feat(5-kyu): kata/josephus-survivor (#490)

docs/README.md

@@ -25,7 +25,7 @@ slug.
 
 | [1 kyu](/kata/1-kyu/index.md) | [2 kyu](/kata/2-kyu/index.md) | [3 kyu](/kata/3-kyu/index.md) | [4 kyu](/kata/4-kyu/index.md) | [5 kyu](/kata/5-kyu/index.md) | [6 kyu](/kata/6-kyu/index.md) | [7 kyu](/kata/7-kyu/index.md) | [8 kyu](/kata/8-kyu/index.md) | [beta](/kata/beta/index.md) | [retired](/kata/retired/index.md) |
 |:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:---------------------------:|:---------------------------------:|
-| 0 | 1 | 2 | 26 | 42 | 416 | 559 | 206 | 55 | 79 |
+| 0 | 1 | 2 | 26 | 43 | 416 | 559 | 206 | 55 | 79 |
 
 **Note:** The source code is written in Java 17 and may use language features that are incompatible
 with Java 8, 11.

kata/5-kyu/index.md

@@ -27,6 +27,7 @@
 - [Is the King in check ?](is-the-king-in-check)
 # J
 - [Josephus Permutation](josephus-permutation)
+- [Josephus Survivor](josephus-survivor)
 # L
 - [Land perimeter](land-perimeter)
 - [Last digit of a large number](last-digit-of-a-large-number)

kata/5-kyu/josephus-survivor/README.md

@@ -0,0 +1,27 @@
+# [Josephus Survivor](https://www.codewars.com/kata/josephus-survivor "https://www.codewars.com/kata/555624b601231dc7a400017a")
+
+In this kata you have to correctly return who is the "survivor", ie: the last element of
+a <a href="http://www.codewars.com/kata/josephus-permutation/" target="_blank" title="Josephus sequence">Josephus
+permutation</a>.
+
+Basically you have to assume that n people are put into a circle and that they are eliminated in steps of k elements,
+like this:
+
+```
+n=7, k=3 => means 7 people in a circle
+one every 3 is eliminated until one remains
+[1,2,3,4,5,6,7] - initial sequence
+[1,2,4,5,6,7] => 3 is counted out
+[1,2,4,5,7] => 6 is counted out
+[1,4,5,7] => 2 is counted out
+[1,4,5] => 7 is counted out
+[1,4] => 5 is counted out
+[4] => 1 counted out, 4 is the last element - the survivor!
+```
+
+The above link about the "base" kata description will give you a more thorough insight about the origin of this kind of
+permutation, but basically that's all that there is to know to solve this kata.
+
+**Notes and tips:** using the solution to the other kata to check your function may be helpful, but as much larger
+numbers will be used, using an array/list to compute the number of the survivor may be too slow; you may assume that
+both n and k will always be >=1.

kata/5-kyu/josephus-survivor/main/JosephusSurvivor.java

@@ -0,0 +1,5 @@
+interface JosephusSurvivor {
+  static int josephusSurvivor(int n, int k) {
+    return n > 1 ? (josephusSurvivor(n - 1, k--) + k) % n + 1 : 1;
+  }
+}

kata/5-kyu/josephus-survivor/test/JosephusSurvivorTest.java

@@ -0,0 +1,14 @@
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+class JosephusSurvivorTest {
+  @Test
+  void sample() {
+    assertEquals(4, JosephusSurvivor.josephusSurvivor(7, 3));
+    assertEquals(10, JosephusSurvivor.josephusSurvivor(11, 19));
+    assertEquals(28, JosephusSurvivor.josephusSurvivor(40, 3));
+    assertEquals(13, JosephusSurvivor.josephusSurvivor(14, 2));
+    assertEquals(100, JosephusSurvivor.josephusSurvivor(100, 1));
+  }
+}