
if (r->ch[0]->size+1>=x) c=0;
else c=1,x-=r->ch[0]->size+1;
if (r->ch[c]==null){
r->ch[c]=new node;
r->ch[c]->fa=r;
r->ch[c]->d=val;
splay(r->ch[c]);
return;
}else r=r->ch[c];
}
}
node *kth(int k){
node *r=ROOT;
while (r!=null){
r->push();
if (r->ch[0]->size>=k) r=r->ch[0];
else if (r->ch[0]->size+1>=k) return r;
else k-=r->ch[0]->size+1,r=r->ch[1];
}
return null;
}
node *pack(int l,int r){
node *ln=kth(l-1),*rn=kth(r+1);
if ((ln==null)&&(rn==null)) return ROOT;
else if (ln==null){
splay(rn); return rn->ch[0];
}else if (rn==null){
splay(ln); return ln->ch[1];
}else{
splay(ln); splay(rn,ROOT);
return rn->ch[0];
}
}
}
int main(){
scanf("%d%d",&n,&m);
for1(i,1,n)scanf("%d",&data[i]);
Splay::Build(); int j,a,b,c;
for1(i,1,m){
scanf("%d",&j);
switch(j){
node *r;
case 1:
scanf("%d%d%d",&a,&b,&c);
r=Splay::pack(a,b);
r->mark(c,0,0);
Splay::splay(r);
break;
case 2:
scanf("%d%d%d",&a,&b,&c);
r=Splay::pack(a,b);
r->mark(c,c,1);
Splay::splay(r);
break;
case 3:
scanf("%d%d",&a,&b);
Splay::insert(a,b);
break;
case 4:
scanf("%d%d",&a,&b);
r=Splay::pack(a,b);
printf("%lld\n",r->sum);
break;
}
}
return 0;
}
还是参照陈竞潇学长的模板写的指针版的BZOJ 3224普通平衡树：
#include<cctype>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define for1(i,a,b) for(int i=(a);i<=(b);++i)
using namespace std;
typedef long long ll;
struct node{
node();
node *ch[2],*fa;
int d,size,sum;
short pl(){return this==fa->ch[1];}
void count(){sum=ch[0]->sum+ch[1]->sum+size;}
}*null;
node::node(){ch[0]=ch[1]=fa=null;size=sum=0;}
int getint(){
char c; int fh=1;
while (!isdigit(c=getchar()))
if (c=='-') fh=-1;
int a=c-'0';
while (isdigit(c=getchar()))
a=a*10+c-'0';
return a*fh;
}
namespace Splay{
node *ROOT;
void Build(){
null=new node;
*null=node();
ROOT=null;
}
void rotate(node *k){
node *r=k->fa; if (k==null||r==null) return;
int x=k->pl()^1;
r->ch[x^1]=k->ch[x];
r->ch[x^1]->fa=r;
if (r->fa!=null) r->fa->ch[r->pl()]=k;
else ROOT=k;
k->fa=r->fa; r->fa=k;
k->ch[x]=r;
r->count(); k->count();
}
void splay(node *r,node *tar=null){
for (;r->fa!=tar;rotate(r))
if (r->fa->fa!=tar) rotate(r->pl()==r->fa->pl()?r->fa:r);
}
void updata(node *r){
while (r!=null){
r->count();
r=r->fa;
}
}
void insert(int x){
node *r=ROOT;
if (ROOT==null){
ROOT=new node;
ROOT->d=x;
ROOT->size=1;
ROOT->sum=1;
return;
}
while (1){
int c;
if (x<r->d) c=0;
else if (x>r->d) c=1;
else {r->size++;r->sum++;splay(r); return;}
if (r->ch[c]==null){
r->ch[c]=new node;
r->ch[c]->fa=r;
r->ch[c]->d=x;
r->ch[c]->size=1;
r->ch[c]->sum=1;
splay(r->ch[c]);
return;
}else r=r->ch[c];
}
}
node *kth(int k){
node *r=ROOT;
while (r!=null){
if (r->ch[0]->sum>=k) r=r->ch[0];
else if (r->ch[0]->sum+r->size>=k) return r;
else k-=r->ch[0]->sum+r->size,r=r->ch[1];
}
return null;
}
node *ques(int k){
node *r=ROOT; int ans=0;
while (r!=null){
