Menu Parser and Serializer

You are tasked with implementing logic to convert a restaurant menu between a plain text format and a tree data structure. The text format uses indentation to represent the hierarchy of categories and items.

Text Format

• The menu is provided as a multi-line string, where each non-empty line describes a single menu item.
• Leading indentation, consisting of zero or more groups of two spaces, indicates the nesting depth relative to top-level categories.
• Following the indentation, fields on each line are separated by the | character in the format: <type>|<id>|<name>|<price>.
  • type: A string label (e.g., CATEGORY, FOOD, SIDE). Do not assume only these three types; treat it as an arbitrary string.
  • id: A unique identifier string for the item.
  • name: Free text that is guaranteed not to contain the | character.
  • price: A decimal number (e.g., 5.99), or the literal - if the item does not have a price (e.g., a category).

Example Input:

CATEGORY|c1|Burgers|-
  FOOD|f1|Classic Burger|5.99
    SIDE|s1|Fries|1.99
  FOOD|f2|Veggie Burger|6.49
CATEGORY|c2|Drinks|-
  FOOD|f3|Cola|1.50
  FOOD|f4|Water|1.00

This example demonstrates a hierarchy like category > food > side, but the general depth and item types can vary.

Tree Structure

Define a language-agnostic data structure, MenuItem, with at least the following fields:

• type: string
• id: string
• name: string
• price: nullable/optional number (should be null if the text price is -)
• children: An ordered list or array of MenuItem objects, representing nested items.

Top-level menu items are those with zero indentation in the text format.

Tasks

1. parseMenu(text): Implement a function that accepts the menu text string and returns the corresponding tree. The output should be a list/array of top-level MenuItem nodes, with all children fields properly populated.
2. serializeMenu(items): Implement a function that accepts the tree (the list/array of top-level MenuItem nodes) and returns a canonical text representation. This output must exactly match the format described above.

Serializer Requirements:

• Use exactly two spaces for each level of indentation deeper than a parent.
• Use | as the field separator.
• Output - for items whose price is null or absent.
• Output a depth-first traversal, ensuring all children of a node appear immediately after their parent, in the order they are stored in the children list.

Assumptions and Constraints:

• You may assume the input text is always a valid, well-formed tree (i.e., no cycles, consistent indentation, and at least one top-level item).
• Design your parsing and serialization logic to run in O(N) time and O(N) extra space, where N is the number of menu items (lines) in the input.