【题解】Luogu P5290 [十二省联考2019]春节十二响

原题传送门

每个点维护一个堆，表示这个点及其子树所需的每段内存的空间

搜索时从下向上做启发式合并堆中信息，最后根节点堆中所有内存空间之和就是答案

#include <bits/stdc++.h>
#define N 200005
#define ll long long
#define getchar nc
using namespace std;
inline char nc(){
    static char buf[100000],*p1=buf,*p2=buf;
    return p1==p2&&(p2=(p1=buf)+fread(buf,1,100000,stdin),p1==p2)?EOF:*p1++;
}
inline int read()
{
    register int x=0,f=1;register char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
    return x*f;
}
inline void write(register ll x)
{
    if(!x)putchar('0');if(x<0)x=-x,putchar('-');
    static int sta[20];register int tot=0;
    while(x)sta[tot++]=x%10,x/=10;
    while(tot)putchar(sta[--tot]+48);
}
inline int Max(register int a,register int b)
{
	return a>b?a:b;
}
struct node{
	int to,next;
}e[N<<1];
int head[N],cnt;
inline void add(register int u,register int v)
{
	e[++cnt]=(node){v,head[u]};
	head[u]=cnt;
}
int n,a[N],dfn[N],tim=0,tmp[N];
priority_queue <int> q[N];
ll ans=0;
inline void dfs(register int x)
{
	dfn[x]=++tim;
	for(register int i=head[x];i;i=e[i].next)
	{
		int v=e[i].to;
		if(dfn[v])
			continue;
		dfs(v);
		if(q[dfn[x]].size()<q[dfn[v]].size())
			dfn[x]^=dfn[v]^=dfn[x]^=dfn[v];
		int m=q[dfn[v]].size();
		for(register int i=1;i<=m;++i)
		{
			tmp[i]=Max(q[dfn[x]].top(),q[dfn[v]].top());
			q[dfn[x]].pop(),q[dfn[v]].pop();
		}
		for(register int i=1;i<=m;++i)
			q[dfn[x]].push(tmp[i]);
	}
	q[dfn[x]].push(a[x]);
}
int main()
{
	n=read();
	for(register int i=1;i<=n;++i)
		a[i]=read();
	for(register int i=2;i<=n;++i)
	{
		int fa=read();
		add(fa,i),add(i,fa);
	}
	dfs(1);
	while(!q[dfn[1]].empty())
	{
		ans+=1ll*q[dfn[1]].top();
		q[dfn[1]].pop();
	}
	write(ans);
	return 0;
}