Bzoj 3122 隨機數生成器
阿新 • • 發佈:2018-11-30
輸入含有多組資料,第一行一個正整數T,表示這個測試點內的資料組數。
接下來T行,每行有五個整數p,a,b,X1,t,表示一組資料。保證X1和t都是合法的頁碼。注意:P一定為質數
output共T行,每行一個整數表示他最早讀到第t頁是哪一天。如果他永遠不會讀到第t頁,輸出-1。
input
3
7 1 1 3 3
7 2 2 2 0
7 2 2 2 1
output
1
3
-1
hint 0<=a<=P-1,0<=b<=P-1,2<=P<=10^9
a^(n−1)≡(Xn+b*inv(a−1))*inv(X1+b*inv(a−1))(modp)推匯出來這個式子,程式碼一直寫不對
//#include <bits/stdc++.h> #include <iostream> #include <cstring> #include <cstdio> #include <cmath> #define X 10005 #define inF 0x3f3f3f3f #define PI 3.141592653589793238462643383 #define IO ios::sync_with_stdio(false),cin.tie(0), cout.tie(0); //#pragma comment(linker, "/STACK:1024000000,1024000000") using namespace std; typedef long long ll; typedef unsigned long long Ull; //2^64 const int maxn = (int)2*1e7 + 10; //const int MOD = 9973;//(int)1e9 + 7; //const ll inf = 9223372036854775807; //const int mod=76532; int MOD; void ex_gcd(ll a, ll b, ll &d, ll &x, ll &y) { if (!b) { x = 1; y = 0; d = a; } else { ex_gcd(b, a%b, d, y, x); y -= x * (a / b); }; } ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; } ll lcm(ll a, ll b) { return b / gcd(a, b)*a; } ll inv_exgcd(ll a, ll m) { ll d, x, y;ex_gcd(a, m, d, x, y);return d == 1 ? (x + m) % m : -1; } ll inv1(ll b) { return b == 1 ? 1 : (MOD - MOD / b)*inv1(MOD%b) % MOD; } //hdu1576用這個板子會爆除0錯誤 ll crt(int n,int *c,int *m){ll M=1,ans=0;for(int i=0;i<n;++i) M*=m[i]; for(int i=0;i<n;++i) ans=(ans+M/m[i]*c[i] %M *inv_exgcd(M/m[i],m[i]))%M; return ans;} ll N; const int mod = (int)1e5 + 10; ll hs[mod],next[mod],head[mod],id[mod],top; int read() { int x=0;char ch=getchar(); while(ch<'0'||ch>'9')ch=getchar(); while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();} return x; } int read() { int x=0;char ch=getchar(); while(ch<'0'||ch>'9')ch=getchar(); while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();} return x; } int T; ll p,a,b,x1,t; ll exgcd(ll a,ll b,ll &x,ll &y) { if(b==0){x=1;y=0;return a;} ll tmp=exgcd(b,a%b,x,y); ll t=x;x=y;y=t-a/b*y; return tmp; } ll kpow(ll a,ll b,ll p) { a%=p;ll ans=1; for(ll i=b;i;i>>=1,a=a*a%p) if(i&1)ans=ans*a%p; return ans; } void insert(ll x,ll y) { ll k=x%mod; hs[top]=x,id[top]=y,next[top]=head[k],head[k]=top++; } int find(ll x) { int k=x%mod; for(ll i=head[k];i!=-1;i=next[i]) if(hs[i]==x) return id[i]; return -1; } ll BSGS(ll a,ll b,ll n) { memset(head,-1,sizeof(head)); top=1; if(b==1)return 0; int m=sqrt(n*1.0),j; ll x=1,p=1; for(int i=0;i<m;++i,p=p*a%n)insert(p*b%n,i); for(ll i=m; ;i+=m) { if((j=find(x=x*p%n))!=-1)return i-j; if(i>n)break; } return -1; } ll cal1() { ll C=(t-x1+p)%p,x,y; ll t=exgcd(b,p,x,y); if(C%t)return -1;C/=t; x=x*C%p; if(x<0)x+=p; return x+1; } ll cal2() { ll c=inv_exgcd(a-1,p),A=(x1+b*c)%p;//kpow(a-1,p-2,p),A=(x1+b*c)%p,也可以用費馬小定理求出逆元, ll C=(t+b*c)%p,x,y; ll t=exgcd(A,p,x,y); x=x%p+p; t=BSGS(a,x*C%p,p); if(t!=-1)return t+1; return -1; } ll solve() { if(x1==t)return 1; if(a==0) { if(b==t)return 2; return -1; } if(a==1)return cal1(); else return cal2(); } int main() { T=read(); while(T--) { p=read();a=read();b=read();x1=read();t=read(); printf("%lld\n",solve()); } return 0; }