回文自动机（BZOJ2565）

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;

  int p,next[100001][27],cnt[100001],len[100001],fail[100001],last,a[100001],maxl[100001],maxr[100001];
  char st[100001];

  int newnode(int l){
    p++;
    for (int i=1;i<=26;i++) next[p][i]=0;
    cnt[p]=0;
    len[p]=l;
    return(p);
  }

  void init(){
    p=-1;
    newnode(0);
    newnode(-1);
    last=1;
    st[0]=-1;
    fail[0]=1;
  }

  int get_fail(int po,int x,int num){
    while (a[po-len[x]-1]!=num) x=fail[x];
    return(x);
  }

  void add(int po,int c){
    int cur=get_fail(po,last,c);
    if (!next[cur][c]){
      int now=newnode(len[cur]+2);
      fail[now]=next[get_fail(po,fail[cur],c)][c];
      next[cur][c]=now;
    }
    last=next[cur][c];
    cnt[last]++;
  }

  void count(){
    for (int i=p;i>=0;i--) cnt[fail[i]]+=cnt[i];
  }
    
  int main(){      
      scanf("%s",&st);
      int n=strlen(st);
      for (int i=1;i<=n;i++) a[i]=st[i-1]-'a'+1;
      
      init();
      for (int i=1;i<=n;i++) 
      add(i,a[i]),maxl[i]=len[last];
      count();
      
      for (int i=1;i<=n/2;i++){
        int t=a[i];a[i]=a[n-i+1];a[n-i+1]=t;    
    }
      init();
      for (int i=1;i<=n;i++) 
      add(i,a[i]),maxr[n-i+1]=len[last];
      count();
  
    int ans=0;    
      for (int i=1;i<n;i++) ans=max(ans,maxl[i]+maxr[i+1]);
      printf("%d\n",ans);
  }

每个节点表示一个本质不同的回文串（最多n个）。

进行count()后，cnt中存每个本质不同的回文串的出现次数。

------------------------------------------------------------------------

CODECHEF APRIL LUNCHTIME 2015 PALPROB

在fail树上转移palindromness

#include <cstdio>
#include <cstring>
#include <iostream>
#include <map>
#define LL long long
using namespace std;

  map <int,int> mp,mpb;
  int p,tr[110001][27],cnt[110001],len[110001],fail[110001],last,a[110001],maxl[110001],maxr[110001];
  int ans[110001],nd[110001],nxt[110001],des[110001],T,scnt;
  char st[110001];

  void addedge(int x,int y){
      nxt[++scnt]=nd[x];des[scnt]=y;nd[x]=scnt;
  }

  int newnode(int l){
    p++;
    for (int i=1;i<=26;i++) tr[p][i]=0;
    cnt[p]=0;ans[p]=0;
    len[p]=l;
    return(p);
  }

  void init(){
    p=-1;
    newnode(0);newnode(-1);
    last=1;
    st[0]=-1;
    fail[0]=1;
  }

  int get_fail(int po,int x,int num){
    while (a[po-len[x]-1]!=num) x=fail[x];
    return(x);
  }

  void add(int po,int c){
    int cur=get_fail(po,last,c);
    if (tr[cur][c]==0){
      int now=newnode(len[cur]+2);
      fail[now]=tr[get_fail(po,fail[cur],c)][c];
      tr[cur][c]=now;
    }
    last=tr[cur][c];
    cnt[last]++;
  }

  void count(){
    for (int i=p;i>=0;i--) cnt[fail[i]]+=cnt[i];
  }
    
  void dfs(int po){
      if (len[po]>=0){
        int t;
      if (len[po]<=1) t=-1;else t=len[po]/2;
      int p=mp[t];
      if (mpb[t])
        ans[po]=ans[p]+1;else
        ans[po]=1;
    }
    
    mpb[len[po]]=1;mp[len[po]]=po;
    for (int p=nd[po];p!=-1;p=nxt[p])
       dfs(des[p]);
     mpb[len[po]]=0;
  } 
    
  int main(){ 
    freopen("a.in","r",stdin);
  
    scanf("%d",&T);
    while (T--){
      scanf("%s",&st);
      int n=strlen(st);
      for (int i=1;i<=n;i++) a[i]=st[i-1]-'a'+1;
      
      init();
      for (int i=1;i<=n;i++) 
        add(i,a[i]);
      count();    
      
      for (int i=0;i<=p;i++) nd[i]=-1;scnt=0;
      for (int i=0;i<=p;i++) if (i!=1) addedge(fail[i],i);
      
      mp.clear();mpb.clear();
      dfs(1);
      
      LL ret=0;
      for (int i=2;i<=p;i++) ret+=(LL)ans[i]*cnt[i];
      printf("%lld\n",ret);
    }    
  }