[权限题][https://www.lydsy.com/JudgeOnline/status.php?problem_id=4712&jresult=4]
这道动态\(dp\)终于不是独立集/覆盖集了
我们来看看暴力转移
设\(dp_x\)表示把\(x\)子树内部全部切断的最小花费
显然有
\[ dp_x=min(a_x,\sum_{(x,v)\in e}dp_v ) \]
于是我们可以考虑把所有轻儿子的\(dp_v\)存下来
之后就能搞了
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
#define LL long long
#define re register
#define maxn 200005
#define inf 99999999999999
inline int read() {
char c=getchar();int x=0;while(c<'0'||c>'9') c=getchar();
while(c>='0'&&c<='9') x=(x<<3)+(x<<1)+c-48,c=getchar();return x;
}
int n,m,num,__;
struct E{int v,nxt;}e[maxn<<1];
struct mat{LL a[2][2];}d[maxn<<2];
int l[maxn<<2],r[maxn<<2];
int deep[maxn],fa[maxn],pos[maxn],sum[maxn],son[maxn];LL dp[maxn];
int id[maxn],dfn[maxn],top[maxn],bot[maxn],head[maxn],a[maxn];
inline void C(int x,int y) {e[++num].v=y;e[num].nxt=head[x];head[x]=num;}
void dfs1(int x) {
sum[x]=1;int maxx=-1;
for(re int i=head[x];i;i=e[i].nxt) {
if(deep[e[i].v]) continue;
deep[e[i].v]=deep[x]+1;fa[e[i].v]=x;
dfs1(e[i].v);sum[x]+=sum[e[i].v];
if(sum[e[i].v]>maxx) maxx=sum[e[i].v],son[x]=e[i].v;
}
}
int dfs2(int x,int topf) {
top[x]=topf;dfn[x]=++__,id[__]=x;
if(!son[x]) return bot[x]=x;
bot[x]=dfs2(son[x],topf);
for(re int i=head[x];i;i=e[i].nxt) {
if(top[e[i].v]) continue;
dfs2(e[i].v,e[i].v);
}
return bot[x];
}
inline mat operator*(mat a,mat b) {
mat c;
c.a[0][0]=min(a.a[0][0]+b.a[0][0],a.a[0][1]+b.a[1][0]);
c.a[0][1]=min(a.a[0][1]+b.a[1][1],a.a[0][0]+b.a[0][1]);
c.a[1][0]=min(a.a[1][0]+b.a[0][0],a.a[1][1]+b.a[1][0]);
c.a[1][1]=min(a.a[1][1]+b.a[1][1],a.a[1][0]+b.a[0][1]);
return c;
}
inline void pushup(int i) {d[i]=d[i<<1]*d[i<<1|1];}
inline void change(int i,int val) {d[i].a[0][1]=val;while(i) {i>>=1;pushup(i);}}
inline void push(int i,mat val) {d[i]=val;while(i) {i>>=1;pushup(i);}}
void build(int x,int y,int i) {
l[i]=x,r[i]=y;
if(x==y) {
int now=id[x];
for(re int j=head[now];j;j=e[j].nxt) {
if(deep[e[j].v]<deep[now]||son[now]==e[j].v) continue;
dp[now]+=dp[e[j].v];
}
if(son[now]) d[i].a[0][0]=dp[now];else d[i].a[0][0]=inf;
d[i].a[0][1]=a[now];
d[i].a[1][0]=inf,d[i].a[1][1]=0;
if(son[now]) dp[now]+=dp[son[now]];
if(!dp[now]||dp[now]>a[now]) dp[now]=a[now];pos[now]=i;
return;
}
int mid=x+y>>1;
build(mid+1,y,i<<1|1),build(x,mid,i<<1);
pushup(i);
}
mat query(int x,int y,int i) {
if(x<=l[i]&&y>=r[i]) return d[i];
int mid=l[i]+r[i]>>1;
if(y<=mid) return query(x,y,i<<1);
if(x>mid) return query(x,y,i<<1|1);
return query(x,y,i<<1)*query(x,y,i<<1|1);
}
int main() {
n=read();
for(re int i=1;i<=n;i++) a[i]=read();
for(re int x,y,i=1;i<n;i++) x=read(),y=read(),C(x,y),C(y,x);
deep[1]=1,dfs1(1),dfs2(1,1),build(1,n,1);
m=read();int x,y;char opt[2];
while(m--) {
scanf("%s",opt);x=read();
if(opt[0]=='Q') {
mat now=query(dfn[x],dfn[bot[x]],1);
printf("%lld\n",min(now.a[0][0],now.a[0][1]));
}
if(opt[0]=='C') {
y=read();a[x]+=y;
mat pre=query(dfn[top[x]],dfn[bot[x]],1);
change(pos[x],a[x]);
while(1) {
if(top[x]==1) break;
mat now=query(dfn[top[x]],dfn[bot[x]],1);
mat t=d[pos[fa[top[x]]]];
t.a[0][0]-=min(pre.a[0][0],pre.a[0][1]);
t.a[0][0]+=min(now.a[0][0],now.a[0][1]);
x=fa[top[x]];
pre=query(dfn[top[x]],dfn[bot[x]],1);push(pos[x],t);
}
}
}
return 0;
}