题解 [HNOI2002]营业额统计 （Splay）

Posted 2020-10-30 Ning_Mew

懒得复制，戳我戳我

Solution:

• \(Splay\)板子题，注意可以选择相等大小

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Code:

//It is coded by Ning_Mew on 4.10
#include<bits/stdc++.h>
#define ls(x) node[x].ch[0]
#define rs(x) node[x].ch[1]
#define fa(x) node[x].fa
#define root node[0].ch[1]
using namespace std;

const int maxn=32800,INF=1e9+7;

int n,tot=0,ans=0;
struct Node{
  int fa,ch[2],val,cnt,size;
}node[maxn];

void update(int x){node[x].size=node[ls(x)].size+node[rs(x)].size+node[x].cnt;}
void connect(int x,int fa,int how){node[x].fa=fa;node[fa].ch[how]=x;}
int ident(int x){return x==node[fa(x)].ch[0]?0:1;}
void rorate(int x){
  int Y=fa(x),R=fa(Y);int Yson=ident(x),Rson=ident(Y);
  connect(node[x].ch[Yson^1],Y,Yson);
  connect(Y,x,Yson^1);
  connect(x,R,Rson);
  update(Y);update(x);return;
}
void Splay(int x,int goal){
  int to=fa(goal);
  while(fa(x)!=to){
    if(fa(fa(x))==to)rorate(x);
    else if(ident(x)==ident(fa(x)))rorate(fa(x)),rorate(x);
    else rorate(x),rorate(x);
  }
}
int newnode(int x,int fa){
  node[++tot].val=x;node[tot].size=node[tot].cnt=1;node[tot].fa=fa;return tot;
}
void ins(int x){
  int now=root;
  if(!now){newnode(x,0);root=tot;return;}
  else{
    while(1){
      node[now].size++;
      if(node[now].val==x){node[now].cnt++;Splay(now,root);return;}
      int nxt=x<node[now].val?0:1;
      if(!node[now].ch[nxt]){
    int p=newnode(x,now);
    node[now].ch[nxt]=p;Splay(p,root);return;
      }
      now=node[now].ch[nxt];
    }
  }
}
int lower(int x){
  int now=root,ans=-INF;
  while(now){
    if(node[now].val<x)ans=max(ans,node[now].val);
    if(node[now].val==x&&node[now].cnt!=1)ans=max(ans,node[now].val);
    int nxt=x<=node[now].val?0:1;
    now=node[now].ch[nxt];
  }return ans;
}
int upper(int x){
  int now=root,ans=INF;
  while(now){
    if(node[now].val>x)ans=min(ans,node[now].val);
    if(node[now].val==x&&node[now].cnt!=1)ans=min(ans,node[now].val);
    int nxt=x<node[now].val?0:1;
    now=node[now].ch[nxt];
  }return ans;
}
int main(){
  scanf("%d",&n);
  int x;
  for(int i=1;i<=n;i++){
    scanf("%d",&x); ins(x);
    //cout<<"ins Finished"<<endl;
    if(i==1)ans=x;
    else {
      int up=upper(x),low=lower(x),box=INF;
      if(up!=INF)box=min(box,abs(up-x));
      if(low!=-INF)box=min(box,abs(low-x));
      //cout<<up<<‘ ‘<<low<<‘ ‘<<box<<endl;
      ans+=box;
    }
    //cout<<"ans changed"<<endl;
  }
  printf("%d\n",ans);
  return 0;
}