BZOJ1500 NOI2005 维修数列 平衡树

题意：给定一个数列，要求维护：1、在p之后加入tot个数  2、删除p之后tot个数  3、将p之后tot个数修改为c  4、翻转p之后tot个数  5、输出p之后tot个数的和  6、输出整个数列的最大子段和。

题解：平衡树很经典的题目了……主要说一下4和6操作，4的话因为翻转操作是可以分治的，所以可以用翻转标记；6我们维护一个节点所维护的区间的的最大子段和ms、从左开始的最大子段和lms、从右开始的最大子段和rms，显然有ms=max(lchild->ms,rchild->ms,lchild->rms(或0)+v+rchild->lms(或0))

Treap和Splay各敲了一遍，现在想想当初学复数个平衡树的我真是个傻X

Splay：

#include <cstdio>
#include <climits>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;

const int MAXN=500000+2;
typedef struct NODE{
    NODE *child[2],*f;
    int s,c,v,ms,lms,rms;
    bool same,rev;
    NODE(){}
    NODE(int _v,NODE *_f):s(_v),v(_v),ms(_v),lms(_v),rms(_v),f(_f){}
} *TREE;
TREE root,Null;
int N,M,a[MAXN];
char Order[20+2];

TREE NewNode(int v,TREE f){
    TREE x=new NODE(v,f);
    x->child[0]=x->child[1]=Null;
    x->c=1,x->same=x->rev=0;
    return x;
}

void Initialization(){
    Null=NewNode(SHRT_MIN,0),Null->c=0;
    root=NewNode(SHRT_MIN,Null);
    root->child[1]=NewNode(SHRT_MIN,root);
    Null->s=root->s=root->child[1]->s=0;
}

void Pushup(TREE x){
    if(x==Null) return;
    x->c=x->child[0]->c+x->child[1]->c+1;
    x->s=x->child[0]->s+x->child[1]->s+x->v;
    x->ms=max(x->child[0]->ms,x->child[1]->ms);
    x->ms=max(x->ms,max(0,x->child[0]->rms)+x->v+max(0,x->child[1]->lms));
    x->lms=max(x->child[0]->lms,x->child[0]->s+x->v+max(0,x->child[1]->lms));
    x->rms=max(x->child[1]->rms,x->child[1]->s+x->v+max(0,x->child[0]->rms));
}

void Pushdown(TREE x){
    if(x==Null) return;
    if(x->rev){
        swap(x->child[0],x->child[1]),swap(x->lms,x->rms);
        x->child[0]->rev^=1,x->child[1]->rev^=1,x->rev=0;
    }
    if(x->same){
        x->s=x->c*x->v,x->same=0;
        x->ms=x->lms=x->rms=max(x->v,x->s);
        x->child[0]->same=1,x->child[0]->v=x->v;
        x->child[1]->same=1,x->child[1]->v=x->v;
    }
}

void Rotate(TREE x,bool t){
    TREE y=x->f;
    Pushdown(x->child[0]),Pushdown(x->child[1]),Pushdown(y->child[t]);

    y->child[!t]=x->child[t],x->child[t]->f=y,x->f=y->f;
    if(y->f->child[0]==y) y->f->child[0]=x;
    else y->f->child[1]=x;
    y->f=x,x->child[t]=y;

    Pushup(y),Pushup(x);
    if(y==root) root=x;
}

void Splay(TREE x,TREE y){
    Pushdown(x);
    while(x->f!=y)
        if(x->f->f==y)
            if(x->f->child[0]==x) Rotate(x,1);
            else Rotate(x,0);
        else if(x->f->f->child[0]==x->f)
            if(x->f->child[0]==x) Rotate(x->f,1),Rotate(x,1);
            else Rotate(x,0),Rotate(x,1);
        else
            if(x->f->child[0]==x) Rotate(x,1),Rotate(x,0);
            else Rotate(x->f,0),Rotate(x,0);
}

void Select(int p,TREE y){
    TREE x=root;Pushdown(x);
    while(p!=x->child[0]->c+1){
        if(p<=x->child[0]->c) x=x->child[0];
        else p-=x->child[0]->c+1,x=x->child[1];
        Pushdown(x);
    }
    Splay(x,y);
}

void Insert(int p,int n,int *a){
    TREE s,t;
    s=t=NewNode(a[1],Null);
    for(int i=2;i<=n;i++) t=t->child[1]=NewNode(a[i],t);

