feat: add greatest common divisor (TheAlgorithms#254)

Co-authored-by: Andrii Siriak <siryaka@gmail.com>

Author: imp2002

DIRECTORY.md

@@ -50,6 +50,7 @@
   * [Lib](https://github.com/TheAlgorithms/Rust/blob/master/src/lib.rs)
   * Math
     * [Extended Euclidean Algorithm](https://github.com/TheAlgorithms/Rust/blob/master/src/math/extended_euclidean_algorithm.rs)
+    * [Greatest Common Divisor](https://github.com/TheAlgorithms/Rust/blob/master/src/math/greatest_common_divisor.rs)
     * [Pascal Triangle](https://github.com/TheAlgorithms/Rust/blob/master/src/math/pascal_triangle.rs)
     * [Perfect Numbers](https://github.com/TheAlgorithms/Rust/blob/master/src/math/perfect_numbers.rs)
     * [Prime Check](https://github.com/TheAlgorithms/Rust/blob/master/src/math/prime_check.rs)

README.md

@@ -34,6 +34,7 @@ RESTART BUILD
 
 ## Math
 - [x] [Extended euclidean algorithm](./src/math/extended_euclidean_algorithm.rs)
+- [x] [Greatest common divisor](./src/math/greatest_common_divisor.rs)
 - [x] [Pascal's triangle](./src/math/pascal_triangle.rs)
 
 ## [Dynamic Programming](./src/dynamic_programming)

src/math/greatest_common_divisor.rs

@@ -0,0 +1,84 @@
+/// Greatest Common Divisor.
+///
+/// greatest_common_divisor(num1, num2) returns the greatest number of num1 and num2.
+///
+/// Wikipedia reference: https://en.wikipedia.org/wiki/Greatest_common_divisor
+/// gcd(a, b) = gcd(a, -b) = gcd(-a, b) = gcd(-a, -b) by definition of divisibility
+
+pub fn greatest_common_divisor_recursive(a: i64, b: i64) -> i64 {
+    if a == 0 {
+        b.abs()
+    } else {
+        greatest_common_divisor_recursive(b % a, a)
+    }
+}
+
+pub fn greatest_common_divisor_iterative(mut a: i64, mut b: i64) -> i64 {
+    while a != 0 {
+        let remainder = b % a;
+        b = a;
+        a = remainder;
+    }
+    b.abs()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn positive_number_recursive() {
+        assert_eq!(greatest_common_divisor_recursive(4, 16), 4);
+        assert_eq!(greatest_common_divisor_recursive(16, 4), 4);
+        assert_eq!(greatest_common_divisor_recursive(3, 5), 1);
+        assert_eq!(greatest_common_divisor_recursive(40, 40), 40);
+        assert_eq!(greatest_common_divisor_recursive(27, 12), 3);
+    }
+
+    #[test]
+    fn positive_number_iterative() {
+        assert_eq!(greatest_common_divisor_iterative(4, 16), 4);
+        assert_eq!(greatest_common_divisor_iterative(16, 4), 4);
+        assert_eq!(greatest_common_divisor_iterative(3, 5), 1);
+        assert_eq!(greatest_common_divisor_iterative(40, 40), 40);
+        assert_eq!(greatest_common_divisor_iterative(27, 12), 3);
+    }
+
+    #[test]
+    fn negative_number_recursive() {
+        assert_eq!(greatest_common_divisor_recursive(-32, -8), 8);
+        assert_eq!(greatest_common_divisor_recursive(-8, -32), 8);
+        assert_eq!(greatest_common_divisor_recursive(-3, -5), 1);
+        assert_eq!(greatest_common_divisor_recursive(-40, -40), 40);
+        assert_eq!(greatest_common_divisor_recursive(-12, -27), 3);
+    }
+
+    #[test]
+    fn negative_number_iterative() {
+        assert_eq!(greatest_common_divisor_iterative(-32, -8), 8);
+        assert_eq!(greatest_common_divisor_iterative(-8, -32), 8);
+        assert_eq!(greatest_common_divisor_iterative(-3, -5), 1);
+        assert_eq!(greatest_common_divisor_iterative(-40, -40), 40);
+        assert_eq!(greatest_common_divisor_iterative(-12, -27), 3);
+    }
+
+    #[test]
+    fn mix_recursive() {
+        assert_eq!(greatest_common_divisor_recursive(0, -5), 5);
+        assert_eq!(greatest_common_divisor_recursive(-5, 0), 5);
+        assert_eq!(greatest_common_divisor_recursive(-64, 32), 32);
+        assert_eq!(greatest_common_divisor_recursive(-32, 64), 32);
+        assert_eq!(greatest_common_divisor_recursive(-40, 40), 40);
+        assert_eq!(greatest_common_divisor_recursive(12, -27), 3);
+    }
+
+    #[test]
+    fn mix_iterative() {
+        assert_eq!(greatest_common_divisor_iterative(0, -5), 5);
+        assert_eq!(greatest_common_divisor_iterative(-5, 0), 5);
+        assert_eq!(greatest_common_divisor_iterative(-64, 32), 32);
+        assert_eq!(greatest_common_divisor_iterative(-32, 64), 32);
+        assert_eq!(greatest_common_divisor_iterative(-40, 40), 40);
+        assert_eq!(greatest_common_divisor_iterative(12, -27), 3);
+    }
+}

src/math/mod.rs

@@ -1,11 +1,15 @@
 mod extended_euclidean_algorithm;
+mod greatest_common_divisor;
 mod pascal_triangle;
 mod perfect_numbers;
 mod prime_check;
 mod prime_numbers;
 mod trial_division;
 
 pub use self::extended_euclidean_algorithm::extended_euclidean_algorithm;
+pub use self::greatest_common_divisor::{
+    greatest_common_divisor_iterative, greatest_common_divisor_recursive,
+};
 pub use self::pascal_triangle::pascal_triangle;
 pub use self::perfect_numbers::perfect_numbers;
 pub use self::prime_check::prime_check;