解決線性遞推求項(xiàng)
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#include <bits/stdc++.h> #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()) using namespace std; 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;} // headlong 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 系數(shù) 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("%d", &n)){ //printf("%I64d\n",linear_seq::gao(VI{1,5,11,36,95,281,781,2245,6336,18061, 51205},n-1));printf("%d\n",linear_seq::gao(VI{1,2,2,3,3,4,4,4,5,5,5,6},n-1));} }

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