    Select(p+1,Null),Select(p+2,root);
    root->child[1]->child[0]=s,s->f=root->child[1];
    Splay(t,Null);
}

void Erase(TREE x){
    if(x==Null) return;
    Erase(x->child[0]),Erase(x->child[1]);
    delete x;
}

void Delete(int p,int n){
    Select(p,Null),Select(p+n+1,root);
    Erase(root->child[1]->child[0]);
    root->child[1]->child[0]=Null;
    Splay(root->child[1],Null);
}

void Reverse(int p,int n){
    Select(p,Null),Select(p+n+1,root);
    root->child[1]->child[0]->rev^=1;
    Splay(root->child[1]->child[0],Null);
}

int Summation(int p,int n){
    Select(p,Null),Select(p+n+1,root);
    Pushdown(root->child[1]->child[0]);
    return root->child[1]->child[0]->s;
}

void Change(int p,int n,int v){
    Select(p,Null),Select(p+n+1,root);
    root->child[1]->child[0]->same=1,root->child[1]->child[0]->v=v;
    Splay(root->child[1]->child[0],Null);
}

int Maximizing(){
    Pushdown(root),Pushup(root);
    return root->ms;
}

int main(){
    Initialization();
    cin >> N >> M;
    for(int i=1;i<=N;i++) scanf("%d",a+i);
    Insert(0,N,a);

    for(int i=1,pos;i<=M;i++){
        scanf("%s",Order);
        if(strstr(Order,"INSERT")){
            scanf("%d %d",&pos,&N);
            for(int i=1;i<=N;i++) scanf("%d",a+i);
            Insert(pos,N,a);
        }
        if(strstr(Order,"DELETE")){
            scanf("%d %d",&pos,&N);
            Delete(pos,N);
        }
        if(strstr(Order,"REVERSE")){
            scanf("%d %d",&pos,&N);
            Reverse(pos,N);
        }
        if(strstr(Order,"GET-SUM")){
            scanf("%d %d",&pos,&N);
            cout << Summation(pos,N) << endl;
        }
        if(strstr(Order,"MAKE-SAM")){
            scanf("%d %d %d",&pos,&N,a);
            Change(pos,N,a[0]);
        }
        if(strstr(Order,"MAX-SUM")) cout << Maximizing() << endl;
    }

    return 0;
}

Treap：

#include <ctime>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <climits>
#include <iostream>
#include <algorithm>
using namespace std;

const int MAXN=500000+2;
typedef struct NODE{
    NODE *child[2];
    int c,v,s,key,ms,lms,rms;
    bool same,rev;
    NODE(){}
    NODE(int _v):v(_v),s(_v),ms(_v),lms(_v),rms(_v){}
} *TREE;
typedef pair<TREE,TREE> ROOT;
TREE Null,root;
int N,M,a[MAXN];
char Order[20+2];

TREE NewNode(int v){
    TREE x=new NODE(v);
    x->child[0]=x->child[1]=Null;
    x->same=x->rev=0,x->c=1,x->key=rand();
    return x;
}

void Initialization(){
    srand(time(Null));
    root=Null=NewNode(SHRT_MIN);
    Null->s=Null->c=0;
}

void Update_Rev(TREE x){
    if(x==Null) return;
    swap(x->child[0],x->child[1]),swap(x->lms,x->rms);
    x->rev^=1;
}

void Update_Same(TREE x,int v){
    if(x==Null) return;
    x->v=v,x->same=1,x->s=x->c*v;
    x->ms=x->lms=x->rms=max(x->v,x->s);
}

