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The Priority Queue abstract data type (operations)

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• Keys and Entries
  • Entry:

    An entry is the item of information that we want to store

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  • Key:

    A key is a property (type of value) of an entry by which comparisons between entries are made The key is a measure of how important an entry is...

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  • Note:

    The value of the key is not necessarily unique I.e.: two different entries can have the same key value (So the key is not used for identifying purpose --- if you know about Database Systems)

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• Properties of keys in a Priority queue
  • The key of the entries in a priority queue defines a total ordering on the entries

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  • The ordering on the keys is imposed by a comparison operator

    The comparison operator is denoted by the symbol

    ≤

    (because the less-than-or-equal operator also satisfies these rules...)

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  • To impose a total ordering, the following properties must hold on the ≤ operator:

    Reflexive property: For any key k: k ≤ k Anti-symmetric property: If (k1 ≤ k2) and (k2 ≤ k1) then:          k1 = k2 Transitive property: If (k1 ≤ k2) and (k2 ≤ k3) then:         k1 ≤ k3

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• Operations on a Priority Queue
  • Insert an entry into the priority queue:

    insert(key k, value x) (The key-value pair is an entry) Effect: Inserts the entry (k, x) into the priority queue

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  • Remove the most important (smallest) entry:

    removeMin() Effect: Removes the entry with the smallest ley from the priority queue

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• Example
  • Initial state:

    (empty)

  • insert(3, "John"):

    { (3, "John") }

  • insert(2, "Peter"):

    { (2, "Peter"), (3, "John") }

  • removeMin(): returns (2, "Peter")

    { (3, "John") }