10.02 T3 打表找递推式+十进制快速幂 九校联考凉心模拟DAY1T1

  1 #include<iostream>
  2 #include<cstring>
  3 #include<cstdio>
  4 using namespace std;
  5 const long long mod=998244353;
  6 struct matrix{
  7     long long a[7][7];
  8 };
  9 long long chang[7][7]={
 10     {0,0,0,0,0,0,0},
 11     {0,1,1,0,0,0,0},
 12     {0,2,0,1,0,0,0},
 13     {0,6,0,0,1,0,0},
 14     {0,1,0,0,0,1,0},
 15     {0,0,0,0,0,0,1},
 16     {0,-1,0,0,0,0,0},
 17 };
 18 long long fan[7][7]={
 19     {0,0,0,0,0,0,0},
 20     {0,0,0,0,0,0,-1},
 21     {0,1,0,0,0,0,1},
 22     {0,0,1,0,0,0,2},
 23     {0,0,0,1,0,0,6},
 24     {0,0,0,0,1,0,1},
 25     {0,0,0,0,0,1,0},
 26 };
 27 matrix mul(matrix a,matrix b){
 28     matrix c;
 29     memset(c.a,0,sizeof c.a);
 30     for(long long i=1;i<=6;i++){
 31         for(long long j=1;j<=6;j++){
 32             for(long long k=1;k<=6;k++){
 33                 c.a[i][j]+=(a.a[i][k]%mod*b.a[k][j])%mod;
 34                 c.a[i][j]%=mod;    
 35             }
 36         }
 37     }
 38     return c;
 39 }
 40 matrix ksm(matrix a,long long b){
 41     matrix ans;
 42     memset(ans.a,0,sizeof ans.a);
 43     ans.a[1][1]=ans.a[2][2]=ans.a[3][3]=ans.a[4][4]=ans.a[5][5]=ans.a[6][6]=1;
 44     for(;b;b>>=1){
 45     //    cout<<b<<‘\n‘;
 46         if(b&1)ans=mul(ans,a);
 47         a=mul(a,a);
 48     }
 49     return ans;
 50 }
 51 void tiaoshi(matrix ans){
 52         for(long long i=1;i<=6;i++){
 53         for(long long j=1;j<=6;j++)
 54         cout<<ans.a[i][j]<<" ";
 55         cout<<‘\n‘;
 56     }    
 57 }
 58 int main(){
 59     freopen("tromino.in","r",stdin);
 60     freopen("tromino.out","w",stdout);
 61     string n;
 62     cin>>n;
 63     if(n.size()==1&&n[0]<=‘6‘){
 64         if(n=="1")cout<<1;
 65         if(n=="2")cout<<3;
 66         if(n=="3")cout<<10;
 67         if(n=="4")cout<<23;
 68         if(n=="5")cout<<62;
 69         if(n=="6")cout<<170;
 70         return 0;
 71     }
 72     matrix base,ans;
 73     memset(ans.a,0,sizeof ans.a);
 74     memset(base.a,0,sizeof base.a);
 75     for(long long i=1;i<=6;i++)
 76         for(long long j=1;j<=6;j++)
 77             base.a[i][j]=chang[i][j];
 78     ans.a[1][1]=ans.a[2][2]=ans.a[3][3]=ans.a[4][4]=ans.a[5][5]=ans.a[6][6]=1;
 79 //    for(long long i=1;i<=6;i++){
 80 //        for(long long j=1;j<=6;j++)
 81 //        cout<<base.a[i][j]<<" ";
 82 //        cout<<‘\n‘;
 83 //    }    
 84     for(long long i=n.size()-1;i>=0;i--){
 85         long long num=n[i]-‘0‘;
 86     //    tiaoshi(ans);
 87     //    cout<<‘\n‘;
 88     //    cout<<num<<endl;
 89         ans=mul(ans,ksm(base,num));
 90     //    tiaoshi(ans);
 91         base=ksm(base,10);
 92     }
 93     matrix ni;
 94     for(long long i=1;i<=6;i++)
 95         for(long long j=1;j<=6;j++)
 96             ni.a[i][j]=fan[i][j];
 97     for(long long i=1;i<=6;i++){
 98         ans=mul(ans,ni);
 99     }
100     cout<<(mod*3+ans.a[1][1]*170%mod+ans.a[2][1]*62%mod+ans.a[3][1]*23%mod+ans.a[4][1]*10%mod+ans.a[5][1]*3%mod+ans.a[6][1]*1%mod)%mod;
101     return 0;
102 }