POJ-1811-Prime Test（pollard_rho模板，快速找最小素因子）

题目传送门

sol:Pollard_Rho的模板题，刚看了Pollard_Rho和Miller_Rabin很多原理性的东西看不懂，只是记住了结论勉强能敲代码。

• Pollard_Rho

  #include "cstdio"
  #include "cstdlib"
  #include "algorithm"
  #include "ctime"
  using namespace std;
  typedef long long LL;
  LL gcd(LL a, LL b) {
      return b == 0 ? a : gcd(b, a % b);
  }
  LL muli_mod(LL n, LL k, LL p) {
      LL m = 0;
      while (k) {
          if (k & 1) m = (m + n) % p;
          n = (n + n) % p;
          k >>= 1;
      }
      return m;
  }
  LL pow_mod(LL n, LL k, LL p) {
      LL m = 1;
      while (k) {
          if (k & 1) m = muli_mod(m, n, p);
          n = muli_mod(n, n, p);
          k >>= 1;
      }
      return m;
  }
  LL miller_rabin(LL n) {
      if (n == 2) return true;
      if (n < 2 || !(n & 1)) return false;
      LL m = n - 1; int s = 0;
      while (!(m & 1)) s++, m >>= 1;
      for (int i = 1; i <= 5; i++) {
          LL r = rand() % (n - 1) + 1;
          LL y = pow_mod(r, m, n);
          for (int j = 1; j <= s; j++) {
              LL x = muli_mod(y, y, n);
              if (x == 1 && y != 1 && y != n - 1) return false;
              y = x;
          }
          if (y != 1) return false;
      }
      return true;
  }
  LL pollard_rho(LL n, LL c) {
      int i = 1, k = 2;
      LL x = rand() % (n - 1) + 1;
      LL y = x;
      while (true) {
          x = (muli_mod(x, x, n) + c) % n;
          LL p = gcd((y - x + n) % n, n);
          if (p > 1 && p < n) return p;
          if (x == y) return n;
          if (++i == k) {
              k <<= 1;
              y = x;
          }
      }
  }
  LL find(LL n) {
      if (miller_rabin(n)) return n;
      LL p = n;
      while (p >= n) p = pollard_rho(p, rand() % (n - 1) + 1);
      return min(find(p), find(n / p));
  }
  int main() {
      int t; LL n;
  //    srand(time(NULL));
      scanf("%d", &t);
      while (t--) {
          scanf("%lld", &n);
          LL p = find(n);
          if (p == n) puts("Prime");
          else printf("%lld\n", p);
      }
      return 0;
  }

  POJ不让用万能头，algorithm下的__gcd也不让用。关键srand用一下还RE，挺坑的。