【BZOJ3224】普通平衡树（splay）

题意：

您需要写一种数据结构（可参考题目标题），来维护一些数，其中需要提供以下操作：
1. 插入x数
2. 删除x数(若有多个相同的数，因只删除一个)
3. 查询x数的排名(若有多个相同的数，因输出最小的排名)
4. 查询排名为x的数
5. 求x的前驱(前驱定义为小于x，且最大的数)
6. 求x的后继(后继定义为大于x，且最小的数)

1.n的数据范围：n<=100000

2.每个数的数据范围：[-1e7,1e7]

 

思路：为了学LCT才去学的splay

看来又入新坑了

插入的时候把x的前一个（注意不是前驱）转到根，后一个（不是后继）转到根的右儿子，

这样根结点右儿子的左儿子就是要插入的x，直接插入

删除时候类似，这样可以保证每次只删去一个数

 var t:array[..,..]of longint;
     sum,b,fa,num:array[..]of longint;
     n,i,x,y,root,cnt,save,tmp,m:longint;
     flag:boolean;

 procedure pushup(x:longint);
 var l,r:longint;
 begin
  l:=t[x,]; r:=t[x,];
  sum[x]:=sum[l]+sum[r]+;
 end;

 procedure rotate(x:longint;var k:longint);
 var y,z,l,r:longint;
 begin
  y:=fa[x]; z:=fa[y];
  if t[y,]=x then l:=
   else l:=;
  r:=l xor ;
  if y<>k then
  begin
   if t[z,]=y then t[z,]:=x
    else t[z,]:=x;
  end
   else k:=x;
  fa[t[x,r]]:=y; fa[x]:=z; fa[y]:=x;
  t[y,l]:=t[x,r]; t[x,r]:=y;
  pushup(y);
  pushup(x);
 end;

 procedure splay(x:longint;var k:longint);
 var y,z:longint;
 begin
  while x<>k do
  begin
   y:=fa[x]; z:=fa[y];
   if y<>k then
   begin
    if (t[z,]=y)xor(t[y,]=x) then rotate(x,k)
     else rotate(y,k);
   end
    else k:=x;
   rotate(x,k);
  end;

 end;

 function pred(x:longint):longint;
 var k,last:longint;
 begin
  k:=root; last:=num[root];
  while k<> do
  begin
   if num[k]<x then begin last:=num[k]; k:=t[k,]; end
    else k:=t[k,];
  end;
  exit(last);
 end;

 function succ(x:longint):longint;
 var k,last:longint;
 begin
  k:=root; last:=num[root];
  while k<> do
  begin
   if num[k]>x then begin last:=num[k]; k:=t[k,]; end
    else k:=t[k,];
  end;
  exit(last);
 end;

 function rank(x:longint):longint;
 var k:longint;
 begin
  x:=pred(x);
  k:=root; rank:=;
  while k> do
  begin
   if num[k]<=x then begin rank:=rank+sum[t[k,]]+; k:=t[k,]; end
    else k:=t[k,];
  end;
  inc(rank);
 end;

 function kth(x:longint):longint;
 var tmp,k:longint;
 begin
  k:=root;
  while true do
  begin
   tmp:=sum[t[k,]]+;
   if tmp=x then exit(k);
   if tmp>x then k:=t[k,]
    else
    begin
     k:=t[k,]; x:=x-tmp;
    end;
  end;
 end;

 function find(x:longint):longint;
 var k:longint;
 begin
  k:=root;
  while true do
  begin
   if num[k]=x then exit(k)
    else if num[k]<x then k:=t[k,]
     else k:=t[k,];
  end;
 end;

 procedure ins(x:longint);
 var tmp,l,r,k1:longint;
 begin
  tmp:=rank(x);
  l:=kth(tmp-);
  r:=kth(tmp);
  splay(l,root);
  splay(r,t[root,]);
  k1:=t[root,];
  inc(cnt); t[k1,]:=cnt; fa[cnt]:=k1; sum[cnt]:=; num[cnt]:=x;
 // inc(sum[k1]);
 // inc(sum[root]);
 end;

 procedure del(x:longint);
 var k1,k2,l,r:longint;
 begin
  tmp:=rank(x);
  l:=kth(tmp-);
  r:=kth(tmp+);
  splay(l,root);
  splay(r,t[root,]);
  k1:=t[root,]; k2:=t[k1,];
  sum[k1]:=sum[t[k1,]]+; fa[k2]:=; sum[k2]:=;
  t[k1,]:=;

  fa[k2]:=; sum[k2]:=; t[k2,]:=; t[k2,]:=;

 end;

 begin
  assign(input,'bzoj3224.in'); reset(input);
  assign(output,'bzoj3224.out'); rewrite(output);
  readln(n);
  num[]:=maxlongint; sum[]:=; t[,]:=; t[,]:=;
  num[]:=-maxlongint; sum[]:=; fa[]:=;
  num[]:=maxlongint; sum[]:=; fa[]:=;

  root:=; cnt:=;
  for i:= to n do
  begin
   readln(x,y);
   case x of
    :
    begin
     ins(y);
     inc(m);
    end;
    :
    begin
     del(y);
     dec(m);
    end;

    :writeln(rank(y)-);

    :writeln(num[kth(y+)]);
    :writeln(pred(y));
    :writeln(succ(y));
   end;
  end;
  close(input);
  close(output);
 end.

