Add Josephus Problem solver (TheAlgorithms#356)

Author: Kalkwst

Algorithms.Tests/Numeric/JosephusProblemTest.cs

@@ -0,0 +1,37 @@
+using System;
+using Algorithms.Numeric;
+using NUnit.Framework;
+
+
+namespace Algorithms.Tests.Numeric;
+
+public class JosephusProblemTest
+{
+
+    [TestCase(10, 0)]
+    [TestCase(10, -1)]
+    public void JosephusProblemInvalidStepSize(long groupSize, long step)
+    {
+        Assert.Throws(Is.TypeOf<ArgumentException>()
+                .And.Message.EqualTo("The step cannot be smaller than 1"),
+            delegate { JosephusProblem.FindWinner(groupSize, step); });
+    }
+
+    [TestCase(10, 12)]
+    public void JosephusProblemStepSizeGreaterThanGroup(long groupSize, long step)
+    {
+        Assert.Throws(Is.TypeOf<ArgumentException>()
+                .And.Message.EqualTo("The step cannot be greater than the size of the group"),
+            delegate { JosephusProblem.FindWinner(groupSize, step); });
+    }
+
+    [TestCase(10, 2, 5)]
+    [TestCase(10, 8, 1)]
+    [TestCase(254, 18, 92)]
+    [TestCase(3948, 614, 2160)]
+    [TestCase(86521, 65903, 29473)]
+    public void JosephusProblemWinnerCalculation(long groupSize, long step, long position)
+    {
+        Assert.That(JosephusProblem.FindWinner(groupSize, step), Is.EqualTo(position));
+    }
+}

Algorithms/Numeric/JosephusProblem.cs

@@ -0,0 +1,33 @@
+using System;
+
+namespace Algorithms.Numeric;
+
+public static class JosephusProblem
+{
+    /// <summary>
+    /// Calculates the winner in the Josephus problem.
+    /// </summary>
+    /// <param name="n">The number of people in the initial circle.</param>
+    /// <param name="k">The count of each step. k-1 people are skipped and the k-th is executed.</param>
+    /// <returns>The 1-indexed position where the player must choose in order to win the game.</returns>
+    public static long FindWinner(long n, long k)
+    {
+        if (k <= 0)
+        {
+            throw new ArgumentException("The step cannot be smaller than 1");
+        }
+
+        if (k > n)
+        {
+            throw new ArgumentException("The step cannot be greater than the size of the group");
+        }
+
+        long winner = 0;
+        for (long stepIndex = 1; stepIndex <= n; ++stepIndex)
+        {
+            winner = (winner + k) % stepIndex;
+        }
+
+        return winner + 1;
+    }
+}

README.md

@@ -82,6 +82,7 @@ find more than one implementation for the same objective but using different alg
     * [Miller-Rabin primality check](./Algorithms/Numeric/MillerRabinPrimalityChecker.cs)
     * [KrishnamurthyNumberChecker](./Algorithms/Numeric/KrishnamurthyNumberChecker.cs)
     * [Automorphic Number](./Algorithms/Numeric/AutomorphicNumber.cs)
+    * [Josephus Problem](./Algorithms/Numeric/JosephusProblem.cs)
     * [Newton's Square Root Calculation](./Algorithms/NewtonSquareRoot.cs)
   * [Searches](./Algorithms/Search)
     * [A-Star](./Algorithms/Search/AStar/)