【bzoj3223】文艺平衡树 Splay & Treap

平衡树做区间翻转

节点维护siz域用于查找当前第k个位置上的数，翻转打标记。

对于splay，翻转[L,R]只要把第L-1个位置转到根，第R+1个位置转到root->R的位置，对root->R->L打翻转标记。

对于合并式treap，翻转[L,R]只要分裂出L到R位置的树打标记即可。

Code:

Splay：

#include<bits/stdc++.h>
using namespace std;
const int maxn = 100005;
const int INF  = 0x3f3f3f3f;
struct node{
int key,siz;
bool fg;
node *ch[2],*fa;
};
node* root=NULL;
int n,m;
node *new_node(node *fa,int key){
node *t = new node;
t->ch[0]=t->ch[1] = NULL;
t->fa = fa;
t->key = key; t->siz = 1;
t->fg = 0;
return t;
}
#define siz(t) (t == NULL ? 0 : t->siz)
void pushup(node *t){
t->siz = siz(t->ch[0])+siz(t->ch[1]) + 1;
}
void pushdown(node *t){
if(!t->fg)return;
t->fg=0;
swap(t->ch[0],t->ch[1]);
if(t->ch[0]) t->ch[0]->fg^=1;
if(t->ch[1]) t->ch[1]->fg^=1;
}
node *build(node* fa,int L,int R){
if(L>R)return NULL;
int mid=(L+R)>>1,key=mid-1;
node *t=new_node(fa,key);
t->ch[0]=build(t,L,mid-1);
t->ch[1]=build(t,mid+1,R);
pushup(t);
return t;
}
void order(node *t){
if(t == NULL)return;
pushdown(t);
order(t->ch[0]);
if(t->key >=1 && t->key <= n) printf("%d ",t->key);
order(t->ch[1]);
}
void rotate(node *x,bool d){
node *y=x->fa;
pushdown(y);pushdown(x);
y->ch[!d]=x->ch[d];
if(x->ch[d]) x->ch[d]->fa=y;
x->fa = y->fa;
if(y->fa){
if(y == y->fa->ch[0])
y->fa->ch[0] = x;
else
y->fa->ch[1] = x;
}
x->ch[d] = y;y->fa=x;
pushup(y);pushup(x);
}
void splay(node *x,node *tar){
pushdown(x);
while( x->fa != tar){
node *y=x->fa;
if( x == y->ch[0]){
if(y->fa != tar && y == y->fa->ch[0])
rotate(y,1);
rotate(x,1);
}else{
if(y->fa != tar && y == y->fa->ch[1])
rotate(y,0);
rotate(x,0);
}
}
pushup(x);
if( tar == NULL ) root=x;
}
node *find_kth(node *x,int kth){
pushdown(x);
int siz=siz(x->ch[0]);
if( siz+1 == kth ) return x;
if( kth <= siz )return find_kth(x->ch[0],kth);
return find_kth(x->ch[1],kth-siz-1);
}
void rev(int L,int R){
node *x=find_kth(root,L),*y=find_kth(root,R+2);
splay(x,NULL);
splay(y,root);
y->ch[0]->fg^=1;
}
int main(){
freopen("input.txt","r",stdin);
freopen("output1.txt","w",stdout);

scanf("%d%d",&n,&m);
root = build(NULL,1,n+2);
for(int L,R,i=1;i<=m;i++){
scanf("%d%d",&L,&R);
rev(L,R);
}
order(root);puts("");
}

Treap:

#include<bits/stdc++.h>
using namespace std;
struct node{
int siz,key,pri;
bool fg;
node *L,*R;
};
node *root = NULL;
int n,m;
node* new_node(int key){
node *x = new node;
x->L = x->R = NULL;
x->key = key;
x->pri = rand();

x->siz = 1;
x->fg = 0;
return x;
}

#define siz(x) (x == NULL ? 0 : x->siz)
void pushup(node *x){
x->siz=siz(x->L)+siz(x->R)+1;
}
void pushdown(node *x){
if(!x->fg)return;
x->fg=0;
swap(x->L,x->R);
if( x->L ) x->L->fg^=1;
if( x->R ) x->R->fg^=1;
}
node *merge(node *x,node *y){
if( x == NULL ) return y;
if( y == NULL ) return x;
pushdown(x);pushdown(y);
if( x->pri < y->pri ){
x->R = merge( x->R , y ); pushup(x); return x;
}else{
y->L = merge( x , y->L ); pushup(y); return y;
}
}
typedef pair<node*,node*>pii;
pii split(node *x,int k){
if( x == NULL )return pii(NULL,NULL);
pushdown(x);
if( k <= siz(x->L) ){
pii tmp = split(x->L,k);
x->L=tmp.second;
pushup(x);
return pii(tmp.first,x);
} else {
pii tmp = split(x->R,k-siz(x->L)-1);
x->R=tmp.first;
pushup(x);
return pii(x,tmp.second);
}
}
node *build(int L,int R){
if(L>R)return NULL;
int mid=(L+R)>>1,key=mid-1;
node *x = new_node(key);
x->L = build(L,mid-1);
x->R = build(mid+1,R);
pushup(x);
return x;
}
void order(node *x){
if( x == NULL ) return;
pushdown(x);
order(x->L);
if(x->key >= 1 && x->key<=n)printf("%d ",x->key);
order(x->R);
}
void rev(int L,int R){
pii tmp1=split(root,R+1);
pii tmp2=split(tmp1.first,L);
tmp2.second->fg^=1;
root = NULL;
root = merge(tmp2.first,tmp2.second);
root = merge(root,tmp1.second);
}

int main(){
freopen("input.txt","r",stdin);
freopen("output2.txt","w",stdout);

srand(619);
scanf("%d%d",&n,&m);
root = build(1,n+2);
for(int L,R,i=1;i<=m;i++){
scanf("%d%d",&L,&R);
rev(L,R);
}
order(root);puts("");
}