UPD(2018.9.15）：C++

 #include<cstdio>
 #include<cstring>
 #include<string>
 #include<cmath>
 #include<iostream>
 #include<algorithm>
 #include<map>
 #include<set>
 #include<queue>
 #include<vector>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef vector<int> VI;
 #define fi first
 #define se second
 #define MP make_pair
 #define N   500000
 #define MOD 1000000007
 #define eps 1e-8
 #define pi acos(-1)
 #define oo 2e9

 int t[N][],size[N],fa[N],num[N],root,cnt;

 int read()
 {
    int v=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,c=getchar();
    return v*f;
 }

 void pushup(int x)
 {
     size[x]=size[t[x][]]+size[t[x][]]+;
 }

 void rotate(int x,int &k)
 {
     int y=fa[x];
     int z=fa[y];
     int l;
     if(t[y][]==x) l=;
      else l=;
     int r=l^;
     if(y!=k)
     {
         if(t[z][]==y) t[z][]=x;
          else t[z][]=x;
     }
      else k=x;
     fa[t[x][r]]=y; fa[x]=z; fa[y]=x;
     t[y][l]=t[x][r]; t[x][r]=y;
     pushup(y);
     pushup(x);
 }

 void splay(int x,int &k)
 {
     while(x!=k)
     {
         int y=fa[x];
         int z=fa[y];
         if(y!=k)
         {
             if((t[z][]==y)^(t[y][]==x)) rotate(x,k);
              else rotate(y,k);
         }
          else k=x;
         rotate(x,k);
     }
 }

 int pred(int x)
 {
     int k=root;
     int last=num[root];
     while(k)
     {
         if(num[k]<x){last=num[k]; k=t[k][];}
          else k=t[k][];
     }
     return last;
 }

 int succ(int x)
 {
     int k=root;
     int last=num[root];
     while(k)
     {
         if(num[k]>x){last=num[k]; k=t[k][];}
          else k=t[k][];
     }
     return last;
 }

 int rank(int x)
 {
     x=pred(x);
     int k=root;
     int s=;
     while(k)
     {
         if(num[k]<=x){s+=size[t[k][]]+; k=t[k][];}
          else k=t[k][];
     }
     s++;
     return s;
 }

 int kth(int x)
 {
     int k=root;
     while()
     {
         int tmp=size[t[k][]]+;
         if(tmp==x) return k;
         if(tmp>x) k=t[k][];
          else{k=t[k][]; x-=tmp;}
     }
 }

 void Insert(int x)
 {
     int tmp=rank(x);
     int l=kth(tmp-);
     int r=kth(tmp);
     splay(l,root);
     splay(r,t[root][]);
     int k=t[root][];
     t[k][]=++cnt; fa[cnt]=k; size[cnt]=; num[cnt]=x;
 }

 void Delete(int x)
 {
     int tmp=rank(x);
     int l=kth(tmp-);
     int r=kth(tmp+);
     splay(l,root);
     splay(r,t[root][]);
      int k1=t[root][];
      int k2=t[k1][];
      size[k1]=size[t[k1][]]+; t[k1][]=;
      fa[k2]=; size[k2]=;
     t[k2][]=; t[k2][]=;
 }

 int main()
 {
     //freopen("bzoj3224.in","r",stdin);
     //freopen("bzoj3224.out","w",stdout);
     int n;
     scanf("%d",&n);
     num[]=-oo; size[]=; t[][]=;
     num[]=oo; size[]=; fa[]=;
     root=; cnt=;
     for(int i=;i<=n;i++)
     {
         int x,y,ans;
         scanf("%d%d",&x,&y);
         if(x==) Insert(y);
         if(x==) Delete(y);
         if(x==)
         {
             ans=rank(y)-;
             printf("%d\n",ans);
         }
         if(x==)
         {
             ans=num[kth(y+)];
             printf("%d\n",ans);
         }
         if(x==)
         {
             ans=pred(y);
             printf("%d\n",ans);
         }
         if(x==)
         {
             ans=succ(y);
             printf("%d\n",ans);
         }
     }
 }