Add primality tests.

Author: trekhleb

README.md

@@ -31,10 +31,10 @@
   * [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
   * [Cartesian Product](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/cartesian-product)
   * [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/power-set)
-  * [Primality Test](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test)
+  * [Primality Test](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (Trial Division)
+  * [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the greatest common divisor (GCD)
   * Collatz Conjecture algorithm
   * Extended Euclidean algorithm
-  * Euclidean algorithm to calculate the Greatest Common Divisor (GCD)
   * Find Divisors
   * Fisher-Yates
   * Greatest Difference

src/algorithms/math/euclidean-algorithm/README.md

@@ -0,0 +1,57 @@
+# Euclidean algorithm
+
+In mathematics, the Euclidean algorithm, or Euclid's algorithm, 
+is an efficient method for computing the greatest common divisor 
+(GCD) of two numbers, the largest number that divides both of 
+them without leaving a remainder.
+
+The Euclidean algorithm is based on the principle that the 
+greatest common divisor of two numbers does not change if 
+the larger number is replaced by its difference with the 
+smaller number. For example, `21` is the GCD of `252` and 
+`105` (as `252 = 21 × 12` and `105 = 21 × 5`), and the same 
+number `21` is also the GCD of `105` and `252 − 105 = 147`. 
+Since this replacement reduces the larger of the two numbers, 
+repeating this process gives successively smaller pairs of 
+numbers until the two numbers become equal. 
+When that occurs, they are the GCD of the original two numbers. 
+
+By reversing the steps, the GCD can be expressed as a sum of 
+the two original numbers each multiplied by a positive or 
+negative integer, e.g., `21 = 5 × 105 + (−2) × 252`. 
+The fact that the GCD can always be expressed in this way is 
+known as Bézout's identity.
+
+![GCD](https://upload.wikimedia.org/wikipedia/commons/3/37/Euclid%27s_algorithm_Book_VII_Proposition_2_3.png)
+
+Euclid's method for finding the greatest common divisor (GCD) 
+of two starting lengths `BA` and `DC`, both defined to be 
+multiples of a common "unit" length. The length `DC` being 
+shorter, it is used to "measure" `BA`, but only once because 
+remainder `EA` is less than `DC`. EA now measures (twice) 
+the shorter length `DC`, with remainder `FC` shorter than `EA`. 
+Then `FC` measures (three times) length `EA`. Because there is 
+no remainder, the process ends with `FC` being the `GCD`. 
+On the right Nicomachus' example with numbers `49` and `21` 
+resulting in their GCD of `7` (derived from Heath 1908:300).
+
+![GCD](https://upload.wikimedia.org/wikipedia/commons/7/74/24x60.svg)
+
+A `24-by-60` rectangle is covered with ten `12-by-12` square 
+tiles, where `12` is the GCD of `24` and `60`. More generally, 
+an `a-by-b` rectangle can be covered with square tiles of 
+side-length `c` only if `c` is a common divisor of `a` and `b`.
+
+![GCD](https://upload.wikimedia.org/wikipedia/commons/1/1c/Euclidean_algorithm_1071_462.gif)
+
+Subtraction-based animation of the Euclidean algorithm. 
+The initial rectangle has dimensions `a = 1071` and `b = 462`. 
+Squares of size `462×462` are placed within it leaving a 
+`462×147` rectangle. This rectangle is tiled with `147×147` 
+squares until a `21×147` rectangle is left, which in turn is 
+tiled with `21×21` squares, leaving no uncovered area. 
+The smallest square size, `21`, is the GCD of `1071` and `462`.
+
+## References
+
+[Wikipedia](https://en.wikipedia.org/wiki/Euclidean_algorithm)

src/algorithms/math/euclidean-algorithm/__test__/euclieanAlgorithm.test.js

@@ -0,0 +1,24 @@
+import euclideanAlgorithm from '../euclideanAlgorithm';
+
+describe('euclideanAlgorithm', () => {
+  it('should calculate GCD', () => {
+    expect(euclideanAlgorithm(0, 0)).toBeNull();
+    expect(euclideanAlgorithm(2, 0)).toBe(2);
+    expect(euclideanAlgorithm(0, 2)).toBe(2);
+    expect(euclideanAlgorithm(1, 2)).toBe(1);
+    expect(euclideanAlgorithm(2, 1)).toBe(1);
+    expect(euclideanAlgorithm(6, 6)).toBe(6);
+    expect(euclideanAlgorithm(2, 4)).toBe(2);
+    expect(euclideanAlgorithm(4, 2)).toBe(2);
+    expect(euclideanAlgorithm(12, 4)).toBe(4);
+    expect(euclideanAlgorithm(4, 12)).toBe(4);
+    expect(euclideanAlgorithm(5, 13)).toBe(1);
+    expect(euclideanAlgorithm(27, 13)).toBe(1);
+    expect(euclideanAlgorithm(24, 60)).toBe(12);
+    expect(euclideanAlgorithm(60, 24)).toBe(12);
+    expect(euclideanAlgorithm(252, 105)).toBe(21);
+    expect(euclideanAlgorithm(105, 252)).toBe(21);
+    expect(euclideanAlgorithm(1071, 462)).toBe(21);
+    expect(euclideanAlgorithm(462, 1071)).toBe(21);
+  });
+});

src/algorithms/math/euclidean-algorithm/euclideanAlgorithm.js

@@ -0,0 +1,24 @@
+/**
+ * @param {number} a
+ * @param {number} b
+ * @return {number|null}
+ */
+export default function euclideanAlgorithm(a, b) {
+  if (a === 0 && b === 0) {
+    return null;
+  }
+
+  if (a === 0 && b !== 0) {
+    return b;
+  }
+
+  if (a !== 0 && b === 0) {
+    return a;
+  }
+
+  if (a > b) {
+    return euclideanAlgorithm(a - b, b);
+  }
+
+  return euclideanAlgorithm(b - a, a);
+}