[CODEVS]数据结构系列 解题报告
用这两道题学了下Splay，也加深了对其的理解。
平衡树的标记与线段树的标记不同，在平衡树中，所有被访问的节点一定不能有标记；否则将其Splay后就找不到其原先的左右子树了。
代码（数据结构1）：
#include<cstdlib>
#include<cstdio>
#include<cstring>
#include<vector>
using namespace std;
#include<iostream>
#include<cmath>
struct SS{
<span style="white-space:pre"> </span>SS * f,* c[2];
<span style="white-space:pre"> </span>int X,data,delta;
<span style="white-space:pre"> </span>bool is_root;
}*null=new SS((SS){null,null,null,0,0,0,0}),*root;
inline void zig(SS * x,bool D){
<span style="white-space:pre"> </span>SS * ftr=x->f;
<span style="white-space:pre"> </span>if(ftr->is_root)x->is_root=1,ftr->is_root=0;
<span style="white-space:pre"> </span>x->f=ftr->f;
<span style="white-space:pre"> </span>if(x->f->c[0]==ftr)x->f->c[0]=x;
<span style="white-space:pre"> </span>else x->f->c[1]=x;
<span style="white-space:pre"> </span>ftr->c[D]=x->c[!D];
<span style="white-space:pre"> </span>ftr->c[D]->f=ftr;
<span style="white-space:pre"> </span>x->c[!D]=ftr;
<span style="white-space:pre"> </span>ftr->f=x;
}
inline void splay(SS * x){
<span style="white-space:pre"> </span>bool D;
<span style="white-space:pre"> </span>//cout<<"S:("<<x->data<<")"<<x->X<<"->"<<x->c[0]->data<<"->"<<x->c[1]->data<<endl;
<span style="white-space:pre"> </span>while(!x->is_root){
<span style="white-space:pre"> </span>D=x->f->c[1]==x;
<span style="white-space:pre"> </span>if(!x->f->is_root&&D==(x->f->f->c[1]==x->f))zig(x->f,D);
<span style="white-space:pre"> </span>zig(x,D);
<span style="white-space:pre"> </span>//cout<<D<<"S:("<<x->data<<")"<<x->X<<"->"<<x->c[0]->data<<"->"<<x->c[1]->data<<endl;
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>root=x;
<span style="white-space:pre"> </span>//cout<<"S:("<<x->data<<")"<<x->X<<"->"<<x->c[0]->data<<"->"<<x->c[1]->data<<endl;
}
inline void paint(SS * x,int A){
<span style="white-space:pre"> </span>if(x==null)return;
<span style="white-space:pre"> </span>x->X+=A;
<span style="white-space:pre"> </span>x->delta+=A;
}
inline void pushdown(SS * x){
<span style="white-space:pre"> </span>if(x->delta){
<span style="white-space:pre"> </span>paint(x->c[0],x->delta);
<span style="white-space:pre"> </span>paint(x->c[1],x->delta);
<span style="white-space:pre"> </span>x->delta=0;
<span style="white-space:pre"> </span>}
}
inline SS * find(SS * x,int A){
<span style="white-space:pre"> </span>pushdown(x);
<span style="white-space:pre"> </span>//cout<<"To "<<A<<" Find:("<<x->data<<")"<<x->X<<"->"<<x->c[0]->data<<"->"<<x->c[1]->data<<endl;
<span style="white-space:pre"> </span>if(A==x->X)return x;
<span style="white-space:pre"> </span>if(A>x->X)return find(x->c[1],A);
<span style="white-space:pre"> </span>return find(x->c[0],A);
}
int N;
inline void prt(SS * x){
<span style="white-space:pre"> </span>if(x==null)return;
<span style="white-space:pre"> </span>pushdown(x);
<span style="white-space:pre"> </span>prt(x->c[0]);
<span style="white-space:pre"> </span>if(x->X<=N)printf("%d ",x->data);
<span style="white-space:pre"> </span>prt(x->c[1]);
}
char * ptr=(char *)malloc(5000000);
inline int in(){
<span style="white-space:pre"> </span>bool flag=0;
<span style="white-space:pre"> </span>while(*ptr<'0'||*ptr>'9')
<span style="white-space:pre"> </span>if(*ptr++=='-')
<span style="white-space:pre"> </span>flag=1;
<span style="white-space:pre"> </span>int x=0;
<span style="white-space:pre"> </span>while(*ptr>47&&*ptr<58)x=x*10+*ptr++-'0';
<span style="white-space:pre"> </span>if(flag)return -x;
<span style="white-space:pre"> </span>return x;
}
int main(){
<span style="white-space:pre"> </span>freopen("codevs2047.in","r",stdin);
