LCT 维护边双 / 点双的模板

用 \(\text{LCT}\) 维护边双的做法是：加入一条非树边时，将这段树上路径合并为一个点代表这个边双，具体实现用并查集合并点，在 \(\text{Splay}\) 与 \(\text{Access}\) 的过程中对辅助树上父亲做路径压缩。

用 \(\text{LCT}\) 维护点双的做法是：加入一条非树边时，将这段树上路径全部砍断，新建一个点代表这个点双，将原来那些点向新点连虚边。

实现方法：直接用 \(\text{Splay}\) 与 \(\text{Access}\) 提取路径并且 \(\text{DFS}\) 遍历这个路径就可以了。

代码是维护路径桥与割点的个数。 洛谷链接

#include<bits/stdc++.h>
using namespace std;

const int N = 200005;

int n,q,lst;

struct bcj
{
	int f[N];
	void init()
	{
		for(int i=1; i<=n; i++)
			f[i]=i;
	}
	int find(int x)
	{
		return f[x]==x?x:f[x]=find(f[x]);
	}
}G;

namespace LCT
{
	const int maxn = N;
	int ch[maxn][2],fa[maxn],s[maxn],rev[maxn];

	#define lc(x) (ch[x][0])
	#define rc(x) (ch[x][1])

	bcj W;
	#define F(x) (W.find(x))

	int g(int x)
	{
		return rc(fa[x]) == x;
	}

	int nrt(int x)
	{
		return lc(fa[x]) == x || rc(fa[x]) == x;
	}

	void pushup(int x)
	{
		s[x] = s[lc(x)] + s[rc(x)] + 1;
	}

	void pushdown(int x)
	{
		if(rev[x])
		{
			swap(lc(lc(x)), rc(lc(x)));
			rev[lc(x)] ^= 1;
			swap(lc(rc(x)), rc(rc(x)));
			rev[rc(x)] ^= 1;
			rev[x] ^= 1;
		}
	}

	void rot(int x)
	{
		int y = fa[x], v = g(x);
		if(nrt(y))
			ch[fa[y]][g(y)] = x;
		fa[x] = fa[y];
		ch[y][v] = ch[x][!v];
		fa[ch[x][!v]] = y;
		ch[x][!v] = y;
		fa[y] = x;
		pushup(y);
	}

	void splay(int x)
	{
		x = F(x);
		int y; vector<int>v;
		for(y = x; nrt(y); y = fa[y] = F(fa[y]))
			v.push_back(y);
		for(pushdown(y); !v.empty(); v.pop_back())
			pushdown(v.back());
		for(y = fa[x]; nrt(x); rot(x), y = fa[x] = F(fa[x]))
			if(nrt(y))
				rot(g(x) ^ g(y) ? x : y);
		pushup(x);
	}

	void access(int x)
	{
		x = F(x);
		for(int y = 0; x; y = x, x = fa[x] = F(fa[x]))
		{
			splay(x);
			rc(x) = y;
		}
	}

	void makeroot(int x)
	{
		x = F(x);
		access(x);
		splay(x);
		swap(lc(x), rc(x));
		rev[x] ^= 1;
	}

	void link(int x, int y)
	{
		x = F(x); y = F(y);
		makeroot(x);
		access(y);
		splay(y);
		fa[x] = y;
	}

	void dfs_merge(int x, int root)
	{
		W.f[x] = root;
		if(lc(x)) dfs_merge(lc(x), root), lc(x) = 0;
		if(rc(x)) dfs_merge(rc(x), root), rc(x) = 0;
	}

	void zip(int x, int y)
	{
		x = F(x); y = F(y);
		makeroot(x);
		access(y);
		splay(y);
		dfs_merge(y, y);
		pushup(y);
	}

	int query(int x, int y)
	{
		x = F(x); y = F(y);
		makeroot(x);
		access(y);
		splay(y);
		return s[y] - 1;
	}

	#undef lc
	#undef rc
	#undef F
}

namespace RST
{
	const int maxn = N << 1;
	int cnt,ch[maxn][2],fa[maxn],s[maxn],rev[maxn];

	#define lc(x) (ch[x][0])
	#define rc(x) (ch[x][1])

	int g(int x)
	{
		return rc(fa[x]) == x;
	}

	int nrt(int x)
	{
		return lc(fa[x]) == x || rc(fa[x]) == x;
	}

	void pushup(int x)
	{
		s[x] = s[lc(x)] + s[rc(x)] + (x <= n);
	}

	void pushdown(int x)
	{
		if(rev[x])
		{
			swap(lc(lc(x)), rc(lc(x)));
			rev[lc(x)] ^= 1;
			swap(lc(rc(x)), rc(rc(x)));
			rev[rc(x)] ^= 1;
			rev[x] ^= 1;
		}
	}

	void rot(int x)
	{
		int y = fa[x], v = g(x);
		if(nrt(y))
			ch[fa[y]][g(y)] = x;
		fa[x] = fa[y];
		ch[y][v] = ch[x][!v];
		fa[ch[x][!v]] = y;
		ch[x][!v] = y;
		fa[y] = x;
		pushup(y);
	}

	void splay(int x)
	{
		int y; vector<int>v;
		for(y = x; nrt(y); y = fa[y])
			v.push_back(y);
		for(pushdown(y); !v.empty(); v.pop_back())
			pushdown(v.back());
		for(y = fa[x]; nrt(x); rot(x), y = fa[x])
			if(nrt(y))
				rot(g(x) ^ g(y) ? x : y);
		pushup(x);
	}

	void access(int x)
	{
		for(int y = 0; x; y = x, x = fa[x])
		{
			splay(x);
			rc(x) = y;
		}
	}

	void makeroot(int x)
	{
		access(x);
		splay(x);
		swap(lc(x), rc(x));
		rev[x] ^= 1;
	}

	void link(int x, int y)
	{
		makeroot(x);
		access(y);
		splay(y);
		fa[x] = y;
	}

	void dfs_merge(int x, int root)
	{
		fa[x] = root;
		if(lc(x)) dfs_merge(lc(x), root), lc(x) = 0;
		if(rc(x)) dfs_merge(rc(x), root), rc(x) = 0;
		pushup(x);
	}

	void zip(int x, int y)
	{
		makeroot(x);
		access(y);
		splay(y);
		dfs_merge(y, ++cnt);
		pushup(cnt);
	}

	int query(int x, int y)
	{
		makeroot(x);
		access(y);
		splay(y);
		return s[y];
	}

	#undef lc
	#undef rc
}

int main()
{
	scanf("%d %d", &n, &q);
	G.init();
	LCT::W.init();
	RST::cnt = n;
	for(int i = 1, opt, x, y; i <= q; i ++)
	{
		scanf("%d %d %d", &opt, &x, &y);
		x = x ^ lst; y = y ^ lst;
		if(opt == 1)
		{
			if(G.find(x) ^ G.find(y))
				LCT::link(x, y), RST::link(x, y), G.f[G.find(x)] = G.find(y);
			else
				LCT::zip(x, y), RST::zip(x, y);
		}
		if(opt == 2)
		{
			if(G.find(x) ^ G.find(y))
				puts("-1");
			else
				printf("%d\n", lst = LCT::query(x, y));
		}
		if(opt == 3)
		{
			if(G.find(x) ^ G.find(y))
				puts("-1");
			else
				printf("%d\n", lst = RST::query(x, y));
		}
	}
	return 0;
}