Index handler with list of unused

Abstract view

Abstract data structure: Index handler

Implementation invariant:

1. There is an array [math]\displaystyle{ A }[/math] with index range [math]\displaystyle{ 1,...,N }[/math], and the component type is the value type of the map.
2. There is a set [math]\displaystyle{ U }[/math] (for unused) of natural numbers.
3. For each [math]\displaystyle{ i\in\{1,...,N_\text{max}\} }[/math] not in [math]\displaystyle{ U }[/math], [math]\displaystyle{ A[i] }[/math] is the value associated with key [math]\displaystyle{ i }[/math].

Methods

1. The constructor takes [math]\displaystyle{ N }[/math] as an argument, creates [math]\displaystyle{ A }[/math] and [math]\displaystyle{ U }[/math], and stores all potential keys [math]\displaystyle{ 1,\ldots,N }[/math] in [math]\displaystyle{ U }[/math].
2. The method for inserting a new value extracts a key [math]\displaystyle{ i }[/math] from [math]\displaystyle{ U }[/math], stores the value at <mah>A[i]</math>and returns [math]\displaystyle{ i }[/math].
3. The method to look up a value for a given key [math]\displaystyle{ i }[/math] returns [math]\displaystyle{ A[i] }[/math].
4. The method to remove a key re-inserts the key in [math]\displaystyle{ U }[/math].