<span style="white-space:pre"> </span>fread(ptr,1,5000000,stdin);
<span style="white-space:pre"> </span>int M,X;
<span style="white-space:pre"> </span>N=in(),M=in();
<span style="white-space:pre"> </span>root=new SS((SS){null,null,null,1,in(),0,1});
<span style="white-space:pre"> </span>SS * tmp=root;
<span style="white-space:pre"> </span>for(int i=2;i<=N;++i){
<span style="white-space:pre"> </span>tmp->c[1]=new SS((SS){tmp,null,null,i,in(),0,0});
<span style="white-space:pre"> </span>tmp=tmp->c[1];
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>
<span style="white-space:pre"> </span>tmp->c[1]=new SS((SS){tmp,null,null,N+1,N+1,0,0});
<span style="white-space:pre"> </span>
<span style="white-space:pre"> </span>int L,R;
<span style="white-space:pre"> </span>while(M--){
<span style="white-space:pre"> </span>L=in(),R=in();
<span style="white-space:pre"> </span>if(--L){
<span style="white-space:pre"> </span>splay(find(root,L));
<span style="white-space:pre"> </span>root->c[1]->is_root=1;
<span style="white-space:pre"> </span>splay(find(root->c[1],R+1));
<span style="white-space:pre"> </span>root->is_root=0;
<span style="white-space:pre"> </span>
<span style="white-space:pre"> </span>tmp=root->c[0];
<span style="white-space:pre"> </span>root->c[0]=null;
<span style="white-space:pre"> </span>root=root->f;
<span style="white-space:pre"> </span>root->X+=R-L;
<span style="white-space:pre"> </span>paint(root->c[0],R-L);
<span style="white-space:pre"> </span>splay(find(root,R-L+1));
<span style="white-space:pre"> </span>
<span style="white-space:pre"> </span>tmp->f=root;
<span style="white-space:pre"> </span>root->c[0]=tmp;
<span style="white-space:pre"> </span>
<span style="white-space:pre"> </span>paint(tmp,-L);
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>
<span style="white-space:pre"> </span>prt(root);
}
代码（数据结构2）：
#include<iostream>
using namespace std;
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
char * ptr=(char *)malloc(5000000);
inline int in(){
<span style="white-space:pre"> </span>bool flag=0;
<span style="white-space:pre"> </span>while(*ptr<'0'||*ptr>'9')
<span style="white-space:pre"> </span>if(*++ptr=='-')
<span style="white-space:pre"> </span>flag=1;
<span style="white-space:pre"> </span>int x=0;
<span style="white-space:pre"> </span>while(*ptr>47&&*ptr<58)x=x*10+*ptr++-'0';
<span style="white-space:pre"> </span>if(flag)return -x;
<span style="white-space:pre"> </span>else return x;
}
struct SS{
<span style="white-space:pre"> </span>SS * f,* c[2];
<span style="white-space:pre"> </span>int key,X;
<span style="white-space:pre"> </span>bool is_root;
<span style="white-space:pre"> </span>int flagb,flagc;
}* null=new SS((SS){null,null,null,-1,-1,0,0,0}),* root=new SS((SS){null,null,null,-0x7f,0,1,1,0});
inline void zig(SS * x,bool w){
<span style="white-space:pre"> </span>SS * ftr=x->f;
<span style="white-space:pre"> </span>x->f=ftr->f;
<span style="white-space:pre"> </span>if(ftr->is_root)ftr->is_root=0,x->is_root=1;
<span style="white-space:pre"> </span>if(x->f->c[0]==ftr)x->f->c[0]=x;
<span style="white-space:pre"> </span>else x->f->c[1]=x;
<span style="white-space:pre"> </span>ftr->c[w]=x->c[!w];
<span style="white-space:pre"> </span>ftr->c[w]->f=ftr;
<span style="white-space:pre"> </span>x->c[!w]=ftr;
<span style="white-space:pre"> </span>ftr->f=x;
}
inline void splay(SS * x){
<span style="white-space:pre"> </span>bool w;
<span style="white-space:pre"> </span>while(!x->is_root){
<span style="white-space:pre"> </span>w=x->f->c[1]==x;
<span style="white-space:pre"> </span>if(!x->f->is_root&&w==(x->f->f->c[1]==x->f))zig(x->f,w);
