平衡树（Splay）：Splaytree POJ 3580 SuperMemo

SuperMemo      

 

Description

Your friend, Jackson is invited to a TV show called SuperMemo in which the participant is told to play a memorizing game. At first, the host tells the participant a sequence of numbers, {A₁, A₂, ... A_n}. Then the host performs a series of operations and queries on the sequence which consists:

1. ADD x y D: Add D to each number in sub-sequence {A_x ... A_y}. For example, performing "ADD 2 4 1" on {1, 2, 3, 4, 5} results in {1, 3, 4, 5, 5}
2. REVERSE x y: reverse the sub-sequence {A_x ... A_y}. For example, performing "REVERSE 2 4" on {1, 2, 3, 4, 5} results in {1, 4, 3, 2, 5}
3. REVOLVE x y T: rotate sub-sequence {A_x ... A_y} T times. For example, performing "REVOLVE 2 4 2" on {1, 2, 3, 4, 5} results in {1, 3, 4, 2, 5}
4. INSERT x P: insert P after A_x. For example, performing "INSERT 2 4" on {1, 2, 3, 4, 5} results in {1, 2, 4, 3, 4, 5}
5. DELETE x: delete A_x. For example, performing "DELETE 2" on {1, 2, 3, 4, 5} results in {1, 3, 4, 5}
6. MIN x y: query the participant what is the minimum number in sub-sequence {A_x ... A_y}. For example, the correct answer to "MIN 2 4" on {1, 2, 3, 4, 5} is 2

To make the show more interesting, the participant is granted a chance to turn to someone else that means when Jackson feels difficult in answering a query he may call you for help. You task is to watch the TV show and write a program giving the correct answer to each query in order to assist Jackson whenever he calls.

Input

The first line contains n (n ≤ 100000).

The following n lines describe the sequence.

Then follows M (M ≤ 100000), the numbers of operations and queries.

The following M lines describe the operations and queries.

Output

For each "MIN" query, output the correct answer.

Sample Input

5
1
2
3
4
5
2
ADD 2 4 1
MIN 4 5

Sample Output

5

　　
　　这也许是我目前见过最全面的平衡树的题目了，相信把这题搞透之后，平衡树也就差不多了，呃。
　　tips：这题我交了好多次才AC ~~~

　　

　　思路其实很简单，主要是程序实现和各种细节给跪了。

 #include <iostream>
 #include <cstring>
 #include <cstdio>
 using namespace std;
 const int maxn=;
 const int INF=;
 int Min[maxn],key[maxn],fa[maxn],ch[maxn][];
 int flip[maxn],add[maxn],sz[maxn],rt,cnt,n,Q;

 void Push_up(int p){
     Min[p]=min(key[p],min(Min[ch[p][]],Min[ch[p][]]));
     sz[p]=sz[ch[p][]]+sz[ch[p][]]+;
 }

 void Add(int p,int d){
     if(p){
         Min[p]+=d;
         key[p]+=d;
         add[p]+=d;
     }
 }

 void Flip(int p){
     swap(ch[p][],ch[p][]);
     flip[p]^=;
 }

 void Push_down(int p){
     if(add[p]){
         Add(ch[p][],add[p]);
         Add(ch[p][],add[p]);
         add[p]=;
     }
     if(flip[p]){
         Flip(ch[p][]);
         Flip(ch[p][]);
         flip[p]=;
     }
 }

 void Rotate(int x){
     int y=fa[x],g=fa[y],c=ch[y][]==x;
     ch[y][c]=ch[x][c^];
     fa[ch[x][c^]]=y;fa[y]=x;
     ch[x][c^]=y;fa[x]=g;
     if(g)
         ch[g][ch[g][]==y]=x;
     Push_up(y);
 }

 void Splay(int x,int g=){
     for(int y;(y=fa[x])!=g;Rotate(x))
         if(fa[y]!=g)
             Rotate((ch[fa[y]][]==y)==(ch[y][]==x)?y:x);
     Push_up(x);
     if(!g)
         rt=x;
 }

