[题解]LuoGu4315：月下“毛景树”

原题传送门
其实也是一道树剖裸题啊
四个操作

• Change：单点修改
• Cover：区间覆盖
• Add：区间加
• Max：区间最值

是不是很裸啊，不过此题有两个特点，也是需要特别注意的地方

• 维护边权，因为线段树维护的是点，所以我们采用以点代边的方法，用一条边两端点中深度更大的那一个点代表这条边，最终跳链跳到两点处于同一条链上时，深度更小的那个点需要id+1
• 区间覆盖操作，要处理覆盖与加法之间的平衡比较麻烦，要全局考虑。这里线段树维护三个值，sum表示区间的最大值，add表示加法的lazytag，tag表示覆盖的lazytag
  覆盖时，需要把add置为0
  pushdown时，先下传tag（同时把子节点的add置为0），再下传add

码量其实也不是很大，156行足矣~

Code：

#include <bits/stdc++.h>
#define maxn 100010
#define ls rt << 1
#define rs rt << 1 | 1
using namespace std;
struct Edge{
	int to, next;
}edge[maxn << 1];
struct Seg{
	int l, r, sum, tag, add;
}seg[maxn << 2];
struct Line{
	int x, y, z;
}line[maxn];
int head[maxn], num, d[maxn], fa[maxn], size[maxn], son[maxn], id[maxn], cnt, top[maxn], w[maxn], wt[maxn], n;

inline int read(){
	int s = 0, w = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') w = -1;
	for (; isdigit(c); c = getchar()) s = (s << 1) + (s << 3) + (c ^ 48);
	return s * w;
}

void add_edge(int x, int y){ edge[++num].to = y; edge[num].next = head[x]; head[x] = num; }

void dfs(int u){
	size[u] = 1, son[u] = -1;
	for (int i = head[u]; i; i = edge[i].next){
		int v = edge[i].to;
		if (v != fa[u]){
			fa[v] = u, d[v] = d[u] + 1;
			dfs(v);
			size[u] += size[v];
			if (son[u] == -1 || son[u] != -1 && size[son[u]] < size[v]) son[u] = v;
		}
	}
}

void dfs(int u, int x){
	id[u] = ++cnt, top[u] = x, wt[cnt] = w[u];
	if (son[u] == -1) return;
	dfs(son[u], x);
	for (int i = head[u]; i; i = edge[i].next){
		int v = edge[i].to;
		if (v != fa[u] && v != son[u]) dfs(v, v);
	}
}

void pushup(int rt){ seg[rt].sum = max(seg[ls].sum, seg[rs].sum); }

void pushdown(int rt){
	if (seg[rt].tag != -1){
		seg[ls].sum = seg[rs].sum = seg[rt].tag;
		seg[ls].add = seg[rs].add = 0;
		seg[ls].tag = seg[rs].tag = seg[rt].tag;
	}
	if (seg[rt].add){
		seg[ls].sum += seg[rt].add;
		seg[rs].sum += seg[rt].add;
		seg[ls].add += seg[rt].add;
		seg[rs].add += seg[rt].add;
	}
	seg[rt].add = 0, seg[rt].tag = -1;
}

void build(int rt, int l, int r){
	seg[rt].l = l, seg[rt].r = r, seg[rt].tag = -1;
	if (l == r){
		seg[rt].sum = wt[l]; return;
	}
	int mid = (l + r) >> 1;
	build(ls, l, mid); build(rs, mid + 1, r);
	pushup(rt);
}

void update(int rt, int l, int r, int k){
	pushdown(rt);
	if (seg[rt].l > r || seg[rt].r < l) return;
	if (seg[rt].l >= l && seg[rt].r <= r){
		seg[rt].sum += k, seg[rt].add += k; return;
	}
	update(ls, l, r, k); update(rs, l, r, k);
	pushup(rt);
}

void change(int rt, int l, int r, int k){
	pushdown(rt);
	if (seg[rt].l > r || seg[rt].r < l) return;
	if (seg[rt].l >= l && seg[rt].r <= r){
		seg[rt].sum = k, seg[rt].add = 0, seg[rt].tag = k; return;
	}
	change(ls, l, r, k); change(rs, l, r, k);
	pushup(rt);
}

int query(int rt, int l, int r){
	if (seg[rt].l > r || seg[rt].r < l) return 0;
	if (seg[rt].l >= l && seg[rt].r <= r) return seg[rt].sum;
	pushdown(rt);
	return max(query(ls, l, r), query(rs, l, r));
}

int main(){
	n = read();
	for (int i = 1; i < n; ++i){
		int x = read(), y = read(), z = read();
		add_edge(x, y); add_edge(y, x);
		line[i].x = x; line[i].y = y; line[i].z = z;
	}
	dfs(1);
	for (int i = 1; i < n; ++i) w[fa[line[i].x] == line[i].y ? line[i].x : line[i].y] = line[i].z;
	dfs(1, 1);
	build(1, 1, n);
	while (1){
		char c = getchar(); for (; c != 'a' && c != 'o' && c != 'd' && c != 'h' && c != 't'; c = getchar());
		if (c == 't') break;
		if (c == 'h'){
			int x = read(), y = read();
			int z = fa[line[x].x] == line[x].y ? line[x].x : line[x].y;
			change(1, id[z], id[z], y);
		}
		if (c == 'o'){
			int x = read(), y = read(), z = read();
			while (top[x] != top[y]){
				if (d[top[x]] < d[top[y]]) swap(x, y);
				change(1, id[top[x]], id[x], z);
				x = fa[top[x]];
			}
			if (d[x] < d[y]) swap(x, y);
			if (id[y] + 1 <= id[x]) change(1, id[y] + 1, id[x], z);
		}
		if (c == 'd'){
			int x = read(), y = read(), z = read();
			while (top[x] != top[y]){
				if (d[top[x]] < d[top[y]]) swap(x, y);
				update(1, id[top[x]], id[x], z);
				x = fa[top[x]];
			}
			if (d[x] < d[y]) swap(x, y);
			if (id[y] + 1 <= id[x]) update(1, id[y] + 1, id[x], z);
		}
		if (c == 'a'){
			int x = read(), y = read(), ans = 0;
			while (top[x] != top[y]){
				if (d[top[x]] < d[top[y]]) swap(x, y);
				ans = max(ans, query(1, id[top[x]], id[x]));
				x = fa[top[x]];
			}
			if (d[x] < d[y]) swap(x, y);
			if (id[y] + 1 <= id[x]) ans = max(ans, query(1, id[y] + 1, id[x]));
			printf("%d\n", ans);
		}
	}
	return 0;
}