<span style="white-space:pre"> </span>zig(x,w);
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>root=x;
}
#define Re(x) x=-x;
inline void paint(SS * x,int b,int c){
<span style="white-space:pre"> </span>if(x==null)return;
<span style="white-space:pre"> </span>int tmp=x->X;
<span style="white-space:pre"> </span>if(b-1){
<span style="white-space:pre"> </span>Re(x->flagb);
<span style="white-space:pre"> </span>Re(x->flagc);
<span style="white-space:pre"> </span>Re(x->X);
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>x->flagc+=c;
<span style="white-space:pre"> </span>x->X+=c;
<span style="white-space:pre"> </span>//cout<<"Paint("<<x->key<<"):"<<tmp<<"->"<<x->X<<"("<<x->flagb<<")\n";
}
inline void pushdown(SS * x){
<span style="white-space:pre"> </span>if(x->flagb-1|x->flagc){
<span style="white-space:pre"> </span>if(x->flagb-1)swap(x->c[0],x->c[1]);
<span style="white-space:pre"> </span>paint(x->c[0],x->flagb,x->flagc);
<span style="white-space:pre"> </span>paint(x->c[1],x->flagb,x->flagc);
<span style="white-space:pre"> </span>x->flagb=1;
<span style="white-space:pre"> </span>x->flagc=0;
<span style="white-space:pre"> </span>}
}
inline SS * find(int A){
<span style="white-space:pre"> </span>SS * x=root;
<span style="white-space:pre"> </span>//cout<<"Find:"<<x->key<<"("<<x->X<<"),"<<A<<"("<<x->flagb<<")"<<"->"<<x->c[0]->key<<"->"<<x->c[1]->key<<endl;
<span style="white-space:pre"> </span>while(x->X!=A){
<span style="white-space:pre"> </span>pushdown(x);
<span style="white-space:pre"> </span>if(x->X<A)x=x->c[1];
<span style="white-space:pre"> </span>else x=x->c[0];
<span style="white-space:pre"> </span>//cout<<"Find:"<<x->key<<"("<<x->X<<"),"<<A<<"("<<x->flagb<<")"<<"->"<<x->c[0]->key<<"->"<<x->c[1]->key<<endl;
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>pushdown(x);
<span style="white-space:pre"> </span>return x;
}
int N;
inline void prt(SS * x){
<span style="white-space:pre"> </span>if(x!=null){
<span style="white-space:pre"> </span>pushdown(x);
<span style="white-space:pre"> </span>prt(x->c[0]);
<span style="white-space:pre"> </span>if(x->X&&x->X<=N)printf("%d ",x->key);
<span style="white-space:pre"> </span>prt(x->c[1]);
<span style="white-space:pre"> </span>}
}
int main(){
<span style="white-space:pre"> </span>freopen("codevs2048.in","r",stdin);
<span style="white-space:pre"> </span>fread(ptr,1,5000000,stdin);
<span style="white-space:pre"> </span>
<span style="white-space:pre"> </span>N=in();
<span style="white-space:pre"> </span>int M=in(),i;
<span style="white-space:pre"> </span>SS * tmp=root;
<span style="white-space:pre"> </span>for(i=1;i<=N;++i){
<span style="white-space:pre"> </span>tmp->c[1]=new SS((SS){tmp,null,null,in(),i,0,1,0});
<span style="white-space:pre"> </span>tmp=tmp->c[1];
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>tmp->c[1]=new SS((SS){tmp,null,null,0x7f,N+1,0,1,0});
<span style="white-space:pre"> </span>
<span style="white-space:pre"> </span>int l,r;
<span style="white-space:pre"> </span>while(M--){
<span style="white-space:pre"> </span>//cout<<"--------"<<M<<"-------\n";
<span style="white-space:pre"> </span>l=in(),r=in();
<span style="white-space:pre"> </span>splay(find(--l));
<span style="white-space:pre"> </span>root->c[1]->is_root=1;
<span style="white-space:pre"> </span>splay(find(++r));
<span style="white-space:pre"> </span>paint(root->c[0],-1,l+r);
<span style="white-space:pre"> </span>root->is_root=0;
<span style="white-space:pre"> </span>root=root->f;
<span style="white-space:pre"> </span>}
<span style="white-space:pre"> </span>prt(root);
}