Merge pull request #277 from bad-eastwind/master

pollardrho_eastwind.cpp

Author: probot-auto-merge[bot]

pollardrho.cpp

@@ -0,0 +1,81 @@
+/* C++ program to find a prime factor of composite using 
+Pollard's Rho algorithm */
+#include<bits/stdc++.h> 
+using namespace std; 
+
+/* Function to calculate (base^exponent)%modulus */
+long long int modular_pow(long long int base, int exponent, 
+						long long int modulus) 
+{ 
+	/* initialize result */
+	long long int result = 1; 
+
+	while (exponent > 0) 
+	{ 
+		/* if y is odd, multiply base with result */
+		if (exponent & 1) 
+			result = (result * base) % modulus; 
+
+		/* exponent = exponent/2 */
+		exponent = exponent >> 1; 
+
+		/* base = base * base */
+		base = (base * base) % modulus; 
+	} 
+	return result; 
+} 
+
+/* method to return prime divisor for n */
+long long int PollardRho(long long int n) 
+{ 
+	/* initialize random seed */
+	srand (time(NULL)); 
+
+	/* no prime divisor for 1 */
+	if (n==1) return n; 
+
+	/* even number means one of the divisors is 2 */
+	if (n % 2 == 0) return 2; 
+
+	/* we will pick from the range [2, N) */
+	long long int x = (rand()%(n-2))+2; 
+	long long int y = x; 
+
+	/* the constant in f(x). 
+	* Algorithm can be re-run with a different c 
+	* if it throws failure for a composite. */
+	long long int c = (rand()%(n-1))+1; 
+
+	/* Initialize candidate divisor (or result) */
+	long long int d = 1; 
+
+	/* until the prime factor isn't obtained. 
+	If n is prime, return n */
+	while (d==1) 
+	{ 
+		/* Tortoise Move: x(i+1) = f(x(i)) */
+		x = (modular_pow(x, 2, n) + c + n)%n; 
+
+		/* Hare Move: y(i+1) = f(f(y(i))) */
+		y = (modular_pow(y, 2, n) + c + n)%n; 
+		y = (modular_pow(y, 2, n) + c + n)%n; 
+
+		/* check gcd of |x-y| and n */
+		d = __gcd(abs(x-y), n); 
+
+		/* retry if the algorithm fails to find prime factor 
+		* with chosen x and c */
+		if (d==n) return PollardRho(n); 
+	} 
+
+	return d; 
+} 
+
+/* driver function */
+int main() 
+{ 
+	long long int n = 10967535067; 
+	printf("One of the divisors for %lld is %lld.", 
+		n, PollardRho(n)); 
+	return 0; 
+}