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Josephus Problem added

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	`1`	`+/**`
	`2`	`+ * An implementation of the Josephus problem Time complexity: O(n)`
	`3`	`+ *`
	`4`	`+ * @author Micah Stairs`
	`5`	`+ */`
	`6`	`+`
	`7`	`+public class JosephusProblem {`
	`8`	`+`
	`9`	`+ // Suppose there are n people in a circle and person`
	`10`	`+ // 0 kill the k'th person, then the k'th person kills`
	`11`	`+ // the 2k'th person and so on until only one person remains.`
	`12`	`+ // The question is who lives?`
	`13`	`+ // Let n be the number of people and k the hop size`
	`14`	`+ public static int josephus(int n, int k) {`
	`15`	`+ int[] dp = new int[n];`
	`16`	`+ for (int i = 1; i < n; i++) dp[i] = (dp[i - 1] + k) % (i + 1);`
	`17`	`+ return dp[n - 1];`
	`18`	`+ }`
	`19`	`+`
	`20`	`+ public static void main(String[] args) {`
	`21`	`+`
	`22`	`+ int n = 41, k = 2;`
	`23`	`+ System.out.println(josephus(n, k));`
	`24`	`+`
	`25`	`+ n = 25;`
	`26`	`+ k = 18;`
	`27`	`+ System.out.println(josephus(n, k));`
	`28`	`+`
	`29`	`+ n = 5;`
	`30`	`+ k = 2;`
	`31`	`+ System.out.println(josephus(n, k));`
	`32`	`+ }`
	`33`	`+}`

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