【洛谷 P3203】 [HNOI2010]弹飞绵羊（LCT）

题目链接

把每个点和能跳到的点连边，于是就构成了一个森林。

查询操作就是该点到根的路径长度，修改操作就相当于删边再重新连边。

显然是\(LCT\)的强项。

查询时\(access(x),splay(x)\)，然后输出\(size[x]\)就行了。

修改时\(access(x),splay(x)\)，然后双向断掉\(x\)与左儿子的边，然后直接和\(x+y\)连边即可。

简化版的\(LCT\)

#include <cstdio>
#define R register int
#define I inline void
#define lc c[x][0]
#define rc c[x][1]
const int MAXN = 300010;
inline int read(){
    int s = 0, w = 1;
    char ch = getchar();
    while(ch < '0' || ch > '9'){ if(ch == '-') w = -1; ch = getchar(); }
    while(ch >= '0' && ch <= '9'){ s = s * 10 + ch - '0'; ch = getchar(); }
    return s * w;
}
int f[MAXN], c[MAXN][2], v[MAXN], s[MAXN], sz[MAXN], st[MAXN], tag[MAXN];
inline int nroot(R x){
	return c[f[x]][0] == x || c[f[x]][1] == x;
}
I pushup(R x){
	s[x] = s[lc] ^ s[rc] ^ v[x];
	sz[x] = sz[lc] + sz[rc] + 1;
}
I swap(R x){
	lc ^= rc; rc = lc ^ rc; lc ^= rc; tag[x] ^= 1;
}
I pushdown(R x){
	if(tag[x]){
		swap(lc); swap(rc);
		tag[x] = 0;
	}
}
I rotate(R x){
	R y = f[x], z = f[y], k = c[y][1] == x, w = c[x][!k];
	if(nroot(y)) c[z][c[z][1] == y] = x;
	c[x][!k] = y; c[y][k] = w; f[y] = x; f[x] = z;
	if(w) f[w] = y;
	pushup(y);
}
I splay(R x){
	R y = x, z = 0;
	st[++z] = y;
	while(nroot(y)) st[++z] = y = f[y];
	while(z) pushdown(st[z--]);
	while(nroot(x)){
		y = f[x]; z = f[y];
		if(nroot(y)) (c[z][1] == y) ^ (c[y][1] == x) ? rotate(x) : rotate(y);
		rotate(x);
	}
	pushup(x);
}
I access(R x){
	for(R y = 0; x; x = f[y = x]){
	   splay(x); rc = y; pushup(x);
    }
}
int n, m, opt, a, b;
int main(){
	n = read();
	for(R i = 1; i <= n; ++i){
	   a = read();
	   if(i + a <= n) f[i] = i + a;
    }
    m = read();
	while(m--){
		opt = read(); a = read() + 1;
		switch(opt){
			case 1 : access(a); splay(a); printf("%d\n", sz[a]); break;
			case 2 : b = read(); access(a); splay(a); c[a][0] = f[c[a][0]] = 0; if(a + b <= n) f[a] = a + b; break;
		}
	}
	return 0;
}