if (k<r->d) r=r->ch[0];
else if (k>r->d) ans+=r->ch[0]->sum+r->size,r=r->ch[1];
else {printf("%d\n",ans+r->ch[0]->sum+1); return r;}
}
return null;
}
node *ques2(int k){
node *r=ROOT;
while (r!=null){
if (k<r->d) r=r->ch[0];
else if (k>r->d) r=r->ch[1];
else return r;
}
return null;
}
node *rightdown(node *r){
while (r->ch[1]!=null){
r=r->ch[1];
}return r;
}
node *leftdown(node *r){
while (r->ch[0]!=null){
r=r->ch[0];
}return r;
}
void deleter(node *r){
if (r->size>1){
splay(r);
r->size--; r->sum--; return;
}else{
splay(r);
if ((r->ch[0]==null)&&(r->ch[1]==null)){
ROOT=null;
delete r;
}else if (r->ch[0]==null){
r->ch[1]->fa=null;
ROOT=r->ch[1];
delete r;
}else if (r->ch[1]==null){
r->ch[0]->fa=null;
ROOT=r->ch[0];
delete r;
}else{
splay(rightdown(r->ch[0]),ROOT);
r->ch[0]->ch[1]=r->ch[1];
r->ch[1]->fa=r->ch[0];
r->ch[0]->fa=null;
r->ch[0]->count();
ROOT=r->ch[0];
delete r;
}
}
}
int predd(node *r,int x){
if (r==null) return -1E7-10;
if (x<=r->d) return predd(r->ch[0],x);
return max(r->d,predd(r->ch[1],x));
}
int pross(node *r,int x){
if (r==null) return 1E7+10;
if (r->d<=x) return pross(r->ch[1],x);
return min(r->d,pross(r->ch[0],x));
}
int predds(int x){
return predd(ROOT,x);
}
int prosss(int x){
return pross(ROOT,x);
}
}
int main()
{
int n,x,num;
n=getint();
Splay::Build();
while (n>0){n--;
x=getint();
switch(x){
node *r;
case 1:
num=getint();
Splay::insert(num);
break;
case 2:
num=getint();
r=Splay::ques2(num);
Splay::deleter(r);
break;
case 3:
num=getint();
r=Splay::ques(num);
break;
case 4:
num=getint();
r=Splay::kth(num);
printf("%d\n",r->d);
break;
case 5:
num=getint();
printf("%d\n",Splay::predds(num));
break;
case 6:
num=getint();
printf("%d\n",Splay::prosss(num));
break;
}
}
return 0;
}
还是参照陈竞潇学长的模板写的BZOJ 3224普通平衡树，数组版，效率和指针版的差不多，但更短，也许是我压代码了吧，，，
#include<cstdio>
#include<algorithm>
#define read(x) x=getint()
using namespace std;
inline const int getint(){char c=getchar();int k=1,r=0;for(;c<'0'||c>'9';c=getchar())if(c=='-')k=-1;for(;c>='0'&&c<='9';c=getchar())r=r*10+c-'0';return k*r;}
struct node{
int fa,ch[2],d,size,sum;
}T[100003];
int chi[100003],top=0,cnt=1,ROOT=0;
inline bool pl(int X){return T[T[X].fa].ch[1]==X;}
inline void newnode(int &X){
if (top) {X=chi[top];top--;} else X=cnt++;
T[X].fa=T[X].ch[0]=T[X].ch[1]=T[X].d=T[X].size=T[X].sum=0;
}
inline void count(int k){T[k].sum=T[T[k].ch[0]].sum+T[T[k].ch[1]].sum+T[k].size;}
inline void rotate(int k){
int r=T[k].fa; if (k==0||r==0) return;
int x=pl(k)^1;
T[r].ch[x^1]=T[k].ch[x];
T[T[r].ch[x^1]].fa=r;
if (T[r].fa!=0) T[T[r].fa].ch[pl(r)]=k;
else ROOT=k;
T[k].fa=T[r].fa; T[r].fa=k; T[k].ch[x]=r;
count(r); count(k);
}
inline void splay(int k,int tar=0){
for(;T[k].fa!=tar;rotate(k))
if (T[T[k].fa].fa!=tar) rotate(pl(k)==pl(T[k].fa)?T[k].fa:k);
}
