Codeforces914E. Palindromes in a Tree

n<=100000的树，每个点上有个字母a-t之一，问有多少这样的链经过每个点：它的某一个排列的字母串起来是回文的。

就是有最多一个字母是奇数个啦。。这样点分算一波即可。。细节较多详见代码

 #include<string.h>
 #include<stdlib.h>
 #include<stdio.h>
 #include<math.h>
 #include<algorithm>
 //#include<queue>
 //#include<iostream>
 using namespace std;

 int n;
 #define maxn 200011
 struct Edge{int to,next;}edge[maxn<<]; int first[maxn],le=,val[maxn]; char s[maxn];
 void in(int x,int y) {Edge &e=edge[le]; e.to=y; e.next=first[x]; first[x]=le++;}
 void insert(int x,int y) {in(x,y); in(y,x);}

 #define maxs 1111111
 int cnt[maxs];

 #define LL long long
 LL ans[maxn]; int size[maxn]; bool die[maxn];
 void getsize(int x,int fa)
 {
     size[x]=;
     for (int i=first[x];i;i=edge[i].next)
     {
         const Edge &e=edge[i]; if (e.to==fa || die[e.to]) continue;
         getsize(e.to,x); size[x]+=size[e.to];
     }
 }

 int getroot(int x,int fa,int tot)
 {
     for (int i=first[x];i;i=edge[i].next)
     {
         const Edge &e=edge[i]; if (e.to==fa || die[e.to]) continue;
         if (size[e.to]*>tot) return getroot(e.to,x,tot);
     }
     return x;
 }

 void dfscnt(int x,int fa,int now,int v)
 {
     now^=<<val[x]; cnt[now]+=v;
     for (int i=first[x];i;i=edge[i].next)
     {
         const Edge &e=edge[i]; if (e.to==fa || die[e.to]) continue;
         dfscnt(e.to,x,now,v);
     }
 }

 LL calc(int x,int fa,int now)
 {
     now^=<<val[x]; LL t=;
     for (int i=;i<;i++) t+=cnt[now^(<<i)];
     t+=cnt[now];
     for (int i=first[x];i;i=edge[i].next)
     {
         const Edge &e=edge[i]; if (e.to==fa || die[e.to]) continue;
         t+=calc(e.to,x,now);
     }
     ans[x]+=t; return t;
 }

 void cd(int x)
 {
     dfscnt(x,,,); die[x]=;
     LL now=;
     for (int i=first[x];i;i=edge[i].next)
     {
         const Edge &e=edge[i]; if (die[e.to]) continue;
         dfscnt(e.to,x,<<val[x],-);
         now+=calc(e.to,x,); //cout<<e.to<<' '<<now<<endl;
         dfscnt(e.to,x,<<val[x],);
     }

     for (int i=;i<;i++) now+=cnt[<<i];
     now+=cnt[]+; ans[x]+=now>>;
     dfscnt(x,,,-);
 //    cout<<x<<endl;
 //    for (int i=1;i<=n;i++) cout<<ans[i]<<' ';cout<<endl;
     for (int i=first[x];i;i=edge[i].next)
     {
         const Edge &e=edge[i]; if (die[e.to]) continue;
         getsize(e.to,); cd(getroot(e.to,,size[e.to]));
     }
 }

 int main()
 {
     scanf("%d",&n);
     for (int i=,x,y;i<n;i++) scanf("%d%d",&x,&y),insert(x,y);
     scanf("%s",s+); for (int i=;i<=n;i++) val[i]=s[i]-'a';
     getsize(,);
     cd(getroot(,,size[]));
     for (int i=;i<=n;i++) printf("%lld ",ans[i]);
     return ;
 }