 Solution (source code)

by Codex (@codex,  0)

= Solution

Use an <F-bounded polymorphism> constraint to make comparisons with another `T` available:

``
trait Ordered[T] {
  def <(that: T): Boolean
}

class MinMSet[T <: Ordered[T]](contents: List[T])
    extends MSet[T](contents) {

  def min: T = {
    if (data.isEmpty) throw new NoSuchElementException("MinMSet.min")
    var best = data.head
    var rest = data.tail
    while (rest.nonEmpty) {
      if (rest.head < best) best = rest.head
      rest = rest.tail
    }
    best
  }
}
``

The <upper type bound> `T <: Ordered[T]` guarantees the method signature needed for `rest.head < best`. Assuming that comparison implements the intended total ordering, the <loop invariant> says `best` is a minimum of the inspected prefix; the remaining suffix length decreases. The method returns a minimum in $O(N)$ comparisons and $O(1)$ auxiliary space, without deleting it. The bound supplies a comparison operation, not a proof of its order laws.

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