题解 黑白树
神仙题，并且我有理由怀疑是新一代 lxl 搞的
- LCT 不支持子树加！
发现 LCT 能且仅能维护出这个连通块，但无法维护和修改相关的任何信息
那么考虑不用 LCT
直接放题解神仙思路好了
将每个同色连通块中深度最浅的点称作 管辖点
那么每次对同色连通块的修改对应的是这个连通块管辖点 dfs 序中的几个子区间
那么考虑魔改线段树
对每个线段树节点维护出它在哪些异色点的子树中
这个数量级比较大，可以用一个类似标记永久化的东西
只在每个恰好被包含的地方的 set 插入，取的时候从根下来带着一个值走就行了
那么可以对每个线段树节点维护出它到根的链上的异色点个数，记为 cnt
发现能 pushup/spread 的条件是子区间的 cnt 等于当前节点的 cnt
发现修改时能向下递归的条件是若查出管辖点的 cnt，记为 lim
那么向下递归的条件是子区间的 cnt \(\leqslant\) lim
查询同理
那么找管辖点可以利用线段树 set 查出到根节点路径上深度最深的异色点
向下找一个儿子就可以了
剩下的操作可以直接树剖，线段树上要再维护一个无条件下传的标记
完全没必要对每种颜色单独开一棵线段树，全放在一棵线段树中反色操作会方便很多
不考虑其它操作，仅线段树+反色的复杂度是 \(O(n\log^2 n)\)，复杂度瓶颈在于线段树+set
其实加上其他操作复杂度也还是 \(O(n\log^2 n)\)
点击查看代码
#include <bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define N 200010
#define fir first
#define sec second
#define ll long long
#define int long long
char buf[1<<21], *p1=buf, *p2=buf;
#define getchar() (p1==p2&&(p2=(p1=buf)+fread(buf, 1, 1<<21, stdin)), p1==p2?EOF:*p1++)
inline int read() {
int ans=0, f=1; char c=getchar();
while (!isdigit(c)) {if (c=='-') f=-f; c=getchar();}
while (isdigit(c)) {ans=(ans<<3)+(ans<<1)+(c^48); c=getchar();}
return ans*f;
}
int n, m;
ll val[N];
int head[N], col[N], deg[N], ecnt, endpos;
struct edge{int to, next;}e[N<<1];
inline void add(int s, int t) {e[++ecnt]={t, head[s]}; head[s]=ecnt;}
namespace force{
int back[N], dep[N], sta[N], top;
void dfs(int u, int fa) {
for (int i=head[u],v; ~i; i=e[i].next) {
v = e[i].to;
if (v==fa) continue;
dep[v]=dep[u]+1;
back[v]=u;
dfs(v, u);
}
}
void get_block(int u, int fa) {
sta[++top]=u;
for (int i=head[u]; ~i; i=e[i].next) if (e[i].to!=fa && col[e[i].to]==col[u])
get_block(e[i].to, u);
}
void add(int u, int fa, int t) {
val[u]+=t;
for (int i=head[u]; ~i; i=e[i].next)
if (e[i].to!=fa) add(e[i].to, u, t);
}
void solve() {
ll ans;
dfs(1, 0);
for (int i=1,op,u,x,y,z; i<=m; ++i) {
op=read();
if (op==1) col[read()]^=1;
else if (op==2) {
x=read(); y=read(); top=0;
get_block(x, 0);
for (int j=1; j<=top; ++j) val[sta[j]]+=y;
}
else if (op==3) {
x=read(); ans=top=0;
get_block(x, 0);
for (int j=1; j<=top; ++j) ans=max(ans, val[sta[j]]);
printf("%lld\n", ans);
}
else if (op==4) {
x=read(); y=read(); z=read();
while (1) {
if (dep[x]<dep[y]) swap(x, y);
val[x]+=z;
if (x==y) break;
x=back[x];
}
}
else {
x=read(); y=read();
add(x, back[x], y);
}
}
}
}
namespace task1{
int bit[N], id[N], rk[N], tot;
inline void upd(int i, int dat) {for (; i<=n; i+=i&-i) bit[i]+=dat;}
inline int query(int i) {int ans=0; for (; i; i-=i&-i) ans+=bit[i]; return ans;}
int tl[N<<2], tr[N<<2]; ll mx[N<<2], tag[N<<2];
#define tl(p) tl[p]
#define tr(p) tr[p]
#define mx(p) mx[p]
#define tag(p) tag[p]
#define pushup(p) mx(p)=max(mx(p<<1), mx(p<<1|1))
void spread(int p) {
if (!tag(p)) return ;
mx(p<<1)+=tag(p); tag(p<<1)+=tag(p);
mx(p<<1|1)+=tag(p); tag(p<<1|1)+=tag(p);
tag(p)=0;
}
void build(int p, int l, int r) {
tl(p)=l; tr(p)=r;
