模板题Pollard_Rho大数分解 A - Prime Test POJ - 1811
题意:是素数就输出Prime,不是就输出最小因子.
#include <cstdio> #include<time.h> #include <algorithm> #include<set> using namespace std; typedef long long llt; int const Repeat = 10; set<llt>sss; //利用二进制计算a*b%mod llt multiMod(llt a, llt b, llt mod){ llt ret = 0LL; a %= mod; while (b){ if (b & 1LL) ret = (ret + a) % mod, --b; b >>= 1LL; a = (a + a) % mod; } return ret; } //计算a^b%mod llt powerMod(llt a, llt b, llt mod){ llt ret = 1LL; a %= mod; while (b){ if (b & 1LL) ret = multiMod(ret, a, mod), --b; b >>= 1LL; a = multiMod(a, a, mod); } return ret; } //Miller-Rabin测试,测试n是否为素数 bool Miller_Rabin(llt n, int repeat){ if (2LL == n || 3LL == n) return true; if (!(n & 1LL)) return false; //将n分解为2^s*d llt d = n - 1LL; int s = 0; while (!(d & 1LL)) ++s, d >>= 1LL; //srand((unsigned)time(0)); for (int i = 0; i<repeat; ++i){//重复repeat次 llt a = rand() % (n - 3) + 2;//取一个随机数,[2,n-1) llt x = powerMod(a, d, n); llt y = 0LL; for (int j = 0; j<s; ++j){ y = multiMod(x, x, n); if (1LL == y && 1LL != x && n - 1LL != x) return false; x = y; } if (1LL != y) return false; } return true; } llt Fac[100];//质因数分解结果(刚返回时是无序的) int FCnt;//质因数的个数。数组小标从0开始 llt gcd(llt a, llt b){ if (0L == a || 0L == b) return 1; if (a < 0) a = -a; if (b < 0) b = -b; while (b){ llt t = a % b; a = b; b = t; } return a; } llt Pollard_Rho(llt n, llt c){ llt i = 1, k = 2; llt x = rand() % n; llt y = x; while (1){ ++i; x = (multiMod(x, x, n) + c) % n; llt d = gcd(y - x, n); if (d != 1LL && d != n) return d; if (y == x) return n; if (i == k) y = x, k <<= 1; } } void find(llt n){ if (4LL == n){ Fac[0] = Fac[1] = 2LL; FCnt = 2; return; } if (Miller_Rabin(n, Repeat)){ Fac[FCnt++] = n; return; } llt p; while ((p = Pollard_Rho(n, rand() % (n - 3) + 3)) == n); find(p); find(n / p); } int main(){ int kase; scanf("%d", &kase); while (kase--){ llt n; scanf("%lld", &n); FCnt = 0; if (Miller_Rabin(n, 10)){ printf("Prime\n"); } else{ find(n); llt ans = Fac[0]; for (int i = 0; i < FCnt;++i) if (ans>Fac[i])ans = Fac[i]; printf("%lld\n", ans); } } return 0; }