【HNOI2008】GT考试

题面
https://www.luogu.org/problem/P3193

题解

// luogu-judger-enable-o2
#include<cstdio>
#include<iostream>
#include<cstring>
#define ri register int
#define N 50
#define LL long long 
using namespace std;
int nex[N],n,m,K;
char s[N];

struct matrix{
  int v[N][N];
  matrix operator * (const matrix &rhs) const {
    matrix ret;
    ret.clear();
    for (ri k=0;k<m;k++) 
      for (ri i=0;i<m;i++)
        for (ri j=0;j<m;j++) (ret.v[i][j]+=v[i][k]*rhs.v[k][j])%=K;
    return ret;
  }
  void clear() {
    memset(v,0,sizeof(v));
  }
} mat;

int main(){
  scanf("%d %d %d",&n,&m,&K);
  scanf("%s",s+1);
  nex[0]=nex[1]=0;
  for (ri i=2;i<=m;i++) {
    int j=nex[i-1];
    while (j && s[j+1]!=s[i]) j=nex[j];
    if (s[j+1]==s[i]) j++;
    nex[i]=j;
  }
  mat.clear();
  for (ri i=0;i<m;i++) {
    for (ri c='0';c<='9';c++) {
      int j=i;
      while (j && s[j+1]!=c) j=nex[j];
      if (s[j+1]==c) j++;
      mat.v[i][j]++;
    }
  }

  matrix fac; fac.clear();
  for (ri i=0;i<m;i++) fac.v[i][i]=1;
  for (;n;n>>=1,mat=mat*mat) if (n&1) fac=fac*mat;
  //for (ri i=1;i<=n;i++) fac=fac*mat;
  int ans=0;
  for (ri i=0;i<m;i++) (ans+=fac.v[0][i])%=K;
  cout<<ans<<endl;
}