牛客國慶集訓派對Day5 B 電音之王
阿新 • • 發佈:2018-12-13
題意:略。
分析:首先用暴力快速乘O(n*logn)t了,取模一個long long範圍內的數太耗時了,但是一直不知道怎麼優化取模,後來才知道有蒙哥馬利演算法優化a*b%c,入門可參考https://blog.csdn.net/zgzczzw/article/details/52712980,網上沒找到實現程式碼,下面的程式碼是杜教的,留著當板子用了。據說O(1)快速乘也能做,我試了下t了,可能資料加強了。
程式碼:
#include <bits/stdc++.h> using namespace std; #define rep(i,a,n) for (int i=a;i<n;i++) #define per(i,a,n) for (int 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) ((int)(x).size()) typedef vector<int> VI; typedef long long ll; typedef pair<int,int> PII; const ll mod=1000000007; 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;} ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;} // head typedef unsigned long long u64; typedef __int128_t i128; typedef __uint128_t u128; int _,k; u64 A0,A1,M0,M1,C,M; struct Mod64 { Mod64():n_(0) {} Mod64(u64 n):n_(init(n)) {} static u64 init(u64 w) { return reduce(u128(w) * r2); } static void set_mod(u64 m) { mod=m; assert(mod&1); inv=m; rep(i,0,5) inv*=2-inv*m; r2=-u128(m)%m; } static u64 reduce(u128 x) { u64 y=u64(x>>64)-u64((u128(u64(x)*inv)*mod)>>64); return ll(y)<0?y+mod:y; } Mod64& operator += (Mod64 rhs) { n_+=rhs.n_-mod; if (ll(n_)<0) n_+=mod; return *this; } Mod64 operator + (Mod64 rhs) const { return Mod64(*this)+=rhs; } Mod64& operator -= (Mod64 rhs) { n_-=rhs.n_; if (ll(n_)<0) n_+=mod; return *this; } Mod64 operator - (Mod64 rhs) const { return Mod64(*this)-=rhs; } Mod64& operator *= (Mod64 rhs) { n_=reduce(u128(n_)*rhs.n_); return *this; } Mod64 operator * (Mod64 rhs) const { return Mod64(*this)*=rhs; } u64 get() const { return reduce(n_); } static u64 mod,inv,r2; u64 n_; }; u64 Mod64::mod,Mod64::inv,Mod64::r2; u64 pmod(u64 a,u64 b,u64 p) { u64 d=(u64)floor(a*(long double)b/p+0.5); ll ret=a*b-d*p; if (ret<0) ret+=p; return ret; } void bruteforce() { u64 ans=1; for (int i=0;i<=k;i++) { ans=pmod(ans,A0,M); u64 A2=pmod(M0,A1,M)+pmod(M1,A0,M)+C; while (A2>=M) A2-=M; A0=A1; A1=A2; } printf("%llu\n",ans); } int main() { for (scanf("%d",&_);_;_--) { scanf("%llu%llu%llu%llu%llu%llu%d",&A0,&A1,&M0,&M1,&C,&M,&k); Mod64::set_mod(M); Mod64 a0(A0),a1(A1),m0(M0),m1(M1),c(C),ans(1),a2(0); for (int i=0;i<=k;i++) { ans=ans*a0; a2=m0*a1+m1*a0+c; a0=a1; a1=a2; } printf("%llu\n",ans.get()); } }