Josephus Problem added

AlgorithmCode/JosephusProblem.java

@@ -0,0 +1,33 @@
+/**
+ * An implementation of the Josephus problem Time complexity: O(n)
+ *
+ * @author Micah Stairs
+ */
+
+public class JosephusProblem {
+
+ // Suppose there are n people in a circle and person
+ // 0 kill the k'th person, then the k'th person kills
+ // the 2k'th person and so on until only one person remains.
+ // The question is who lives?
+ // Let n be the number of people and k the hop size
+ public static int josephus(int n, int k) {
+ int[] dp = new int[n];
+ for (int i = 1; i < n; i++) dp[i] = (dp[i - 1] + k) % (i + 1);
+ return dp[n - 1];
+ }
+
+ public static void main(String[] args) {
+
+ int n = 41, k = 2;
+ System.out.println(josephus(n, k));
+
+ n = 25;
+ k = 18;
+ System.out.println(josephus(n, k));
+
+ n = 5;
+ k = 2;
+ System.out.println(josephus(n, k));
+ }
+}