【BZOJ4864】神秘物质 [Splay]

神秘物质

Time Limit: 10 Sec  Memory Limit: 256 MB

Description

Input

　　

Output

　　

Sample Input

　　

Sample Output

　　1
　　2
　　1
　　5

HINT

　　

Main idea

　　每个点有一个权值，维护一个结构，支持合并相邻两点，删除单点，加入单点，查询区间子集极差的最大值和最小值。

Solution

　　首先我们可以发现，区间子集极差的最大值显然就是整个区间的最大值-区间最小值，然后区间子集极差最小值只有相邻点的才会产生贡献。

　　那么我们用Splay来维护这个结构即可，维护一下子树最大值、子树最小值、子树邻差最小值即可。

Code

 #include<iostream>
 #include<string>
 #include<algorithm>
 #include<cstdio>
 #include<cstring>
 #include<cstdlib>
 #include<cmath>
 using namespace std;
 typedef long long s64;

 const int ONE = ;
 const int INF = ;

 int n,m;
 int x,y,a[ONE];
 int root,cnt;
 int lc[ONE],rc[ONE],fa[ONE];
 int size[ONE],val[ONE];
 int maxx[ONE],minn[ONE],del[ONE];
 int Ls[ONE],Rs[ONE];
 char ch[];

 inline int get()
 {
         int res=,Q=;  char c;
         while( (c=getchar())< || c>)
         if(c=='-')Q=-;
         if(Q) res=c-;
         while((c=getchar())>= && c<=)
         res=res*+c-;
         return res*Q;
 }

 void Up(int i)
 {
         size[i] = size[lc[i]] + size[rc[i]] + ;
         maxx[i] = minn[i] = val[i];
         del[i] = INF;
         Ls[i] = Rs[i] = i;
         if(lc[i])
         {
             Ls[i] = Ls[lc[i]];
             maxx[i] = max(maxx[i], maxx[lc[i]]);
             minn[i] = min(minn[i], minn[lc[i]]);
             del[i] = min(del[i], del[lc[i]]);
             del[i] = min(del[i], abs( val[i]-val[Rs[lc[i]]] ) );
         }
         if(rc[i])
         {
             Rs[i] = Rs[rc[i]];
             maxx[i] = max(maxx[i], maxx[rc[i]]);
             minn[i] = min(minn[i], minn[rc[i]]);
             del[i] = min(del[i], del[rc[i]]);
             del[i] = min(del[i], abs( val[i]-val[Ls[rc[i]]] ) );
         }
 }

 void Turn(int x)
 {
         int y = fa[x], z = fa[y];
         int b = x==lc[y] ? rc[x]:lc[x];

         fa[y] = x;    fa[x] = z;
         if(b) fa[b] = y;

         if(z)
         {
             if(y == lc[z]) lc[z] = x;
             else rc[z] = x;
         }

         if(x==lc[y]) rc[x] = y,lc[y] = b;
         else lc[x] = y, rc[y] = b;

         Up(y);    Up(x);
 }

 void Splay(int x,int pos)
 {
         while(fa[x] != pos)
         {
             if(fa[fa[x]] != pos)
             {
                 if( (lc[fa[x]]==x) == (lc[fa[fa[x]]]==fa[x]) ) Turn(fa[x]);
                 else Turn(x);
             }
             Turn(x);
         }
         if(pos == ) root = x;
 }

 int Build(int i,int l,int r)
 {
         int mid = l+r >> ;
         fa[mid] = i;
         if(l <= mid-) lc[mid] = Build(mid, l,mid-);
         if(mid+ <= r) rc[mid] = Build(mid, mid+,r);
         Up(mid);
         return mid;
 }

 int Getid(int num)
 {
         int i = root;
         while(size[lc[i]] +  != num)
         {
             if(size[lc[i]] +  < num)
                 num -= size[lc[i]] + ,    i = rc[i];
             else i = lc[i];
         }
         return i;
 }

 void Delete(int i)
 {
         int x = Getid(i);
         Splay(x, );
         int L = Rs[lc[x]];    Splay(L,);
         int R = Ls[rc[x]];    Splay(R,L);
         lc[R] = ;
         Splay(R,);
 }

 void Insert(int i,int Val)
 {
         int x = Getid(i);
         Splay(x,);
         int R = Ls[rc[x]];    Splay(R,x);
         val[++cnt] = Val; fa[cnt] = R; lc[R] = cnt;
         Splay(cnt,);
 }

 int main()
 {
         n=get();    m=get();
         for(int i=;i<=n;i++)
             val[i+] = get();
         val[] = val[n+] = INF;

         cnt = n+;
         root = n+ >> ;
         Build(,,n+);

         while(m--)
         {
             scanf("%s",ch+);    x=get();    y=get();
             x++;

             if(ch[] == 'r')
             {
                 Insert(x+,y);
                 Delete(x);    Delete(x);
             }
             if(ch[] == 's')
                 Insert(x,y);
             if(ch[] == 'x')
             {
                 y++;
                 x = Getid(x-);    y = Getid(y+);
                 Splay(x,);    Splay(y,x);
                 printf("%d\n", maxx[lc[y]] - minn[lc[y]]);
             }
             if(ch[] == 'n')
             {
                 y++;
                 x = Getid(x-);    y = Getid(y+);
                 Splay(x,);    Splay(y,x);
                 printf("%d\n", del[lc[y]]);
             }

         }
 }