BM Du teach recursive version

#include <bits/stdc++.h>

using namespace std;
#define rep(i,a,n) for (long long i=a;i<n;i++)
#define per(i,a,n) for (long long i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((long long)(x).size())
typedef vector<long long> VI;
typedef long long ll;
typedef pair<long long,long long> PII;
const ll mod=1e9+7;
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
// head

long long _,n;
namespace linear_seq
{
    const long long N=10010;
    ll res[N],base[N],_c[N],_md[N];

    vector<long long> Md;
    void mul(ll *a,ll *b,long long k)
    {
        rep(i,0,k+k) _c[i]=0;
        rep(i,0,k) if (a[i]) rep(j,0,k)
            _c[i+j]=(_c[i+j]+a[i]*b[j])%mod;
        for (long long i=k+k-1;i>=k;i--) if (_c[i])
            rep(j,0,SZ(Md)) _c[i-k+Md[j]]=(_c[i-k+Md[j]]-_c[i]*_md[Md[j]])%mod;
        rep(i,0,k) a[i]=_c[i];
    }
    long long solve(ll n,VI a,VI b)
    { // a 系数 b 初值 b[n+1]=a[0]*b[n]+...
//        printf("%d\n",SZ(b));
        ll ans=0,pnt=0;
        long long k=SZ(a);
        assert(SZ(a)==SZ(b));
        rep(i,0,k) _md[k-1-i]=-a[i];_md[k]=1;
        Md.clear();
        rep(i,0,k) if (_md[i]!=0) Md.push_back(i);
        rep(i,0,k) res[i]=base[i]=0;
        res[0]=1;
        while ((1ll<<pnt)<=n) pnt++;
        for (long long p=pnt;p>=0;p--)
        {
            mul(res,res,k);
            if ((n>>p)&1)
            {
                for (long long i=k-1;i>=0;i--) res[i+1]=res[i];res[0]=0;
                rep(j,0,SZ(Md)) res[Md[j]]=(res[Md[j]]-res[k]*_md[Md[j]])%mod;
            } 
        } 
        Receives (and 0 , k) = years (years + nothing [i] * b [i])% mod;
        f (years < 0 ) ans = + mod;
        return years; 
    } 
    VI BM (VI s) 
    { 
        VI C ( 1 , 1 ), B ( 1 , 1 );
        long  length L = 0 , m = 1 , b = 1 ; 
        receives (n, 0 , SZ (s)) 
        { 
            ll d = 0 ; 
            receives (and 0,L+1) d=(d+(ll)C[i]*s[n-i])%mod;
            if (d==0) ++m;
            else if (2*L<=n)
            {
                VI T=C;
                ll c=mod-d*powmod(b,mod-2)%mod;
                while (SZ(C)<SZ(B)+m) C.pb(0);
                rep(i,0,SZ(B)) C[i+m]=(C[i+m]+c*B[i])%mod;
                L=n+1-L; B=T; b=d; m=1;
            }
            else
            {
                ll c=mod-d*powmod(b,mod-2)%mod;
                while (SZ(C)<SZ(B)+m) C.pb(0);
                rep(i,0,SZ(B)) C[i+m]=(C[i+m]+c*B[i])%mod;
                ++m;
            }
        }
        return C;
    }
    long long gao(VI a,ll n)
    {
        VI c=BM(a);
        c.erase(c.begin());
        rep(i,0,SZ(c)) c[i]=(mod-c[i])%mod;
        return solve(n,c,VI(a.begin(),a.begin()+SZ (C))); 
    } 
}; 

int main () 
{ 
    the while (~ Scanf ( " % I64d " , & n)) 
    { 
        / * find the n-th item * / 
        the printf ( " % I64d \ n " , linear_seq :: Gao ({Vl . 1 , . 5 , . 11 , 36 , 95 , 281 is , 781 , 2245 , 6336 , 18061 , 51205 }, N- . 1 )); 

        / * output coefficients * / 
        / * first k entries recursion need 2 * k items can be determined*/
        VI res = linear_seq::BM(VI{1,5,11,36,95,281,781,2245,6336,18061, 51205});
        for(int i = 1;i < res.size();i++)  printf("%lld\n", (mod-res[i]) % mod);

        //f(n) = f(n-1) + 5*f(n-2) + f(n-3) - f(n-4)
    }
}

 

Several board test data:

Input 1
1 2 4 9 20 40 90

Output 1

0 10 0

Input 2 
2 4 8 16 32 64 128 256 512 2 4 8 16 32 64 128 256 512

Output 2 
0 0 0 0 0 0 0 1

 

 

Code From:

https://blog.csdn.net/qq_36876305/article/details/80275708

https://blog.csdn.net/running_acmer/article/details/82722111

Data From:

https://www.cnblogs.com/zhouzhendong/p/Berlekamp-Massey.html