feat: implement Pollard's Rho algorithm for integer factorization

Author: PrasanBora

Maths/PollardsRho.js

@@ -0,0 +1,33 @@
+/**
+ * Pollard’s Rho Algorithm for Integer Factorization
+ *
+ * Pollard’s Rho is a probabilistic algorithm for integer factorization, especially effective for large composite numbers.
+ * Reference: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
+ */
+
+function gcd(a, b) {
+  while (b !== 0) {
+    [a, b] = [b, a % b]
+  }
+  return a
+}
+
+/**
+ * Returns a non-trivial factor of n, or n if n is prime
+ * @param {number} n - Integer to factor
+ * @returns {number} - A non-trivial factor of n
+ */
+export function pollardsRho(n) {
+  if (n % 2 === 0) return 2
+  let x = 2, y = 2, d = 1, f = v => (v * v + 1) % n
+  while (d === 1) {
+    x = f(x)
+    y = f(f(y))
+    d = gcd(Math.abs(x - y), n)
+  }
+  return d === n ? n : d
+}
+
+// Example usage:
+// const n = 8051;
+// console.log(pollardsRho(n)); // Output: a non-trivial factor of 8051