# Priority Queues - Ed. 2. and 3.: Chapter 7 – - Ed. 4.: Chapter 8 -

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Priority Queues - Ed. 2. and 3.: Chapter 7 – - Ed. 4.: Chapter 8 -

Priority Queues (Chapter 7) Priority Queue ADT -Keys, Priorities, and Total order Relations - Sorting with a Priority Queue Priority Queue implementation -Implementation with an unsorted sequence - Implementation with a sorted sequence

The Priority Queue Abstract Data Type

We want a comparison rule that will never contradict itself. This requires that the rule define a total order relation. total order relation: Reflexive property: k  k. Antisymmetric property: if k 1  k 2 and k 2  k 1, then k 1 = k 2. Transitive property: if k 1  k 2 and k 2  k 3, then k 1  k 3. Examples: Integers, real numbers, lexicographic order of character sequence.

v1  v2 if x2 - x1 = = x4 - x3 Then we have 4 - 1 = 7 - 4 Therefore, (1, 4)  (4, 7) and (4, 7)  (1, 4). But (1,4)  (7, 4), namely, the relation does not satisfy the antisymmetric property.

If a comparison rule defines a total order relation, it will never lead to a comparison contradiction. the smallest key: If we have a finite number of elements with a total order relation, then the smallest key, denoted by k min, is well-defined: k min is the key that satisfies k min  k for any other key k. Being able to find the smallest key is very important because in many cases, we want to have the element with the smallest key.

Sorting with a Priority Queue

Methods of a Priority Queue

Items in a Priority Queue

The Comparator Abstract Data Type

Class Lexicographic

Data Structure Exercises 14.1

Implementing a Priority Queue with a Sequence

O(n)

Class SortedSequencePriorityQueue

Selection Sort and Insertion Sort

O(n)O(n 2 ) O(n)

Data Structure Exercises 15.1

Implementing a Priority Queue with a Sequence

Class SortedSequencePriorityQueue

Selection Sort and Insertion Sort

Data Structure Exercises 15.1

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