BM递推杜教版

Posted 2022-11-01 lfri

#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;
            
        
        rep(i,0,k) ans=(ans+res[i]*b[i])%mod;
        if (ans<0) ans+=mod;
        return ans;
    
    VI BM(VI s)
    
        VI C(1,1),B(1,1);
        long long L=0,m=1,b=1;
        rep(n,0,SZ(s))
        
            ll d=0;
            rep(i,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()

    while(~scanf("%I64d", &n))
    
        /*求第n项*/
        printf("%I64d\\n",linear_seq::gao(VI1,5,11,36,95,281,781,2245,6336,18061, 51205,n-1));

        /*输出系数*/
        /*前k项递推，需要2*k项能确定*/
        VI res = linear_seq::BM(VI1,5,11,36,95,281,781,2245,6336,18061, 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)
    

 

几个测试板子的数据：

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