 void Make_root(int x,int g=){
     int p=rt;
     while(true){
         Push_down(p);
         if(sz[ch[p][]]+==x)break;
         if(sz[ch[p][]]+<x){
             x-=sz[ch[p][]]+;
             p=ch[p][];
         }
         else
             p=ch[p][];
     }
     Splay(p,g);
 }

 int Build(int pre,int l,int r){
     if(l>r)return ;
     int mid=(l+r)>>;
     ch[mid][]=Build(mid,l,mid-);
     if(mid>&&mid<n)
         scanf("%d",&key[mid]);
     else
         key[mid]=INF;
     Min[mid]=key[mid];
     fa[mid]=pre;sz[mid]=;
     ch[mid][]=Build(mid,mid+,r);
     Push_up(mid);
     return mid;
 }

 int main(){
     Min[]=;
     scanf("%d",&n);n+=;
     rt=Build(,,n);cnt=n;
     scanf("%d",&Q);
     char s[];int a,b,x;
     while(Q--){
         scanf("%s",s);
         if(!strcmp(s,"ADD")){
             scanf("%d%d%d",&a,&b,&x);a++;b++;
             Make_root(a-);
             Make_root(b+,rt);
             Push_down(rt);
             Push_down(ch[rt][]);
             Add(ch[ch[rt][]][],x);
         }
         else if(!strcmp(s,"MIN")){
             scanf("%d%d",&a,&b);a++;b++;
             Make_root(a-);
             Make_root(b+,rt);
             Push_down(rt);
             Push_down(ch[rt][]);
             printf("%d\n",Min[ch[ch[rt][]][]]);
         }
         else if(!strcmp(s,"DELETE")){
             scanf("%d",&x);x++;
             Make_root(x-);
             Make_root(x+,rt);
             ch[ch[rt][]][]=;
             Push_up(ch[rt][]);
             Push_up(rt);
         }
         else if(!strcmp(s,"REVERSE")){
             scanf("%d%d",&a,&b);a++;b++;
             Make_root(a-);
             Make_root(b+,rt);
             Flip(ch[ch[rt][]][]);
         }
         else if(!strcmp(s,"INSERT")){
             scanf("%d%d",&a,&x);a++;
             Make_root(a);
             Make_root(a+,rt);
             int p=++cnt;sz[p]=;
             ch[ch[rt][]][]=p;
             key[p]=Min[p]=x;
             fa[p]=ch[rt][];
             Push_up(ch[rt][]);
             Push_up(rt);
         }
         else if(!strcmp(s,"REVOLVE"))
         {
             scanf("%d%d%d",&a,&b,&x);a++;b++;
             Make_root(a-);
             Make_root(b+,rt);
             x%=b-a+;
             if(x){
                 Make_root(b-x);
                 Make_root(b+,rt);
                 int tmp=ch[ch[rt][]][];
                 ch[ch[rt][]][]=;
                 Push_up(ch[rt][]);
                 Push_up(rt);
                 Make_root(a-);
                 Make_root(a,rt);
                 ch[ch[rt][]][]=tmp;
                 fa[tmp]=ch[rt][];
                 Push_up(ch[rt][]);
                 Push_up(rt);
             }
         }
     }
     return ;
 }

　　时隔多月，我学会了treap，再AC了一遍。

 #include <iostream>
 #include <cstring>
 #include <cstdlib>
 #include <cstdio>
 using namespace std;
 const int maxn=;
 const int INF=;
 int key[maxn],flip[maxn],add[maxn],cnt,rt;
 int Min[maxn],sz[maxn],ch[maxn][],fix[maxn];
 int x,y,z,t1,t2;
 struct Treap{
     void Init(){
         Min[]=INF;
         //srand(time(NULL)); poj上不能在G++上用这个，否则RE
     }

     int Newnode(int v){
         sz[++cnt]=;
         Min[cnt]=key[cnt]=v;
         flip[cnt]=add[cnt]=;
         ch[cnt][]=ch[cnt][]=;
         fix[cnt]=rand();
         return cnt;
     }

