[斐波那契 數學技巧] 洛谷 P1306 斐波那契公約數
阿新 • • 發佈:2019-01-27
gcd(fib[n],fib[m])==fib[gcd(n,m)];
#include<cstdio> #include<cstdlib> #include<algorithm> using namespace std; typedef long long ll; namespace F{ struct Matrix{ ll a,b,c,d; Matrix(ll a=0,ll b=0,ll c=0,ll d=0):a(a),b(b),c(c),d(d) { } }; inline Matrix Mul(Matrix A,Matrix B,ll p){ return Matrix((A.a*B.a+A.b*B.c)%p,(A.a*B.b+A.b*B.d)%p,(A.c*B.a+A.d*B.c)%p,(A.c*B.b+A.d*B.d)%p); } inline Matrix Pow(Matrix a,ll b,ll p){ Matrix ret(1,0,0,1); for (;b;b>>=1,a=Mul(a,a,p)) if (b&1) ret=Mul(ret,a,p); return ret; } inline ll f(ll n,ll p){ if (!n) return 0; return Pow(Matrix(1,1,1,0),n-1,p).a; } } int main(){ int n,m; freopen("t.in","r",stdin); freopen("t.out","w",stdout); scanf("%d%d",&n,&m); n=__gcd(n,m); printf("%lld\n",F::f((ll)n,100000000LL)); return 0; }