/* -----------------------------------------------------------------------------
Copyright 2021 Kevin P. Barry

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
----------------------------------------------------------------------------- */

// Author: Kevin P. Barry [ta0kira@gmail.com]

concrete TreeSet<#k> {
  refines Container
  refines DefaultOrder<#k>
  refines SetReader<#k>
  refines SetWriter<#k>
  #k defines LessThan<#k>

  // Create a new set.
  @type new () -> (#self)

  // Traverse in the default order.
  //
  // Notes:
  // - This is from DefaultOrder, but is made explicit for documentation.
  // - Traversal of the entire set is amortized O(n); however, the cost of any
  //   particular iteration could be up to O(log n).
  // - The overall memory cost is O(log n).
  @value defaultOrder () -> (optional Order<#k>)

  // Traverse the set in the reverse order of defaultOrder().
  //
  // Notes:
  // - Traversal of the entire set is amortized O(n); however, the cost of any
  //   particular iteration could be up to O(log n).
  // - The overall memory cost is O(log n).
  @value reverseOrder () -> (optional Order<#k>)

  // Start forward traversal (same as defaultOrder()) from the specified key.
  //
  // Notes:
  // - If the key does not exist in the SearchTree, the position right after
  //   where it would be (in the forward direction) is returned.
  @value getForward (#k) -> (optional Order<#k>)

  // Start reverse traversal (same as reverseOrder()) from the specified key.
  //
  // Notes:
  // - If the key does not exist in the SearchTree, the position right after
  //   where it would be (in the reverse direction) is returned.
  @value getReverse (#k) -> (optional Order<#k>)
}