if (l==r) {mx(p)=val[rk[l]]; return ;}
int mid=(l+r)>>1;
build(p<<1, l, mid);
build(p<<1|1, mid+1, r);
pushup(p);
}
void upd(int p, int l, int r, int dat) {
if (l<=tl(p)&&r>=tr(p)) {mx(p)+=dat; tag(p)+=dat; return ;}
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (l<=mid) upd(p<<1, l, r, dat);
if (r>mid) upd(p<<1|1, l, r, dat);
pushup(p);
}
ll query(int p, int l, int r) {
if (l<=tl(p)&&r>=tr(p)) return mx(p);
spread(p);
int mid=(tl(p)+tr(p))>>1; ll ans=0;
if (l<=mid) ans=max(ans, query(p<<1, l, r));
if (r>mid) ans=max(ans, query(p<<1|1, l, r));
return ans;
}
pair<int, int> get_block(int x) {
pair<int, int> ans;
if (col[x]) {
x=id[x];
int l, r, mid;
l=x; r=n;
while (l<=r) {
mid=(l+r)>>1;
if (query(mid)-query(x)==mid-x) l=mid+1;
else r=mid-1;
}
ans.sec=l-1;
l=1, r=x;
while (l<=r) {
mid=(l+r)>>1;
if (query(x)-query(mid-1)==x-mid+1) r=mid-1;
else l=mid+1;
}
ans.fir=r+1;
}
else {
x=id[x];
int l, r, mid;
l=x; r=n;
while (l<=r) {
mid=(l+r)>>1;
if (query(mid)-query(x)==0) l=mid+1;
else r=mid-1;
}
ans.sec=l-1;
l=1, r=x;
while (l<=r) {
mid=(l+r)>>1;
if (query(x)-query(mid-1)==0) r=mid-1;
else l=mid+1;
}
ans.fir=r+1;
}
return ans;
}
void dfs(int u, int fa) {
rk[id[u]=++tot]=u;
for (int i=head[u]; ~i; i=e[i].next)
if (e[i].to!=fa) dfs(e[i].to, u);
}
void solve() {
ll ans;
dfs(endpos, 0);
build(1, 1, n);
for (int i=1; i<=n; ++i) if (col[i]) upd(id[i], 1);
// cout<<"id: "; for (int i=1; i<=n; ++i) cout<<id[i]<<' '; cout<<endl;
for (int i=1,op,u,x,y,z; i<=m; ++i) {
op=read();
if (op==1) {
x=read();
if (col[x]) upd(id[x], -1);
else upd(id[x], 1);
col[x]^=1;
}
else if (op==2) {
x=read(); y=read();
pair<int, int> range=get_block(x);
upd(1, range.fir, range.sec, y);
}
else if (op==3) {
x=read(); ans=0;
pair<int, int> range=get_block(x);
printf("%lld\n", query(1, range.fir, range.sec));
}
else if (op==4) {
x=read(); y=read(); z=read();
if (id[x]>id[y]) swap(x, y);
upd(1, id[x], id[y], z);
}
else {
x=read(); y=read();
if (x==1) upd(1, 1, n, y);
else if (id[x]>id[1]) upd(1, id[x], n, y);
else upd(1, 1, id[x], y);
}
}
}
}
namespace task2{
int back[N], dep[N], sta[N], top[N], rk[N], stop;
int id[N], siz[N], msiz[N], mson[N], tot;
int tl[N<<2], tr[N<<2]; ll mx[N<<2], tag[N<<2];
#define tl(p) tl[p]
#define tr(p) tr[p]
#define mx(p) mx[p]
#define tag(p) tag[p]
#define pushup(p) mx(p)=max(mx(p<<1), mx(p<<1|1))
void spread(int p) {
if (!tag(p)) return ;
mx(p<<1)+=tag(p); tag(p<<1)+=tag(p);
mx(p<<1|1)+=tag(p); tag(p<<1|1)+=tag(p);
tag(p)=0;
}
void build(int p, int l, int r) {
tl(p)=l; tr(p)=r;
if (l==r) {mx(p)=val[rk[l]]; return ;}
int mid=(l+r)>>1;
build(p<<1, l, mid);
build(p<<1|1, mid+1, r);
pushup(p);
}
void upd(int p, int l, int r, int dat) {
if (l<=tl(p)&&r>=tr(p)) {mx(p)+=dat; tag(p)+=dat; return ;}
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (l<=mid) upd(p<<1, l, r, dat);
if (r>mid) upd(p<<1|1, l, r, dat);
pushup(p);
