【Foreign】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

  1 #include<iostream>
  2 #include<string>
  3 #include<algorithm>
  4 #include<cstdio>
  5 #include<cstring>
  6 #include<cstdlib>
  7 #include<cmath>
  8 using namespace std;
  9 typedef long long s64;
 10
 11 const int ONE = 300005;
 12 const int INF = 2147483640;
 13
 14 int n,m;
 15 int x,y,a[ONE];
 16 int root,cnt;
 17 int lc[ONE],rc[ONE],fa[ONE];
 18 int size[ONE],val[ONE];
 19 int maxx[ONE],minn[ONE],del[ONE];
 20 int Ls[ONE],Rs[ONE];
 21 char ch[10];
 22
 23 inline int get()
 24 {
 25         int res=1,Q=1;  char c;
 26         while( (c=getchar())<48 || c>57)
 27         if(c==‘-‘)Q=-1;
 28         if(Q) res=c-48;
 29         while((c=getchar())>=48 && c<=57)
 30         res=res*10+c-48;
 31         return res*Q;
 32 }
 33
 34 void Up(int i)
 35 {
 36         size[i] = size[lc[i]] + size[rc[i]] + 1;
 37         maxx[i] = minn[i] = val[i];
 38         del[i] = INF;
 39         Ls[i] = Rs[i] = i;
 40         if(lc[i])
 41         {
 42             Ls[i] = Ls[lc[i]];
 43             maxx[i] = max(maxx[i], maxx[lc[i]]);
 44             minn[i] = min(minn[i], minn[lc[i]]);
 45             del[i] = min(del[i], del[lc[i]]);
 46             del[i] = min(del[i], abs( val[i]-val[Rs[lc[i]]] ) );
 47         }
 48         if(rc[i])
 49         {
 50             Rs[i] = Rs[rc[i]];
 51             maxx[i] = max(maxx[i], maxx[rc[i]]);
 52             minn[i] = min(minn[i], minn[rc[i]]);
 53             del[i] = min(del[i], del[rc[i]]);
 54             del[i] = min(del[i], abs( val[i]-val[Ls[rc[i]]] ) );
 55         }
 56 }
 57
 58 void Turn(int x)
 59 {
 60         int y = fa[x], z = fa[y];
 61         int b = x==lc[y] ? rc[x]:lc[x];
 62
 63         fa[y] = x;    fa[x] = z;
 64         if(b) fa[b] = y;
 65
 66         if(z)
 67         {
 68             if(y == lc[z]) lc[z] = x;
 69             else rc[z] = x;
 70         }
 71
 72         if(x==lc[y]) rc[x] = y,lc[y] = b;
 73         else lc[x] = y, rc[y] = b;
 74
 75         Up(y);    Up(x);
 76 }
 77
 78 void Splay(int x,int pos)
 79 {
 80         while(fa[x] != pos)
 81         {
 82             if(fa[fa[x]] != pos)
 83             {
 84                 if( (lc[fa[x]]==x) == (lc[fa[fa[x]]]==fa[x]) ) Turn(fa[x]);
 85                 else Turn(x);
 86             }
 87             Turn(x);
 88         }
 89         if(pos == 0) root = x;
 90 }
 91
 92 int Build(int i,int l,int r)
 93 {
 94         int mid = l+r >> 1;
 95         fa[mid] = i;
 96         if(l <= mid-1) lc[mid] = Build(mid, l,mid-1);
 97         if(mid+1 <= r) rc[mid] = Build(mid, mid+1,r);
 98         Up(mid);
 99         return mid;
100 }
101
102 int Getid(int num)
103 {
104         int i = root;
105         while(size[lc[i]] + 1 != num)
106         {
107             if(size[lc[i]] + 1 < num)
108                 num -= size[lc[i]] + 1,    i = rc[i];
109             else i = lc[i];
110         }
111         return i;
112 }
113
114 void Delete(int i)
115 {
116         int x = Getid(i);
117         Splay(x, 0);
118         int L = Rs[lc[x]];    Splay(L,0);
119         int R = Ls[rc[x]];    Splay(R,L);
120         lc[R] = 0;
121         Splay(R,0);
122 }
123
124 void Insert(int i,int Val)
125 {
126         int x = Getid(i);
127         Splay(x,0);
128         int R = Ls[rc[x]];    Splay(R,x);
129         val[++cnt] = Val; fa[cnt] = R; lc[R] = cnt;
130         Splay(cnt,0);
131 }
132
133 int main()
134 {
135         n=get();    m=get();
136         for(int i=1;i<=n;i++)
137             val[i+1] = get();
138         val[1] = val[n+2] = INF;
139
140         cnt = n+2;
141         root = n+3 >> 1;
142         Build(0,1,n+2);
143
144         while(m--)
145         {
146             scanf("%s",ch+1);    x=get();    y=get();
147             x++;
148
149             if(ch[3] == ‘r‘)
150             {
151                 Insert(x+1,y);
152                 Delete(x);    Delete(x);
153             }
154             if(ch[3] == ‘s‘)
155                 Insert(x,y);
156             if(ch[3] == ‘x‘)
157             {
158                 y++;
159                 x = Getid(x-1);    y = Getid(y+1);
160                 Splay(x,0);    Splay(y,x);
161                 printf("%d\n", maxx[lc[y]] - minn[lc[y]]);
162             }
163             if(ch[3] == ‘n‘)
164             {
165                 y++;
166                 x = Getid(x-1);    y = Getid(y+1);
167                 Splay(x,0);    Splay(y,x);
168                 printf("%d\n", del[lc[y]]);
169             }
170
171         }
172 }