[dsu on tree] Codeforces #741D. Arpa's letter-marked tree and Mehrdad's Dokhtar-kosh paths

考虑一个字符集，若能排成回文串，则出现个数是奇数的字符种数是0或1。字符有22种，就想到异或。
合法的链 (x,y)(x,y) 满足 s(x) xor s(y)=0或2is(x)\text{ xor }s(y)=0或2^{i}。
直接 dsu on tree 瞎搞。

 #include<cstdio>
#include<vector>
#include<algorithm>
using namespace std;
const int maxn=500005,maxe=500005;
int n,ans[maxn],dfn[maxn],df[maxn],out[maxn],Tim,s[maxn],sz[maxn],dep[maxn],hvy[maxn];
int fir[maxn],nxt[maxe],son[maxe],w[maxe],tot;
int d_max[8388615],res;
void add(int x,int y,int z){son[++tot]=y; w[tot]=z; nxt[tot]=fir[x]; fir[x]=tot;
}
void dfs_info(int x,int pre){dfn[x]=++Tim; df[Tim]=x;sz[x]=1;for(int j=fir[x];j;j=nxt[j]) if(son[j]!=pre){dep[son[j]]=dep[x]+1; s[son[j]]=s[x]^(1<<w[j]);dfs_info(son[j],x); sz[x]+=sz[son[j]]; if(sz[hvy[x]]<sz[son[j]]) hvy[x]=son[j];}out[x]=Tim;
}
void AllClear(int x){res=0; for(int i=dfn[x];i<=out[x];i++) d_max[s[df[i]]]=0;
}
void dfs(int x,int pre){for(int j=fir[x];j;j=nxt[j]) if(son[j]!=pre) if(son[j]!=hvy[x]) dfs(son[j],x), AllClear(son[j]);if(hvy[x]) dfs(hvy[x],x); res=ans[hvy[x]];if(d_max[s[x]]) res=max(res,d_max[s[x]]-dep[x]); for(int i=0;i<=21;i++) if(d_max[s[x]^(1<<i)]) res=max(res,d_max[s[x]^(1<<i)]-dep[x]);d_max[s[x]]=max(d_max[s[x]],dep[x]); for(int j=fir[x];j;j=nxt[j]) if(son[j]!=pre) if(son[j]!=hvy[x]){res=max(res,ans[son[j]]);for(int i=dfn[son[j]];i<=out[son[j]];i++){int y=df[i];if(d_max[s[y]]) res=max(res,d_max[s[y]]+dep[y]-2*dep[x]); for(int i=0;i<=21;i++) if(d_max[s[y]^(1<<i)])res=max(res,d_max[s[y]^(1<<i)]+dep[y]-2*dep[x]); }for(int i=dfn[son[j]];i<=out[son[j]];i++){int y=df[i];d_max[s[y]]=max(d_max[s[y]],dep[y]);}}ans[x]=res;
}
int main(){freopen("cf741D.in","r",stdin);freopen("cf741D.out","w",stdout);scanf("%d",&n);for(int i=2;i<=n;i++){int x; char ch; scanf("%d %c",&x,&ch);add(x,i,ch-'a');}dep[1]=1; dfs_info(1,1);dfs(1,1);for(int i=1;i<=n;i++) printf("%d ",ans[i]);return 0;
}

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[dsu on tree] Codeforces #741D. Arpa's letter-marked tree and Mehrdad's Dokhtar-kosh paths

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