void Pushup(TREE x){
    if(x==Null) return;
    x->c=x->child[0]->c+x->child[1]->c+1;
    x->s=x->child[0]->s+x->child[1]->s+x->v;
    x->ms=max(x->child[0]->ms,x->child[1]->ms);
    x->ms=max(x->ms,max(0,x->child[0]->rms)+x->v+max(0,x->child[1]->lms));
    x->lms=max(x->child[0]->lms,x->child[0]->s+x->v+max(0,x->child[1]->lms));
    x->rms=max(x->child[1]->rms,x->child[1]->s+x->v+max(0,x->child[0]->rms));
}

void Pushdown(TREE x){
    if(x==Null) return;
    if(x->rev){
        Update_Rev(x->child[0]),Update_Rev(x->child[1]);
        x->rev=0;
    }
    if(x->same){
        Update_Same(x->child[0],x->v),Update_Same(x->child[1],x->v);
        x->same=0;
    }
}

ROOT Split(TREE x,int p){
    if(x==Null) return ROOT(Null,Null);
    Pushdown(x);

    ROOT y;
    if(x->child[0]->c>=p){
        y=Split(x->child[0],p);
        x->child[0]=y.second,y.second=x;
    }
    else{
        y=Split(x->child[1],p-x->child[0]->c-1);
        x->child[1]=y.first,y.first=x;
    }
    Pushup(x);

    return y;
}

TREE Merge(TREE x,TREE y){
    if(x==Null) return y;
    if(y==Null) return x;

    if(x->key<y->key){
        Pushdown(x);
        x->child[1]=Merge(x->child[1],y);
        Pushup(x);
        return x;
    }
    else{
        Pushdown(y);
        y->child[0]=Merge(x,y->child[0]);
        Pushup(y);
        return y;
    }
}

void Insert(int p,int n,int *a){
    TREE x=NewNode(a[1]);
    for(int i=2;i<=n;i++) x=Merge(x,NewNode(a[i]));

    ROOT y=Split(root,p);
    root=Merge(y.first,Merge(x,y.second));
}

void Erase(TREE x){
    if(x==Null) return;
    Erase(x->child[0]),Erase(x->child[1]);
    delete x;
}

void Delete(int p,int n){
    ROOT x=Split(root,p-1),y=Split(x.second,n);
    Erase(y.first);
    root=Merge(x.first,y.second);
}

void Change(int p,int n,int v){
    ROOT x=Split(root,p-1),y=Split(x.second,n);
    Update_Same(y.first,v);
    root=Merge(x.first,Merge(y.first,y.second));
}

void Reverse(int p,int n){
    ROOT x=Split(root,p-1),y=Split(x.second,n);
    Update_Rev(y.first);
    root=Merge(x.first,Merge(y.first,y.second));
}

int Summation(int p,int n){
    ROOT x=Split(root,p-1),y=Split(x.second,n);
    int ret=y.first->s;
    root=Merge(x.first,Merge(y.first,y.second));
    return ret;
}

int Maximizing(){ return root->ms;}

int main(){
    Initialization();

    cin >> N >> M;
    for(int i=1;i<=N;i++) cin >> a[i];
    Insert(1,N,a);

    for(int i=1,pos;i<=M;i++){
        scanf("%s",Order);
        if(strstr(Order,"INSERT")){
            scanf("%d %d",&pos,&N);
            for(int i=1;i<=N;i++) scanf("%d",a+i);
            Insert(pos,N,a);
        }
        if(strstr(Order,"DELETE")){
            scanf("%d %d",&pos,&N);
            Delete(pos,N);
        }
        if(strstr(Order,"REVERSE")){
            scanf("%d %d",&pos,&N);
            Reverse(pos,N);
        }
        if(strstr(Order,"GET-SUM")){
            scanf("%d %d",&pos,&N);
            cout << Summation(pos,N) << endl;
        }
        if(strstr(Order,"MAKE-SAM")){
            scanf("%d %d %d",&pos,&N,a);
            Change(pos,N,a[0]);
        }
        if(strstr(Order,"MAX-SUM")) cout << Maximizing() << endl;
    }

    return 0;
}