[洛谷P4315] 月下”毛景“树

题目链接：##

点我

题目分析：##

树剖。将边权下放到下方点上（为什么要选深度更深的点？一个父亲可能对应多个儿子，但一个儿子只有一个父亲，即可以保证每个点只保存一条边权）成为经典点权+树剖裸题

注意链计算时不能把LCA算进去，其余细节较多，具体见代码。

代码：##

#include<bits/stdc++.h>
#define N (100000 + 5)
#define inf (1000000000+7)
using namespace std;
inline int read() {
	int cnt = 0, f = 1; char c;
	c = getchar();
	while(!isdigit(c)) {
		if (c == '-') f = -f;
		c = getchar();
	}
	while(isdigit(c)) {
		cnt = cnt * 10 + c - '0';
		c = getchar();
	}
	return cnt * f;
}
int nxt[N * 2], first[N * 2], to[N * 2], w[N * 2], a[N], tot;
int father[N], top[N], siz[N], dep[N], son[N], num[N], id[N], idx;
int n, u, v, W, k;
char opr[20];
struct node{
	int l, r;
	long long cov, add, gmax;
	#define l(p) tree[p].l
	#define r(p) tree[p].r
	#define cov(p) tree[p].cov
	#define add(p) tree[p].add
	#define gmax(p) tree[p].gmax
} tree[N * 4];

struct edge{
	int u; int v;
}e[N * 2];

void Add(int x, int y, int z) {
	nxt[++tot] = first[x];
	first[x] = tot;
	to[tot] = y;
	w[tot] = z;
}

void dfs1(int cur, int fa) {
	father[cur] = fa; siz[cur] = 1; dep[cur] = dep[fa] + 1;
	for (register int i = first[cur]; i; i = nxt[i]) {
		int v = to[i];
		if(v != fa) {
			a[v] = w[i];
			dfs1(v, cur);
			siz[cur] += siz[v];
			if(siz[son[cur]] < siz[v]) son[cur] = v;
		}
	}
}

void dfs2(int cur, int tp) {
	top[cur] = tp; num[cur] = ++idx; id[idx] = cur;
	if (son[cur]) dfs2(son[cur], tp);
	for (register int i = first[cur]; i; i = nxt[i]) {
		int v = to[i];
		if (!num[v]) dfs2(v, v);
	}
}

void pushup(int p) {
	gmax(p) = max(gmax(p << 1), gmax(p << 1 | 1));
}
void pushcover(int p, int v){cov(p) = v; add(p) = 0; gmax(p) = v;}
void pushadd(int p,int v){ add(p)+=v; gmax(p)+=v;}
void pushdown(int p) {
	if (cov(p) >= 0) {
		pushcover(p<<1, cov(p)); pushcover(p<<1|1, cov(p)); cov(p) = -1;
	}
	if (add(p)) {
		pushadd(p<<1, add(p)); pushadd(p<<1|1, add(p)); add(p) = 0;
	}
}

void build_tree(int p, int l, int r) {
	l(p) = l; r(p) = r;	cov(p) = -1;
	if(l == r) {
		gmax(p) = a[id[l]];
	//	cout<<l<<" "<<r<<" "<<gmax(p)<<endl;
		return;
	}
	int mid = (l + r) >> 1;
	build_tree(p << 1, l, mid);
	build_tree(p << 1 | 1, mid + 1, r);
	pushup(p);
}
void debug(int u,int l,int r){
	if(l==r){
		cout<<id[l]<<" "<<gmax(u)<<endl;return;
	}int mid=(l+r)>>1;
	debug(u*2,l,mid);debug(u*2+1,mid+1,r);
}
void Cover(int p, int l, int r, int d) {
	if (l > r) return;
	if (l <= l(p) && r >= r(p)) {
		pushcover(p, d);
		return;
	}
	pushdown(p);
	int mid = (l(p) + r(p)) >> 1;
	if (l <= mid) Cover(p << 1, l, r, d);
	if (r > mid) Cover(p << 1 | 1, l, r, d);
	pushup(p);
}

