Add Josephus Problem Recursive Solution (#3208)

src/main/java/com/thealgorithms/maths/JosephusProblem.java

@@ -0,0 +1,36 @@
+package com.thealgorithms.maths;
+
+     /** There are n friends that are playing a game. The friends are sitting in a circle and are    numbered from 1 to n in clockwise order. More formally, moving clockwise from the ith friend brings you to the (i+1)th friend for 1 <= i < n, and moving clockwise from the nth friend brings you to the 1st friend.
+    */
+
+    /** The rules of the game are as follows:
+
+        1.Start at the 1st friend.
+        2.Count the next k friends in the clockwise direction including the friend you started at. The counting wraps around the circle and may count some friends more than once.
+        3.The last friend you counted leaves the circle and loses the game.
+        4.If there is still more than one friend in the circle, go back to step 2 starting from the friend immediately clockwise of the friend who just lost and repeat.
+        5.Else, the last friend in the circle wins the game.
+
+        @author Kunal
+    */
+
+public class JosephusProblem {
+
+    /**
+     * Find the Winner of the Circular Game.
+     *
+     * @param number of friends, n, and an integer k
+     * @return return the winner of the game
+     */
+
+    public static int findTheWinner(int n, int k) {
+        return winner(n, k) + 1;
+    }
+    
+    public static int winner(int n, int k){
+        if (n == 1){
+            return 0;
+        }
+        return (winner(n -1, k) + k) % n;
+    }
+}

src/test/java/com/thealgorithms/maths/JosephusProblemTest.java

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+package com.thealgorithms.maths;
+
+import org.junit.jupiter.api.Test;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+public class JosephusProblemTest {
+
+    @Test
+    void testJosephusProblem(){
+        assertEquals(3, JosephusProblem.findTheWinner(5,2));
+        assertEquals(5, JosephusProblem.findTheWinner(6,4));
+    }
+
+}