     void Push_up(int x){
         sz[x]=sz[ch[x][]]+sz[ch[x][]]+;
         Min[x]=min(min(Min[ch[x][]],Min[ch[x][]]),key[x]);
     }

     void Flip(int x){
         swap(ch[x][],ch[x][]);
         flip[x]^=;
     }

     void Add(int x,int d){
         if(!x)return;
         key[x]+=d;
         Min[x]+=d;
         add[x]+=d;
     }

     void Push_down(int x){
         if(add[x]){
             Add(ch[x][],add[x]);
             Add(ch[x][],add[x]);
             add[x]=;
         }
         if(flip[x]){
             Flip(ch[x][]);
             Flip(ch[x][]);
             flip[x]=;
         }
     }

     int Merge(int x,int y){
         if(!x||!y)return x|y;
         Push_down(x);
         Push_down(y);
         if(fix[x]<=fix[y]){
             ch[x][]=Merge(ch[x][],y);
             Push_up(x);
             return x;
         }
         else{
             ch[y][]=Merge(x,ch[y][]);
             Push_up(y);
             return y;
         }
     }

     void Split(int x,int k){
         Push_down(x);
         if(k>sz[x]){t1=x;t2=;return;}

         if(sz[ch[x][]]+==k){
             t1=ch[x][];t2=x;
             ch[x][]=;
             Push_up(x);
             return;
         }

         if(sz[ch[x][]]+<k){
             k-=sz[ch[x][]]+;
             Split(ch[x][],k);
             ch[x][]=t1;t1=x;
             Push_up(x);
         }

         else{
             Split(ch[x][],k);
             ch[x][]=t2;t2=x;
             Push_up(x);
         }
     }

     void Insert(int k,int v){
         Split(rt,k+);
         t1=Merge(t1,Newnode(v));
         rt=Merge(t1,t2);
     }

     void Delete(int k){
         int tmp;
         Split(rt,k);tmp=t1;
         Split(t2,);t1=tmp;
         rt=Merge(t1,t2);
     }

     void Divide(int l,int r){
         Split(rt,l);x=t1;
         Split(t2,r-l+);y=t1;z=t2;
     }

     void Converge(){
         x=Merge(x,y);
         rt=Merge(x,z);
     }

     void Add(int l,int r,int d){
         Divide(l,r);Add(y,d);
         Converge();
     }

     void Reverse(int l,int r){
         Divide(l,r);Flip(y);
         Converge();
     }

     void Revolve(int l,int r,int k){
         Divide(l,r);
         k%=sz[y];
         if(k){
             Split(y,sz[y]-k+);
             y=Merge(t2,t1);
         }
         Converge();
     }

     int Query(int l,int r){
         Divide(l,r);
         int ret=Min[y];
         Converge();
         return ret;
     }
 }T;

 int n,Q;
 char op[];

 int main(){
     T.Init();
     scanf("%d",&n);
     for(int i=,a;i<=n;i++){
         scanf("%d",&a);
         T.Insert(i,a);
     }
     int l,r,k;
     scanf("%d",&Q);
     while(Q--){
         scanf("%s",op);
         if(!strcmp(op,"ADD")){
             scanf("%d%d%d",&l,&r,&k);
             T.Add(l,r,k);
         }
         else if(!strcmp(op,"REVERSE")){
             scanf("%d%d",&l,&r);
             T.Reverse(l,r);
         }
         else if(!strcmp(op,"REVOLVE")){
             scanf("%d%d%d",&l,&r,&k);
             T.Revolve(l,r,k);
         }
         else if(!strcmp(op,"INSERT")){
             scanf("%d%d",&l,&k);
             T.Insert(l,k);
         }
         else if(!strcmp(op,"DELETE")){
             scanf("%d",&k);
             T.Delete(k);
         }
         else if(!strcmp(op,"MIN")){
             scanf("%d%d",&l,&r);
             printf("%d\n",T.Query(l,r));
         }
     }
     return ;
 }

　　有些地方没打好，很丑……

　　决定日后整理为模板。