Add pollard rho algorithm (#3260)

src/main/java/com/thealgorithms/maths/PollardRho.java

@@ -0,0 +1,74 @@
+package com.thealgorithms.maths;
+
+/*
+ * Java program for pollard rho algorithm
+ * The algorithm is used to factorize a number n = pq,
+ * where p is a non-trivial factor. 
+ * Pollard's rho algorithm is an algorithm for integer factorization
+ * and it takes as its inputs n, the integer to be factored; 
+ * and g(x), a polynomial in x computed modulo n.
+ * In the original algorithm, g(x) = ((x ^ 2) − 1) mod n,
+ * but nowadays it is more common to use g(x) = ((x ^ 2) + 1 ) mod n. 
+ * The output is either a non-trivial factor of n, or failure.
+ * It performs the following steps:
+ *     x ← 2
+ *     y ← 2
+ *     d ← 1
+
+ *     while d = 1:
+ *         x ← g(x)
+ *         y ← g(g(y))
+ *         d ← gcd(|x - y|, n)
+
+ *     if d = n: 
+ *         return failure
+ *     else:
+ *         return d
+
+ * Here x and y corresponds to xi and xj in the previous section. 
+ * Note that this algorithm may fail to find a nontrivial factor even when n is composite.
+ * In that case, the method can be tried again, using a starting value other than 2 or a different g(x)
+ * 
+ * Wikipedia: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
+ * 
+ * Author: Akshay Dubey (https://github.com/itsAkshayDubey)
+ * 
+ * */
+public class PollardRho {
+	
+	/**
+	 * This method returns a polynomial in x computed modulo n
+	 *
+	 * @param base Integer base of the polynomial
+	 * @param modulus Integer is value which is to be used to perform modulo operation over the polynomial 
+	 * @return Integer (((base * base) - 1) % modulus)
+	 */
+	static int g(int base,int modulus) {
+		return ((base * base) - 1) % modulus;
+	}
+	
+	/**
+	 * This method returns a non-trivial factor of given integer number  
+	 *
+	 * @param number Integer is a integer value whose non-trivial factor is to be found
+	 * @return Integer non-trivial factor of number
+	 * @throws RuntimeException object if GCD of given number cannot be found
+	 */
+	static int pollardRho(int number) {
+		int x = 2, y = 2, d = 1;
+		while(d == 1) {
+			//tortoise move
+			x = g(x, number);
+			
+			//hare move
+			y = g(g(y, number), number);
+			
+			//check GCD of |x-y| and number
+			d = GCD.gcd(Math.abs(x - y), number);
+		}
+		if(d == number) {
+			throw new RuntimeException("GCD cannot be found.");
+		}
+		return d;
+	}
+}