[洛谷P3979]遥远的国度

题目大意：有一棵$n$个点的树，每个点有一个点权，有三种操作：

1. $1\;x：$把根变成$x$
2. $2\;u\;v\;x：$把路径$u->v$上的点权改为$x$
3. $3\;x：$询问以$x$为根的子树中最小的点权

题解：树剖，发现换根操作比较困难，可以进行一波分类讨论（下面的$lca$以及子树都是在以$1$为根的情况下（其实任意一个固定的点均可）

1. $root=x：$就是询问整棵树
2. $lca(root,x)\not=x：$就是正常询问$x$的子树
3. $lca(root,x)=x：$就是整棵树减去$root$所在的子树

然后步骤三的减去$root$所在的子树中的找这棵子树可以用倍增来求

卡点：步骤三中只查询了$x$的子树减去$root$子树

 

C++ Code：

#include <algorithm>
#include <cstdio>
#include <cctype>
namespace std {
	struct istream {
#define M (1 << 24 | 3)
		char buf[M], *ch = buf - 1;
		inline istream() {
#ifndef ONLINE_JUDGE
			freopen("input.txt", "r", stdin);
#endif
			fread(buf, 1, M, stdin);
		}
		inline istream& operator >> (int &x) {
			while (isspace(*++ch));
			for (x = *ch & 15; isdigit(*++ch); ) x = x * 10 + (*ch & 15);
			return *this;
		}
#undef M
	} cin;
	struct ostream {
#define M (1 << 24 | 3)
		char buf[M], *ch = buf - 1;
		inline ostream& operator << (int x) {
			if (!x) {
				*++ch = '0';
				return *this;
			}
			static int S[20], *top; top = S;
			while (x) {
				*++top = x % 10 ^ 48;
				x /= 10;
			}
			for (; top != S; --top) *++ch = *top;
			return *this;
		}
		inline ostream& operator << (const char x) {*++ch = x; return *this;}
		inline ~ostream() {
#ifndef ONLINE_JUDGE
			freopen("output.txt", "w", stdout);
#endif
			fwrite(buf, 1, ch - buf + 1, stdout);
		}
#undef M
	} cout;
}

#define maxn 100010
const int inf = 0x7fffffff;

int head[maxn], cnt;
struct Edge {
	int to, nxt;
} e[maxn << 1];
inline void addedge(int a, int b) {
	e[++cnt] = (Edge) {b, head[a]}; head[a] = cnt;
	e[++cnt] = (Edge) {a, head[b]}; head[b] = cnt;
}

int n, m;
int w[maxn], W[maxn];
namespace SgT {
	int V[maxn << 2], tg[maxn << 2];
	inline void pushdown(int rt) {
		int &__tg = tg[rt];
		V[rt << 1] = tg[rt << 1] = V[rt << 1 | 1] = tg[rt << 1 | 1] = __tg;
		__tg = 0;
	}

	int L, R, num;
	void build(int rt, int l, int r) {
		if (l == r) {
			V[rt] = W[l];
			return ;
		}
		int mid = l + r >> 1;
		build(rt << 1, l, mid);
		build(rt << 1 | 1, mid + 1, r);
		V[rt] = std::min(V[rt << 1], V[rt << 1 | 1]);
	}
	void __modify(int rt, int l, int r) {
		if (L <= l && R >= r) {
			V[rt] = tg[rt] = num;
			return ;
		}
		int mid = l + r >> 1;
		if (tg[rt]) pushdown(rt);
		if (L <= mid) __modify(rt << 1, l, mid);
		if (R > mid) __modify(rt << 1 | 1, mid + 1, r);
		V[rt] = std::min(V[rt << 1], V[rt << 1 | 1]);
	}
	void modify(int __L, int __R, int __num) {
		L = __L, R = __R, num = __num;
		__modify(1, 1, n);
	}

	int ans;
	void __query(int rt, int l, int r) {
		if (L <= l && R >= r) {
			ans = std::min(ans, V[rt]);
			return ;
		}
		int mid = l + r >> 1;
		if (tg[rt]) pushdown(rt);
		if (L <= mid) __query(rt << 1, l, mid);
		if (R > mid) __query(rt << 1 | 1, mid + 1, r);
	}
	int query(int __L, int __R) {
		L = __L, R = __R;
		ans = inf;
		__query(1, 1, n);
		return ans;
	}
}

int root;
int fa[maxn], sz[maxn], dfn[maxn], idx;
int son[maxn], top[maxn], dep[maxn];

namespace BZ {
#define M 17
	int fa[maxn][M + 1];
	inline void init(int u) {
		*fa[u] = ::fa[u];
		for (int i = 1; i <= M; i++) fa[u][i] = fa[fa[u][i - 1]][i - 1];
	}
	inline int get_son(int x, int y) {
		for (int i = M; ~i; i--) if (dep[fa[x][i]] > dep[y]) x = fa[x][i];
		return x;
	}
#undef M
}
using BZ::get_son;

void dfs1(int u) {
	BZ::init(u);
	sz[u] = 1;
	for (int i = head[u]; i; i = e[i].nxt) {
		int v = e[i].to;
		if (v != fa[u]) {
			fa[v] = u;
			dep[v] = dep[u] + 1;
			dfs1(v);
			sz[u] += sz[v];
			if (!son[u] || sz[v] > sz[son[u]]) son[u] = v;
		}
	}
}
void dfs2(int u) {
	dfn[u] = ++idx;
	int v = son[u];
	if (v) top[v] = top[u], dfs2(v);
	for (int i = head[u]; i; i = e[i].nxt) {
		int v = e[i].to;
		if (v != fa[u] && v != son[u]) {
			top[v] = v;
			dfs2(v);
		}
	}
}
inline int LCA(int x, int y) {
	if (x == y) return x;
	while (top[x] != top[y]) {
		if (dep[top[x]] < dep[top[y]]) std::swap(x, y);
		x = fa[top[x]];
	}
	return dep[x] > dep[y] ? y : x;
}
void modify(int x, int y, int z) {
	while (top[x] != top[y]) {
		if (dep[top[x]] < dep[top[y]]) std::swap(x, y);
		SgT::modify(dfn[top[x]], dfn[x], z);
		x = fa[top[x]];
	}
	if (dep[x] > dep[y]) std::swap(x, y);
	SgT::modify(dfn[x], dfn[y], z);
}
inline int query(int x) {
	if (root == x) return SgT::query(1, n);
	if (LCA(x, root) != x) return SgT::query(dfn[x], dfn[x] + sz[x] - 1);
	const int S = get_son(root, x), l = dfn[S], r = dfn[S] + sz[S] - 1;
	int ans = inf;
	if (1 < l) ans = SgT::query(1, l - 1);
	if (r < n) ans = std::min(ans, SgT::query(r + 1, n));
	return ans;
}

int main() {
	std::cin >> n >> m;
	for (int i = 1, a, b; i < n; i++) {
		std::cin >> a >> b;
		addedge(a, b);
	}
	dfs1(1);
	dfs2(top[1] = 1);
	for (int i = 1; i <= n; i++) std::cin >> w[i];
	for (int i = 1; i <= n; i++) W[dfn[i]] = w[i];
	SgT::build(1, 1, n);
	std::cin >> root;
	while (m --> 0) {
		int op, u, v, x;
		std::cin >> op >> u;
		switch (op) {
			case 1:
				root = u;
				break;
			case 2:
				std::cin >> v >> x;
				modify(u, v, x);
				break;
			case 3:
				std::cout << query(u) << '\n';
		}
	}
	return 0;
}