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<<1]; int first[maxn],le=2,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]=1;
    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]*2>tot) return getroot(e.to,x,tot);
    }
    return x;
}

void dfscnt(int x,int fa,int now,int v)
{
    now^=1<<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^=1<<val[x]; LL t=0;
    for (int i=0;i<20;i++) t+=cnt[now^(1<<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,0,0,1); die[x]=1;
    LL now=0;
    for (int i=first[x];i;i=edge[i].next)
    {
        const Edge &e=edge[i]; if (die[e.to]) continue;
        dfscnt(e.to,x,1<<val[x],-1);
        now+=calc(e.to,x,0); //cout<<e.to<<' '<<now<<endl;
        dfscnt(e.to,x,1<<val[x],1);
    }
    
    for (int i=0;i<20;i++) now+=cnt[1<<i];
    now+=cnt[0]+1; ans[x]+=now>>1;
    dfscnt(x,0,0,-1);
//    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,0); cd(getroot(e.to,0,size[e.to]));
    }
}

int main()
{
    scanf("%d",&n);
    for (int i=1,x,y;i<n;i++) scanf("%d%d",&x,&y),insert(x,y);
    scanf("%s",s+1); for (int i=1;i<=n;i++) val[i]=s[i]-'a';
    getsize(1,0);
    cd(getroot(1,0,size[1]));
    for (int i=1;i<=n;i++) printf("%lld ",ans[i]);
    return 0;
}