BZOJ2959 长跑（LCT维护边双后缩点）

本文搬运自本人高中时期CSDN博客，若图片加载不出来，可到原文查看：https://blog.csdn.net/zhangtingxiqwq/article/details/141937532

https://www.luogu.com.cn/problem/P10658

显然，一个边双内的点可以全部在一起，也就是可以缩成一个点

此时我们可以用LCT来维护，正常的连边显然，当要缩点时就把这点链提取出来，然后把整棵splay遍历一遍，搞一起即可

要拿个并查集维护实际对应点。

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#include<bits/stdc++.h>
using namespace std;
#ifdef LOCALd
 #define debug(...) fprintf(stdout, ##__VA_ARGS__)

 #define debag(...) fprintf(stderr, ##__VA_ARGS__)

#else
 #define debug(...) void(0)

 #define debag(...) void(0)

#endif
//#define int long long

#ifdef nLOCAL
inline int read(){int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;
ch=getchar();}while(ch>='0'&&ch<='9'){x=(x<<1)+
(x<<3)+(ch^48);ch=getchar();}return x*f;}
#else 
	int read() { long long x; scanf("%lld", &x); return (int)x; }
#endif
#define Z(x) (x)*(x)

#define pb push_back

#define fi first

#define se second

//#define M
//#define mo
#define N 300100

int n, m, i, j, k, T;
int mp[N], a[N], A[N]; 

int F(int x) {
//	debug("ka sai find Fa %lld %lld\n", x, mp[x]); 
	if(mp[x] == x) return mp[x]; 
	return mp[x] = F(mp[x]); 
}

namespace LCT {
#define ls(k) (son[k][0])

#define rs(k) (son[k][1])

	int son[N][2], s[N], rev[N], f[N]; 
	int fa(int x) { return F(f[x]); }
	void push_up(int k) {
		s[k] = s[ls(k)] + s[rs(k)] + a[k]; 
	}
	void push_down(int k) {
		if(rev[k]) {
			swap(ls(k), rs(k)); 
			if(ls(k)) rev[ls(k)] ^= 1; 
			if(rs(k)) rev[rs(k)] ^= 1; 
			rev[k] = 0; 	
		}
	}
	int zh(int x) {
		return rs(fa(x)) == x; 
	}
	bool isRoot(int x) {
		if(!fa(x)) return true; 
		return ls(fa(x)) != x && rs(fa(x)) != x; 
	}
	void Rotate(int x) {
//		debug("In Rotate\n"); 
		int y = fa(x), z = fa(y); 
		int k = zh(x), w = son[x][k ^ 1]; 
		if(z && !isRoot(y)) son[z][zh(y)] = x; 
		if(w) f[w] = y, son[y][k] = w; else son[y][k] = 0; 
		f[x] = z; f[y] = x; son[x][k ^ 1] = y; 
		push_up(y); push_up(x); push_up(z); 
//		debug("End Rotate\n"); 
	}
	void Splay(int x) {
		stack<int>sta; sta.push(x); 
		for(int y = x; !isRoot(y); y = fa(y)) sta.push(fa(y)); 
		while(!sta.empty()) push_down(sta.top()), sta.pop(); 
		while(!isRoot(x)) {
			int y = fa(x); 
//			debag("ka zai Splay"); 
			if(!isRoot(y)) {
				if(zh(x) == zh(y)) Rotate(y); 
				else Rotate(x); 
			}
			Rotate(x); 
//			debag("End now splay"); 
		}
	}
	void access(int x) {
		for(int y = 0; x; y = x, x = fa(x)) {
//			debug("%lld ===> %lld \n", y, x); 
			Splay(x); rs(x) = y; push_up(x); 
		}
	}
	void makeRoot(int x) {
//		debug("makeRoot(%lld)\n", x); 
		access(x); 
//		debug("makeRoot(%lld)\n", x); 
		Splay(x); rev[x] ^= 1; 
	}
	int findRoot(int x) {
		Splay(x); 
		while(push_down(x), ls(x)) x = ls(x); 
		Splay(x); 
		return x; 
	}
	bool check(int x, int y) {
//		debug("&&"); 
		makeRoot(x); 
		access(y); 
//		debug("$$ [%lld]%lld\n", x, findRoot(y));  
		return findRoot(y) == x; 
	}
	void Link(int x, int y) {
//		debug("[]]]]]]] Link %lld %lld\n", x, y); 
		makeRoot(x); f[x] = y; 
	}
	void add(int x, int k) {
		makeRoot(x); Splay(x); a[x] += k; s[x] += k; 
	}
	void dfs(int x, int rt) {
//		debug("dfsing(%lld)[%lld %lld] %lld\n", x, ls(x), rs(x), rt); 
		mp[x] = rt; if(x != rt) a[rt] += a[x]; 
		if(ls(x)) dfs(ls(x), rt); 
		if(rs(x)) dfs(rs(x), rt); 
		son[x][0] = son[x][1] = 0; 		
	}
	void Combine(int rt) {
		queue<int>q; q.push(rt); 
		while(!q.empty()) {
			int x = q.front(); q.pop(); 
			mp[x] = rt; if(x != rt) a[rt] += a[x]; 
			if(ls(x)) q.push(ls(x)); 
			if(rs(x)) q.push(rs(x)); 
			son[x][0] = son[x][1] = 0; 		
		}
		s[rt] = a[rt]; 
		son[rt][0] = son[rt][1] = 0; 
	}
	void print() {
	#ifdef LOCAL
		for(int i = 1; i <= n; ++i)	
			if(mp[i] == i)
		 	debug("%lld : %lld(%lld) [%lld %lld] %lld %lld\n", i, fa(i), (int)isRoot(i), ls(i), rs(i), a[i], s[i]); 
		debug("================\n"); 
	#endif
	}
}

signed main()
{
	#ifdef LOCAL
	  freopen("in.txt", "r", stdin);
	  freopen("out.txt", "w", stdout);
	#endif
//	srand(time(NULL));
//	T=read();
//	while(T--) {
//
//	}
	n = read(); m = read(); 
	for(i = 1; i <= n; ++i) mp[i] = i; 
	for(i = 1; i <= n; ++i) k = read(), LCT :: add(i, k), A[i] = k; 
	for(i = 1; i <= m; ++i) {
		int op = read(), u, v; 
//		debag("===== %lld\n", i); 
		if(op == 1) {
			u = read(); v = read(); u = F(u); v = F(v); 
			if(u == v) continue; 
//			debug("Want to know %lld %lld\n", u, v); 
			if(!LCT :: check(u, v)) LCT :: Link(u, v); 
			else {
//				debug("Try to comb %lld %lld\n", u, v); 
				LCT :: makeRoot(u); LCT :: access(v); LCT :: Splay(u); 
				LCT :: Combine(u); 
			}
		}
		if(op == 2) {
			u = read(); k = read(); j = k - A[u]; A[u] = k; 
			u = F(u); LCT :: add(u, j); 
		}
		if(op == 3) {
			u = read(); v = read(); u = F(u); v = F(v); 
//			debug("qry(%lld %lld)\n", u, v); 
			if(!LCT :: check(u, v)) { printf("-1\n"); continue; }
			LCT :: makeRoot(u); 
			LCT :: access(v); 
//			LCT :: print(); 
			LCT :: Splay(v); 
			printf("%d\n", LCT :: s[v]); 
		}
//		LCT :: print(); 
	}
	return 0;
}