}
ll query(int p, int l, int r) {
if (l<=tl(p)&&r>=tr(p)) return mx(p);
spread(p);
int mid=(tl(p)+tr(p))>>1; ll ans=0;
if (l<=mid) ans=max(ans, query(p<<1, l, r));
if (r>mid) ans=max(ans, query(p<<1|1, l, r));
return ans;
}
void dfs1(int u, int fa) {
siz[u]=1;
for (int i=head[u],v; ~i; i=e[i].next) {
v = e[i].to;
if (v==fa) continue;
dep[v]=dep[u]+1;
back[v]=u;
dfs1(v, u);
siz[u]+=siz[v];
if (siz[v]>msiz[u]) msiz[u]=siz[v], mson[u]=v;
}
}
void dfs2(int u, int fa, int t) {
top[u]=t;
rk[id[u]=++tot]=u;
if (!mson[u]) return ;
dfs2(mson[u], u, t);
for (int i=head[u],v; ~i; i=e[i].next) {
v = e[i].to;
if (v==fa||v==mson[u]) continue;
dfs2(v, u, v);
}
}
void get_block(int u, int fa) {
sta[++stop]=u;
for (int i=head[u]; ~i; i=e[i].next) if (e[i].to!=fa && col[e[i].to]==col[u])
get_block(e[i].to, u);
}
void upd(int u, int v, int dat) {
while (top[u]!=top[v]) {
if (dep[top[u]]<dep[top[v]]) swap(u, v);
upd(1, id[top[u]], id[u], dat);
u=back[top[u]];
}
if (dep[u]>dep[v]) swap(u, v);
upd(1, id[u], id[v], dat);
}
void solve() {
ll ans;
dfs1(1, 0); dfs2(1, 0, 1); build(1, 1, n);
for (int i=1,op,u,x,y,z; i<=m; ++i) {
op=read();
if (op==1) col[read()]^=1;
else if (op==2) {
x=read(); y=read(); stop=0;
get_block(x, 0);
for (int j=1; j<=stop; ++j) upd(1, id[sta[j]], id[sta[j]], y);
}
else if (op==3) {
x=read(); ans=stop=0;
get_block(x, 0);
for (int j=1; j<=stop; ++j) ans=max(ans, query(1, id[sta[j]], id[sta[j]]));
printf("%lld\n", ans);
}
else if (op==4) {
x=read(); y=read(); z=read();
upd(x, y, z);
}
else {
x=read(); y=read();
upd(1, id[x], id[x]+siz[x]-1, y);
}
}
}
}
namespace task{
bool vis[N];
int id[N], siz[N], msiz[N], mson[N], tot;
int back[N], dep[N], sta[N], top[N], rk[N], tval[N], stop;
struct seg{
bool inuse[N<<2];
set<pair<int, int>> st[N<<2];
int tl[N<<2], tr[N<<2], cnt[N<<2];
ll mx[N<<2], stag[N<<2], btag[N<<2], tag[N<<2];
#define tl(p) tl[p]
#define tr(p) tr[p]
#define mx(p) mx[p]
#define st(p) st[p]
#define cnt(p) cnt[p]
#define tag(p) tag[p]
#define stag(p) stag[p]
#define btag(p) btag[p]
#define inuse(p) inuse[p]
#undef pushup
void pushup(int p) {
mx(p)=0;
if (cnt(p<<1)==cnt(p)) mx(p)=max(mx(p), mx(p<<1));
if (cnt(p<<1|1)==cnt(p)) mx(p)=max(mx(p), mx(p<<1|1));
}
void spread(int p) {
// cout<<"spread: "<<p<<endl;
if (stag(p)) {
cnt(p<<1)+=stag(p); stag(p<<1)+=stag(p);
cnt(p<<1|1)+=stag(p); stag(p<<1|1)+=stag(p);
stag(p)=0;
}
if (btag(p)) {
// cout<<cnt(p<<1|1)<<' '<<cnt(p)<<endl;
if (cnt(p<<1)==cnt(p)) mx(p<<1)+=btag(p), btag(p<<1)+=btag(p);
if (cnt(p<<1|1)==cnt(p)) mx(p<<1|1)+=btag(p), btag(p<<1|1)+=btag(p);
btag(p)=0;
}
if (tag(p)) {
if (inuse(p<<1)) mx(p<<1)+=tag(p), tag(p<<1)+=tag(p);
if (inuse(p<<1|1)) mx(p<<1|1)+=tag(p), tag(p<<1|1)+=tag(p);
tag(p)=0;
}
}
void build(int p, int l, int r) {
tl(p)=l; tr(p)=r; inuse(p)=1;
if (l==r) {mx(p)=tval[rk[l]]; inuse(p)=vis[rk[l]]; return ;}
int mid=(l+r)>>1;