inline void insect(int x){
int k=ROOT;
if (ROOT==0){
newnode(ROOT);
T[ROOT].d=x; T[ROOT].size=T[ROOT].sum=1;
return;
}
while (1){
int c;
if (x<T[k].d) c=0;
else if (x>T[k].d) c=1;
else {T[k].size++;T[k].sum++;splay(k);return;}
if (T[k].ch[c]==0){
newnode(T[k].ch[c]);
T[T[k].ch[c]].fa=k;
T[T[k].ch[c]].d=x;
T[T[k].ch[c]].size=1;
T[T[k].ch[c]].sum=1;
splay(T[k].ch[c]);
return;
}else k=T[k].ch[c];
}
}
inline void del(int x){top++; chi[top]=x;}
inline int rightdown(int x){
while (T[x].ch[1]!=0) x=T[x].ch[1];
return x;
}
inline void deletr(int x){
int k=ROOT;
while (k){
if (x<T[k].d) k=T[k].ch[0];
else if (x>T[k].d) k=T[k].ch[1];
else break;
}if (k==0) return;
if (T[k].size>1){
splay(k);
T[k].size--;T[k].sum--;return;
}else{
splay(k);
if ((T[k].ch[0]==0)&&(T[k].ch[1]==0)){
ROOT=0; del(k);
}else if (T[k].ch[0]==0){
T[T[k].ch[1]].fa=0;
ROOT=T[k].ch[1];
del(k);
}else if (T[k].ch[1]==0){
T[T[k].ch[0]].fa=0;
ROOT=T[k].ch[0];
del(k);
}else{
splay(rightdown(T[k].ch[0]),ROOT);
T[T[k].ch[0]].ch[1]=T[k].ch[1];
T[T[k].ch[1]].fa=T[k].ch[0];
T[T[k].ch[0]].fa=0;
count(T[k].ch[0]);
ROOT=T[k].ch[0];
del(k);
}
}
}
inline void query(int x){
int k=ROOT,s=0;
while (k){
if (x<T[k].d) k=T[k].ch[0];
else if (x>T[k].d) s+=T[T[k].ch[0]].sum+T[k].size,k=T[k].ch[1];
else break;
}printf("%d\n",s+T[T[k].ch[0]].sum+1);
}
inline void queryk(int x){
int k=ROOT;
while (k){
if (T[T[k].ch[0]].sum>=x) {k=T[k].ch[0];}
else {if (T[T[k].ch[0]].sum+T[k].size>=x) break;
else x-=T[T[k].ch[0]].sum+T[k].size;k=T[k].ch[1];}
}printf("%d\n",T[k].d);
}
inline int pre(int k,int x){
if (k==0) return -1E7-10;
if (x<=T[k].d) return pre(T[k].ch[0],x);
return max(pre(T[k].ch[1],x),T[k].d);
}
inline int pro(int k,int x){
if (k==0) return 1E7+10;
if (T[k].d<=x) return pro(T[k].ch[1],x);
return min(pro(T[k].ch[0],x),T[k].d);
}
int main(){
int t,opt,x; read(t);
while (t--){
read(opt); read(x);
switch (opt){
case 1:
insect(x);
break;
case 2:
deletr(x);
break;
case 3:
query(x);
break;
case 4:
queryk(x);
break;
case 5:
printf("%d\n",pre(ROOT,x));
break;
case 6:
printf("%d\n",pro(ROOT,x));
break;
}
}return 0;
}
指针版的内存池，补上：
#include<cctype>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define for1(i,a,b) for(int i=(a);i<=(b);++i)
using namespace std;
typedef long long ll;
struct node{
node *ch[2],*fa;
int d,size,sum;
short pl(){return this==fa->ch[1];}
void count(){sum=ch[0]->sum+ch[1]->sum+size;}
}*null;
int getint(){char c;int fh=1;while(!isdigit(c=getchar()))if(c=='-')fh=-1;int a=c-'0';while(isdigit(c=getchar()))a=a*10+c-'0';return a*fh;}
namespace Splay{
node *ROOT,pool[100003];
int tot=0;
node *newnode(){
node *t=&pool[tot++];
t->ch[0]=t->ch[1]=t->fa=null;
t->size=t->sum=0;
return t;
}
void Build(){
null=newnode();
null->ch[0]=null->ch[1]=null->fa=null;
ROOT=null;
}
void rotate(node *k){
