feat: add method DoubleFactorial (#567)

Author: Lê Nam Khánh

Algorithms.Tests/Numeric/DoubleFactorialTests.cs

@@ -0,0 +1,54 @@
+using System.Numerics;
+using Algorithms.Numeric;
+
+namespace Algorithms.Tests.Numeric;
+
+/// <summary>
+/// Tests for the DoubleFactorial class methods.
+/// </summary>
+public static class DoubleFactorialTests
+{
+    /// <summary>
+    /// Tests the calculation of double factorial for non-negative integers.
+    /// Includes base cases (0, 1), odd numbers (5, 11), even numbers (6, 12), 
+    /// and a large number (20) that benefits from BigInteger.
+    /// </summary>
+    /// <param name="input">The number N to calculate N!!.</param>
+    /// <param name="expected">The expected result as a string (for BigInteger parsing).</param>
+    [TestCase(0, "1")]     // Base Case: 0!! = 1
+    [TestCase(1, "1")]     // Base Case: 1!! = 1
+    [TestCase(5, "15")]    // Odd: 5 * 3 * 1 = 15
+    [TestCase(6, "48")]    // Even: 6 * 4 * 2 = 48
+    [TestCase(11, "10395")]// Larger Odd: 11 * 9 * 7 * 5 * 3 * 1 = 10395
+    [TestCase(12, "46080")] // Larger Even: 12 * 10 * 8 * 6 * 4 * 2 = 46080
+    [TestCase(20, "3715891200")] // Large Even
+    public static void GetsDoubleFactorial(int input, string expected)
+    {
+        // Arrange
+        BigInteger expectedBigInt = BigInteger.Parse(expected);
+
+        // Act
+        var result = DoubleFactorial.Calculate(input);
+
+        // Assert
+        Assert.That(result, Is.EqualTo(expectedBigInt));
+    }
+
+    /// <summary>
+    /// Tests that calculating double factorial for negative numbers throws an ArgumentException.
+    /// </summary>
+    /// <param name="num">A negative integer input.</param>
+    [TestCase(-1)]
+    [TestCase(-5)]
+    [TestCase(-10)]
+    public static void GetsDoubleFactorialExceptionForNegativeNumbers(int num)
+    {
+        // Arrange
+
+        // Act
+        void Act() => DoubleFactorial.Calculate(num);
+
+        // Assert
+        _ = Assert.Throws<ArgumentException>(Act);
+    }
+}

Algorithms/Numeric/DoubleFactorial.cs

@@ -0,0 +1,48 @@
+using System.Numerics;
+
+namespace Algorithms.Numeric;
+
+/// <summary>
+///     The double factorial of a positive integer n, denoted by n!!,
+///     is the product of all integers from 1 up to n that have the same parity (odd or even) as n.
+///     E.g., 5!! = 5 * 3 * 1 = 15, and 6!! = 6 * 4 * 2 = 48.
+/// </summary>
+public static class DoubleFactorial
+{
+    /// <summary>
+    ///     Calculates the double factorial of a non-negative integer number.
+    /// </summary>
+    /// <param name="inputNum">Non-negative integer input number.</param>
+    /// <returns>Double factorial of the integer input number.</returns>
+    public static BigInteger Calculate(int inputNum)
+    {
+        // Don't calculate double factorial if input is a negative number.
+        if (inputNum < 0)
+        {
+            throw new ArgumentException("Double factorial is only defined for non-negative integers (num >= 0).");
+        }
+
+        // Base cases: 0!! = 1 and 1!! = 1
+        if (inputNum <= 1)
+        {
+            return BigInteger.One;
+        }
+
+        // Initialize result.
+        BigInteger result = BigInteger.One;
+
+        // Start the iteration from the input number and step down by 2.
+        // This handles both odd (n, n-2, ..., 3, 1) and even (n, n-2, ..., 4, 2) cases naturally.
+        BigInteger current = inputNum;
+
+        while (current > BigInteger.Zero)
+        {
+            result *= current;
+
+            // Decrease the current number by 2 for the next factor.
+            current -= 2;
+        }
+
+        return result;
+    }
+}