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