2002: [Hnoi2010]Bounce 弹飞绵羊
https://www.lydsy.com/JudgeOnline/problem.php?id=2002
分析：
绵羊在弹飞的路径中相当于一棵树，这棵树需要更改形态，删一条边，加一条边，所以LCT维护一下。
代码：
1 #include<bits/stdc++.h> 2 using namespace std; 3 typedef long long LL; 4 5 inline int read() { 6 int x=0,f=1;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-1; 7 for (;isdigit(ch);ch=getchar())x=x*10+ch-'0';return x*f; 8 } 9 10 const int N = 200100; 11 int ch[N][2],fa[N],rev[N],val[N],siz[N],sk[N],a[N],Top,n; 12 13 void pushup(int x) { 14 siz[x] = siz[ch[x][0]] + siz[ch[x][1]] + 1; 15 } 16 void pushdown(int x) { 17 if (rev[x]) { 18 rev[ch[x][0]] ^= 1; rev[ch[x][1]] ^= 1; 19 swap(ch[x][0], ch[x][1]); 20 rev[x] ^= 1; 21 } 22 } 23 bool isroot(int x) { 24 return ch[fa[x]][0] != x && ch[fa[x]][1] != x; 25 } 26 int son(int x) { 27 return x == ch[fa[x]][1]; 28 } 29 void rotate(int x) { 30 int y = fa[x],z = fa[y],b = son(x),c = son(y),a = ch[x][!b]; 31 if (!isroot(y)) ch[z][c] = x;fa[x] = z; 32 ch[x][!b] = y;fa[y] = x; 33 ch[y][b] = a;if (a) fa[a] = y; 34 pushup(y);pushup(x); 35 } 36 void splay(int x) { 37 sk[Top = 1] = x; 38 for (int i=x; !isroot(i); i=fa[i]) sk[++Top] = fa[i]; 39 while (Top) pushdown(sk[Top--]); 40 while (!isroot(x)) { 41 int y = fa[x]; 42 if (isroot(y)) rotate(x); 43 else { 44 if (son(x) == son(y)) rotate(y), rotate(x); 45 else rotate(x), rotate(x); 46 } 47 } 48 } 49 void access(int x) { 50 for (int last=0; x; last=x, x=fa[x]) { 51 splay(x); ch[x][1] = last; pushup(x); 52 } 53 } 54 void makeroot(int x) { 55 access(x); splay(x); rev[x] ^= 1; 56 } 57 int find(int x) { 58 access(x); splay(x); 59 while (ch[x][0]) x = ch[x][0]; 60 return x; 61 } 62 void link(int x,int y) { 63 makeroot(x); 64 fa[x] = y; 65 } 66 void cut(int x,int y) { 67 makeroot(x); access(y); splay(y); 68 if (fa[x] == y && !ch[x][1]) fa[x] = ch[y][0] = 0; 69 } 70 71 void query() { 72 makeroot(n + 1); 73 int p = read() + 1; 74 access(p); 75 splay(p); 76 printf("%d ",siz[p] - 1); 77 } 78 void change() { 79 int p = read() + 1,x = read(),t = p+x > n+1 ? n+1: p+x; // --- 判断是否大于n+1，不判luogu上80 80 cut(p,a[p]); 81 a[p] = t; 82 link(p,a[p]); 83 } 84 85 int main() { 86 n = read(); 87 for (int i=1; i<=n; ++i) { 88 a[i] = i + read(); 89 a[i] = a[i] > n+1 ? n+1 : a[i]; 90 } 91 for (int i=1; i<=n; ++i) link(i,a[i]); 92 int m = read(); 93 while (m--) { 94 int opt = read(); 95 if (opt == 1) query(); 96 else change(); 97 } 98 return 0; 99 }