node *r=k->fa; if (k==null||r==null) return;
int x=k->pl()^1;
r->ch[x^1]=k->ch[x];
r->ch[x^1]->fa=r;
if (r->fa!=null) r->fa->ch[r->pl()]=k;
else ROOT=k;
k->fa=r->fa; r->fa=k;
k->ch[x]=r;
r->count(); k->count();
}
void splay(node *r,node *tar=null){
for (;r->fa!=tar;rotate(r))
if (r->fa->fa!=tar) rotate(r->pl()==r->fa->pl()?r->fa:r);
}
void updata(node *r){
while (r!=null){
r->count();
r=r->fa;
}
}
void insert(int x){
node *r=ROOT;
if (ROOT==null){
ROOT=newnode();
ROOT->d=x;
ROOT->size=1;
ROOT->sum=1;
return;
}
while (1){
int c;
if (x<r->d) c=0;
else if (x>r->d) c=1;
else {r->size++;r->sum++;splay(r); return;}
if (r->ch[c]==null){
r->ch[c]=newnode();
r->ch[c]->fa=r;
r->ch[c]->d=x;
r->ch[c]->size=1;
r->ch[c]->sum=1;
splay(r->ch[c]);
return;
}else r=r->ch[c];
}
}
node *kth(int k){
node *r=ROOT;
while (r!=null){
if (r->ch[0]->sum>=k) r=r->ch[0];
else if (r->ch[0]->sum+r->size>=k) return r;
else k-=r->ch[0]->sum+r->size,r=r->ch[1];
}
return null;
}
node *ques(int k){
node *r=ROOT; int ans=0;
while (r!=null){
if (k<r->d) r=r->ch[0];
else if (k>r->d) ans+=r->ch[0]->sum+r->size,r=r->ch[1];
else {printf("%d\n",ans+r->ch[0]->sum+1); return r;}
}
return null;
}
node *ques2(int k){
node *r=ROOT;
while (r!=null){
if (k<r->d) r=r->ch[0];
else if (k>r->d) r=r->ch[1];
else return r;
}
return null;
}
node *rightdown(node *r){
while (r->ch[1]!=null){
r=r->ch[1];
}return r;
}
node *leftdown(node *r){
while (r->ch[0]!=null){
r=r->ch[0];
}return r;
}
void deleter(node *r){
if (r->size>1){
splay(r);
r->size--; r->sum--; return;
}else{
splay(r);
if ((r->ch[0]==null)&&(r->ch[1]==null)){
ROOT=null;
}else if (r->ch[0]==null){
r->ch[1]->fa=null;
ROOT=r->ch[1];
}else if (r->ch[1]==null){
r->ch[0]->fa=null;
ROOT=r->ch[0];
}else{
splay(rightdown(r->ch[0]),ROOT);
r->ch[0]->ch[1]=r->ch[1];
r->ch[1]->fa=r->ch[0];
r->ch[0]->fa=null;
r->ch[0]->count();
ROOT=r->ch[0];
}
}
}
int predd(node *r,int x){
if (r==null) return -1E7-10;
if (x<=r->d) return predd(r->ch[0],x);
return max(r->d,predd(r->ch[1],x));
}
int pross(node *r,int x){
if (r==null) return 1E7+10;
if (r->d<=x) return pross(r->ch[1],x);
return min(r->d,pross(r->ch[0],x));
}
int predds(int x){
return predd(ROOT,x);
}
int prosss(int x){
return pross(ROOT,x);
}
}
int main()
{
int n,x,num;
n=getint();
Splay::Build();
while (n>0){n--;
x=getint();
switch(x){
node *r;
case 1:
num=getint();
Splay::insert(num);
break;
case 2:
num=getint();
r=Splay::ques2(num);
Splay::deleter(r);
break;
case 3:
num=getint();
r=Splay::ques(num);
break;
case 4:
num=getint();
r=Splay::kth(num);
printf("%d\n",r->d);
break;
case 5:
num=getint();
printf("%d\n",Splay::predds(num));
break;
case 6:
num=getint();
printf("%d\n",Splay::prosss(num));
break;
}
}
return 0;
}
差不多了
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