void Modify(int p, int l, int r, int d) {
	if (l > r) return;
	if (l <= l(p) && r >= r(p)) {
//		if(cov(p) >= 0) {
//			cov(p) += d;
//			gmax(p) += d;
//		} else {
//			pushadd(p, d);
//		}
		pushadd(p, d);
		return;
	}
	pushdown(p);
	int mid = (l(p) + r(p)) >> 1;
	if (l <= mid) Modify(p << 1, l, r, d);
	if (r > mid) Modify(p << 1 | 1, l, r, d);
	pushup(p);
}

long long query(int p, int l, int r) {
//	cout<<p<<" "<<l(p)<<" "<<r(p)<<endl;
	if (l <= l(p) && r >= r(p)) return gmax(p);
	int mid = (l(p) + r(p)) >> 1;
	pushdown(p);
	//cout<<p<<endl;
	long long val = -inf;
	if (l <= mid) val = max (val, query(p << 1, l, r));
	if (r > mid) val = max(val, query(p << 1 | 1, l, r));
	return val;
}

void chain_cover(int u, int v, int d) {
	while (top[u] != top[v]) {
		if (dep[top[u]] < dep[top[v]]) swap(u, v);
		Cover(1, num[top[u]], num[u], d);
		u = father[top[u]];
	}
	if (dep[u] < dep[v]) swap(u, v);
//	if (u == v) Cover(1, num[v], num[u], d);
	Cover(1, num[v] + 1, num[u], d);
}

void chain_modify(int u, int v, int d) {
	while (top[u] != top[v]) {
		if (dep[top[u]] < dep[top[v]]) swap(u, v);
		Modify(1, num[top[u]], num[u], d);
		u = father[top[u]];
	}
	if (dep[u] < dep[v]) swap(u, v);
//	if (u == v) Modify(1, num[v], num[u], d);
	Modify(1, num[v] + 1, num[u], d);
}

long long chain_query(int u, int v) {
	long long ans = -inf;
	while (top[u] != top[v]) {//cout<<u<<endl;
	//	cout<<top[u]<<" "<<top[v]<<endl;
		if (dep[top[u]] < dep[top[v]]) swap(u, v);
	//	cout<<top[u]<<" "<<top[v]<<endl;
	//	cout<<num[top[u]]<<" "<<num[u]<<endl;
	//	cout<<query(1,num[top[u]],num[u])<<"###"<<endl;
		ans = max(ans, query(1, num[top[u]], num[u]));//cout<<"#";
		u = father[top[u]];
	//	cout<<ans<<endl;
	}
	if (dep[u] < dep[v]) swap(u, v);
	ans = max(ans, query(1, num[v] + 1, num[u]));
	return ans;
}

void solve() {
	n = read();
	for (register int i = 1; i < n; i++) {
		u = read(); v = read(); W = read();
		e[i].u = u; e[i].v = v;
		Add(u, v, W); Add(v, u, W);
	}
	dfs1(1, 0); dfs2(1, 1);
//	for(int i=1;i<=n;i++)cout<<a[i]<<" ";cout<<endl;
//	for(int i=1;i<=n;i++)cout<<id[i]<<" ";cout<<endl;
	build_tree(1, 1, n);
//	debug(1,1,n);
//	cout<<"#"<<endl;
	for (;;) {
		scanf("%s", opr + 1);
		if (opr[1] == 'M') {
			u = read(); v = read();
			printf("%lld\n", chain_query(u, v));
		}
		if (opr[1] == 'C') {
			if (opr[2] == 'o') {
				u = read(); v = read(); W = read();
				chain_cover(u, v, W);
			}
			if (opr[2] == 'h') {
				u = read(); W = read();
				if (dep[e[u].u] < dep[e[u].v]) swap(e[u].u, e[u].v);
//				cout<<"nmsl"<<e[u].u<<" "<<e[u].v<<endl;
//				cout<<"##"<<num[e[u].u]<<"WWW"<<W<<endl;
//				chain_cover(num[e[u].u], num[e[u].v], W);
				Cover(1, num[e[u].u], num[e[u].u], W);
			}
		}
		if (opr[1] == 'A') {
			u = read(); v = read(); W = read();
			chain_modify(u, v, W);
		}
		if (opr[1] == 'S') break;
//		debug(1,1,n);cout<<endl;
	}
	return;
}

int main() {
//	freopen("input.in","r",stdin);
	solve();
	return 0;
}