Dial implementation

General information

Abstract Data Structure: Bounded monotonous priority queue

Implementation Invariant:

1. For each object of "Dial implementation", there is
   1. a specific maximum span of keys [math]\displaystyle{ S_\text{max}\in\mathbb{N} }[/math],
   2. an array [math]\displaystyle{ A }[/math] with index set [math]\displaystyle{ \{0,\ldots,S-1\} }[/math] sets of (key,value)-pairs,
   3. a current position [math]\displaystyle{ P\in\mathbb{N}_{0} }[/math], which is dynamically changing,

All keys at an index of [math]\displaystyle{ A }[/math] are equal. For [math]\displaystyle{ i=P,P+1,P+2,\ldots, }[/math]

In particular, the minimum key is associated with …

Remark

The implementations of the methods Bounded priority queue: number and Bounded priority queue: find minimum are trivial and, hence, left out here.