【BZOJ4864】神秘物质 [Splay]
神秘物质
Time Limit: 10 Sec Memory Limit: 256 MBDescription
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 }