build(p<<1, l, mid);
build(p<<1|1, mid+1, r);
pushup(p);
}
void upd(int p, int l, int r, int dat) {
if (l<=tl(p)&&r>=tr(p)) {mx(p)+=dat; tag(p)+=dat; return ;}
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (l<=mid) upd(p<<1, l, r, dat);
if (r>mid) upd(p<<1|1, l, r, dat);
pushup(p);
}
void bupd(int p, int l, int r, int dat, int lim) {
if (l<=tl(p)&&r>=tr(p)) {mx(p)+=dat; btag(p)+=dat; return ;}
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (l<=mid&&cnt(p<<1)<=lim) bupd(p<<1, l, r, dat, lim);
if (r>mid&&cnt(p<<1|1)<=lim) bupd(p<<1|1, l, r, dat, lim);
pushup(p);
}
void cover(int p, int l, int r, pair<int, int> dat) {
if (l<=tl(p)&&r>=tr(p)) {st[p].insert(dat); ++cnt(p); ++stag(p); return ;}
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (l<=mid) cover(p<<1, l, r, dat);
if (r>mid) cover(p<<1|1, l, r, dat);
pushup(p);
}
void uncover(int p, int l, int r, pair<int, int> dat) {
if (l<=tl(p)&&r>=tr(p)) {st[p].erase(dat); --cnt(p); --stag(p); return ;}
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (l<=mid) uncover(p<<1, l, r, dat);
if (r>mid) uncover(p<<1|1, l, r, dat);
pushup(p);
}
int qtop(int p, int pos, pair<int, int> dat) {
if (st[p].size() && st[p].rbegin()->fir>dat.fir) dat=*st[p].rbegin();
if (tl(p)==tr(p)) return dat.sec;
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (pos<=mid) return qtop(p<<1, pos, dat);
else return qtop(p<<1|1, pos, dat);
}
int qcnt(int p, int pos) {
if (tl(p)==tr(p)) return cnt(p);
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (pos<=mid) return qcnt(p<<1, pos);
else return qcnt(p<<1|1, pos);
}
ll query(int p, int l, int r, int lim) {
if (l<=tl(p)&&r>=tr(p)) return mx(p);
spread(p);
int mid=(tl(p)+tr(p))>>1; ll ans=0;
if (l<=mid&&cnt(p<<1)<=lim) ans=max(ans, query(p<<1, l, r, lim));
if (r>mid&&cnt(p<<1|1)<=lim) ans=max(ans, query(p<<1|1, l, r, lim));
return ans;
}
ll reset(int p, int pos) {
if (tl(p)==tr(p)) {int ans=mx(p); mx(p)=0; inuse(p)=0; return ans;}
spread(p);
int mid=(tl(p)+tr(p))>>1, ans;
if (pos<=mid) ans=reset(p<<1, pos);
else ans=reset(p<<1|1, pos);
pushup(p);
return ans;
}
void setup(int p, int pos, int val) {
if (tl(p)==tr(p)) {mx(p)=val; inuse(p)=1; return ;}
spread(p);
int mid=(tl(p)+tr(p))>>1;
if (pos<=mid) setup(p<<1, pos, val);
else setup(p<<1|1, pos, val);
pushup(p);
}
void show(int p) {
cout<<setw(2)<<p<<" ["<<tl(p)<<','<<tr(p)<<"]: "<<"cnt("<<cnt(p)<<"), mx("<<mx(p)<<")"<<endl;
if (tl(p)==tr(p)) return ;
spread(p);
show(p<<1); show(p<<1|1);
}
}seg[2];
void dfs1(int u, int fa) {
siz[u]=1;
for (int i=head[u],v; ~i; i=e[i].next) {
v = e[i].to;
if (v==fa) continue;
dep[v]=dep[u]+1;
back[v]=u;
dfs1(v, u);
siz[u]+=siz[v];
if (siz[v]>msiz[u]) msiz[u]=siz[v], mson[u]=v;
}
}
void dfs2(int u, int fa, int t) {
top[u]=t;
rk[id[u]=++tot]=u;
if (!mson[u]) return ;
dfs2(mson[u], u, t);
for (int i=head[u],v; ~i; i=e[i].next) {
