P4718 【模板】Pollard-Rho算法
1 #include <bits/stdc++.h> 2 using namespace std; 3 typedef long long ll; 4 typedef __int128 lll; 5 char buf[700000000]; 6 int cnt = 0; 7 ll ans; 8 template<typename T> inline T read(T a) { 9 T res = 0, f = 1; 10 char ch = buf[cnt++]; 11 while (!isdigit(ch)) { 12 if (ch == '-') f = -1; 13 ch = buf[cnt++]; 14 } 15 while (isdigit(ch)) { 16 res = (res<<3)+(res<<1) + ch - 48; 17 ch = buf[cnt++]; 18 } 19 return res*f; 20 } 21 template<typename T> inline void write(T x) { 22 if (x < 0) { 23 putchar('-'); 24 write(-x); 25 return; 26 } 27 if (x > 9) write(x/10); 28 putchar(x%10+48); 29 } 30 inline ll gcd(ll a, ll b) { 31 if (b == 0) return a; 32 return gcd(b,a%b); 33 } 34 inline ll qpow(ll a, ll b, ll mod) { 35 ll res = 1; 36 while (b) { 37 if (b&1) res = (lll)res*a%mod; 38 a = (lll)a*a%mod; 39 b >>= 1; 40 } 41 return res; 42 } 43 inline bool test(ll x, ll b) { 44 ll k = x-1; 45 while (k) { 46 ll cur = qpow(b,k,x); 47 if (cur!=1 && cur!=x-1) return false; 48 if ((k&1)==1 || cur==x-1) return true; 49 k >>= 1; 50 } 51 return true; 52 } 53 inline bool Miller_Rabin(ll x) { 54 if (x==46856248255981LL || x<2) return false; 55 if (x==2 || x==3 || x==7 || x==61 || x==24251) return true; 56 return test(x,2)&&test(x,61); 57 } 58 inline ll pollard_rho(ll x) { 59 ll s = 0, t = 0, c = 1LL*rand()%(x-1)+1; 60 ll val = 1; 61 for (int goal = 1;; goal<<=1, s=t, val=1) { 62 for (int stp = 1; stp<=goal; ++stp) { 63 t = ((lll)t*t+c)%x; 64 val = (lll)val*abs(t-s)%x; 65 if ((stp%127) == 0) { 66 ll d = gcd(val,x); 67 if (d>1) return d; 68 } 69 } 70 ll d = gcd(val,x); 71 if (d>1) return d; 72 } 73 } 74 inline void findfac(ll x) { 75 if (x <= ans || x < 2) return; 76 if (Miller_Rabin(x)) { 77 ans = ans > x ? ans : x; 78 return; 79 } 80 ll p = x; 81 while (p >= x) p = pollard_rho(x); 82 while ((x%p) == 0) x /= p; 83 findfac(x), findfac(p); 84 } 85 int main() { 86 fread(buf,1,700000000,stdin); 87 int t; t = read(t); 88 while (t--) { 89 ll n; n = read(n); 90 ans = 0; 91 findfac(n); 92 if (ans == n) puts("Prime"); 93 else write(ans), putchar('\n'); 94 } 95 return 0; 96 }
