【JZOJ6431】【luoguP5658】【CSP-S2019】括號樹

description

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analysis

• 用棧維護一下樹上路徑未匹配的左括號，然後在樹上找右括號匹配，設$f[i]$爲$i$節點的貢獻，$g[i]$是答案

• 爲左括號可以直接繼承父節點的信息，爲右括號且棧非空則可以匹配，貢獻值是棧頂左括號的父節點的貢獻$+1$

• 這個其實就是當前子序列可以拼上左括號父親的序列，然後每一位的答案就是父節點的答案加上當前點的貢獻

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code

#pragma GCC optimize("O3")
#pragma G++ optimize("O3")
#include<stdio.h>
#include<string.h>
#include<algorithm>
#define MAXN 500005
#define ll long long
#define reg register ll
#define fo(i,a,b) for (reg i=a;i<=b;++i)
#define fd(i,a,b) for (reg i=a;i>=b;--i)
#define rep(i,a) for (reg i=las[a];i;i=nex[i])

using namespace std;

ll las[MAXN],nex[MAXN],tov[MAXN];
ll f[MAXN],g[MAXN],fa[MAXN],stack[MAXN];
char s[MAXN];
ll n,tot,top,ans;

inline ll read()
{
	ll x=0,f=1;char ch=getchar();
	while (ch<'0' || '9'<ch){if (ch=='-')f=-1;ch=getchar();}
	while ('0'<=ch && ch<='9')x=x*10+ch-'0',ch=getchar();
	return x*f;
}
inline void link(ll x,ll y){nex[++tot]=las[x],las[x]=tot,tov[tot]=y;}
inline void dfs(ll x)
{
	ll tmp=0;
	if (s[x]=='(')stack[++top]=x;
	else if (top)tmp=stack[top],f[x]=f[fa[tmp]]+1,--top;
	g[x]=g[fa[x]]+f[x],ans^=x*g[x];
	rep(i,x)dfs(tov[i]);
	if (tmp)stack[++top]=tmp;
	else if (top)--top;
}
int main()
{
	n=read(),scanf("%s",s+1);
	fo(i,2,n)link(fa[i]=read(),i);
	dfs(1),printf("%lld\n",ans);
	return 0;
}