func josephus(circleSize: Int, num: Int)-> Int {
    var last = 0
    for index in 2...circleSize {
        last=(last + num) % index 
    }
    return last + 1 
}

print(josephus(circleSize: 3014603, num:2))

I don’t even need to spend a whole lot of time on this.  I grabbed the recurrence relation from Wikipedia, and used dynamic programming to transform this into a simple linear loop.

Part 2

Part two threw me for a loop (no pun intended).  I was fully expecting to see the number go up, but instead, the trick was that instead of every Kth person being eliminated, it was the person directly across who got eliminated.

I tried to do a bunch of mathematical induction and proofs to figure this one out, but kept getting stuck.  I had to go sleep on it, and came up with a better way.  The first person to get eliminated will be n/2 positions away from your index.

First I created a circular linked list to represent the elves in this example.

public class Node {
    var value: Int
    init(value: Int) {
        self.value = value
    }

    var next: Node? = nil
    weak var previous: Node?
}

func createList(size: Int) -> Node {
    let head:Node = Node(value: 1)
    var tail:Node = head
    for index in 2...size {
        let node = Node(value:index)
        node.previous = tail
        tail.next = node
        tail = node
    }
    head.previous = tail
    tail.next = head
    return head
}

Then, I advanced n/2 positions.  Then it was a simple pattern of who got eliminated.  If the circle size was odd, it was n/2 and then you skipped n/2 +1.  If the circle size was even, it was just n/2 (no skipping after).  Thus you get in the pattern, eliminate eliminate skip eliminate eliminate skip eliminate eliminate skip….. and so on.

func removeSelf(node: Node) -> Node {
    let nextNode = node.next!
    let previousNode = node.previous!
    previousNode.next = nextNode
    nextNode.previous = previousNode
    return nextNode
}

func josephus(circleSize: Int)-> Int {
    var list: Node = createList(size: circleSize)
    for _ in 1...circleSize/2 {
        list=list.next!
    }
    for size in stride(from: circleSize, to: 1, by: -1) {
        list = removeSelf(node:list)
        if (size % 2 == 1){
            list=list.next!
        }
    }
    return list.value
}

This got the right answer.

Wrap-up