v = e[i].to;
if (v==fa||v==mson[u]) continue;
dfs2(v, u, v);
}
}
void upd(int u, int v, int dat) {
while (top[u]!=top[v]) {
if (dep[top[u]]<dep[top[v]]) swap(u, v);
seg[0].upd(1, id[top[u]], id[u], dat);
seg[1].upd(1, id[top[u]], id[u], dat);
u=back[top[u]];
}
if (dep[u]>dep[v]) swap(u, v);
seg[0].upd(1, id[u], id[v], dat);
seg[1].upd(1, id[u], id[v], dat);
}
int anc(int u, int v) {
while (top[u]!=top[v]) {
if (back[top[v]]==u) return top[v];
// cout<<"v: "<<v<<' '<<top[v]<<endl;
v=back[top[v]];
}
return rk[id[u]+1];
}
void solve() {
ll ans;
dep[1]=1; dfs1(1, 0); dfs2(1, 0, 1);
for (int i=1; i<=n; ++i) {tval[i]=!col[i]?val[i]:0; vis[i]=!col[i]?1:0;} seg[0].build(1, 1, n);
for (int i=1; i<=n; ++i) {tval[i]=col[i]?val[i]:0; vis[i]=col[i]?1:0;} seg[1].build(1, 1, n);
for (int i=1; i<=n; ++i) seg[col[i]^1].cover(1, id[i], id[i]+siz[i]-1, {dep[i], i});
// for (int i=1; i<=n; ++i) cout<<seg[col[i]].qtop(1, id[i], {0, 1})<<' '; cout<<endl;
// for (int i=1; i<=n; ++i) cout<<qcnt(1, id[i])<<endl;
// cout<<"id: "; for (int i=1; i<=n; ++i) cout<<id[i]<<' '; cout<<endl;
// seg[0].show(1);
// seg[0].bupd(1, id[3], id[3]+siz[3]-1, 2, 3); //, cout<<id[3]<<' '<<id[3]+siz[3]-1<<endl;
// cout<<seg[0].query(1, id[2], id[2]+siz[2]-1)<<endl;
for (int i=1,op,u,x,y,z,top; i<=m; ++i) {
// cout<<"i: "<<i<<endl;
op=read();
if (op==1) {
x=read();
y=seg[col[x]].reset(1, id[x]);
seg[col[x]^1].uncover(1, id[x], id[x]+siz[x]-1, {dep[x], x});
col[x]^=1;
seg[col[x]^1].cover(1, id[x], id[x]+siz[x]-1, {dep[x], x});
seg[col[x]].setup(1, id[x], y);
}
else if (op==2) {
x=read(); y=read();
// cout<<"qtop: "<<seg[col[x]].qtop(1, id[x], {0, 0})<<endl;
top=anc(seg[col[x]].qtop(1, id[x], {0, 0}), x);
// cout<<"top: "<<top<<endl;
seg[col[x]].bupd(1, id[top], id[top]+siz[top]-1, y, seg[col[x]].qcnt(1, id[top]));
}
else if (op==3) {
x=read();
// cout<<"qtop: "<<seg[col[x]].qtop(1, id[x], {0, 0})<<endl;
top=anc(seg[col[x]].qtop(1, id[x], {0, 0}), x);
// cout<<"top: "<<top<<endl;
// cout<<"cnt: "<<seg[col[x]].qcnt(1, id[top])<<endl;
printf("%lld\n", seg[col[x]].query(1, id[top], id[top]+siz[top]-1, seg[col[x]].qcnt(1, id[top])));
}
else if (op==4) {
x=read(); y=read(); z=read();
upd(x, y, z);
}
else {
x=read(); y=read();
seg[0].upd(1, id[x], id[x]+siz[x]-1, y);
seg[1].upd(1, id[x], id[x]+siz[x]-1, y);
}
}
}
}
signed main()
{
freopen("astill.in", "r", stdin);
freopen("astill.out", "w", stdout);
n=read(); m=read();
memset(head, -1, sizeof(head));
bool is_chain=1;
for (int i=1,u,v; i<n; ++i) {
u=read(); v=read();
add(u, v); add(v, u);
++deg[u]; ++deg[v];
}
for (int i=1; i<=n; ++i) col[i]=read();
for (int i=1; i<=n; ++i) val[i]=read();
for (int i=1; i<=n; ++i)
if (deg[i]<=1) endpos=i;
else if (deg[i]>2) is_chain=0;
// if (n<=1000&&m<=1000) force::solve();
// else if (is_chain) task1::solve();
// else task2::solve();
task::solve();
return 0;
}
