Remove Nth Node From End of List

Similar to k-th element to last of a LinkedList

Given a linked list, remove the nth node from the end of list and return its head.

For example,

Given linked list:

1->2->3->4->5

and

n = 2

After removing the second node from the end, the linked list becomes

1->2->3->5

Note: Given n will always be valid. Try to do this in one pass.

trait Node {
  def value: Int
  def next: Node
}

object Empty extends Node {
  def value: Int = throw new Error("access empty variable")
  def next: Node = throw new Error("access empty variable")
}

class NonEmpty(var value: Int, var next: Node = Empty) extends Node

def toLinkedList(lst: List[Int]): Node = {
  if (lst.isEmpty) Empty
  else new NonEmpty(lst.head, toLinkedList(lst.tail))
}

def printLinkedList(head: Node): Unit = head match {
  case Empty =>
  case node: NonEmpty => {
    println(node.value)
    printLinkedList(node.next)
  }
}

/**
  * @param head
  * @param k
  * @return
  */
def removeNthElement(head: Node, k: Int):Node = head match {
  case Empty => head
  case node: NonEmpty =>
    if (node.next == Empty) Empty
    else {
      var prev: Node = Empty
      var slow: Node = head
      var fast: Node = head.next
      for (i <- 0 until k - 1 if fast != Empty) {
        fast = fast.next
      }
      while (fast != Empty) {
        prev = slow
        slow = slow.next
        fast = fast.next
      }
      prev match {
        case Empty => slow.next
        case p:NonEmpty => {
          if (p.next != Empty)
            p.next = p.next.next
          head
        }
      }
    }
}

val node = removeNthElement(toLinkedList(List(1,2,3)), 2)
printLinkedList(node)