【NOI2016】优秀的拆分

题面

https://www.luogu.org/problem/P1117

题解

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define ll long long
#define N 305000

int log[69500],st[N],en[N];
char ts[N],s[N];

struct SuffixArray {
  int n,m,rank[N],sa[N],tax[N],tp[N],height[N];
  int minh[N][20];
  char s[N];
  void clear() {
    memset(s,0,sizeof(s));
    memset(minh,0,sizeof(minh));
    memset(rank,0,sizeof(rank));
    memset(sa,0,sizeof(sa));
    memset(tax,0,sizeof(tax));
    memset(tp,0,sizeof(tp));
    memset(height,0,sizeof(height));
  }
  void cntsort() {
    for (int i=0;i<=m;i++) tax[i]=0;
    for (int i=1;i<=n;i++) tax[rank[i]]++;
    for (int i=1;i<=m;i++) tax[i]+=tax[i-1];
    for (int i=n;i>=1;i--) sa[tax[rank[tp[i]]]--]=tp[i];
  }
  void suffixsort() {
    m=30;
    for (int i=1;i<=n;i++) rank[i]=s[i]-'a'+1,tp[i]=i;
    cntsort();
    for (int w=1,p=0;p<n;m=p,w<<=1) {
      p=0;
      for (int i=1;i<=w;i++) tp[++p]=n-w+i;
      for (int i=1;i<=n;i++) if (sa[i]>w) tp[++p]=sa[i]-w;
      cntsort();
      swap(tp,rank);
      rank[sa[1]]=p=1;
      for (int i=2;i<=n;i++) 
        rank[sa[i]]=(tp[sa[i-1]]==tp[sa[i]] && tp[sa[i-1]+w]==tp[sa[i]+w]) ? p:++p;
    }
  }
  void getheight() {
    int k=0;
    for (int i=1;i<=n;i++) {
      if (k) k--;
      int j=sa[rank[i]-1];
      while (s[i+k]==s[j+k]) k++;
      height[rank[i]]=k;
    }
  }
  void build() {
    int i,j;
    for (i=1;i<=n;i++) minh[i][0]=height[i];
    for (i=1;i<=16;i++) {
      int len=(1<<(i-1));
      for (j=1;j<=n;j++) minh[j][i]=min(minh[j][i-1],minh[j+len][i-1]);
    }
  }
  int lcp(int x,int y) {
    x=rank[x],y=rank[y];
    if (x>y) swap(x,y);
    if (x==y) return 0;
    int cnt=log[y-x]-1;
    return min(minh[x+1][cnt],minh[y-(1<<cnt)+1][cnt]);
  }
} a,b;

int main(){
  int nx,x;
  log[0]=0;
  log[1]=1;
  x=1;
  for (int i=1;i<=15;i++) {
    nx=(1<<(i+1))-1;
    for (int j=x+1;j<=nx;j++) log[j]=i+1;
    x=nx;
  }
  int T;
  scanf("%d",&T);
  while (T--) {
    memset(st,0,sizeof(st));
    memset(en,0,sizeof(en));
    a.clear(); b.clear();
    scanf("%s",s+1);
    int l=a.n=b.n=strlen(s+1);
    for (int i=1;i<=l;i++) a.s[i]=s[i]; a.s[l+1]='\0';
    for (int i=1;i<=l;i++) b.s[l-i+1]=s[i]; b.s[l+1]='\0';
    a.suffixsort(); a.getheight(); a.build();
    b.suffixsort(); b.getheight(); b.build();
    for (int L=1;L<=l/2;L++) {
      for(int i=L,j=i+L;j<=l;i+=L,j+=L) {
        int x=min(a.lcp(i,j),L),y=min(b.lcp(l-(i-1)+1,l-(j-1)+1),L-1);
        int t=x+y-L+1;
        if(x+y>=L) {
          st[i-y]++; st[i-y+t]--;
          en[j+x-t]++; en[j+x]--;
        }
      }
    }
    for (int i=1;i<=l;i++) st[i]+=st[i-1],en[i]+=en[i-1];
    ll ans=0;
    for (int i=1;i<=l;i++) ans+=en[i]*1LL*st[i+1];
    cout<<ans<<endl;
  }
}