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

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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

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The Priority Queue Abstract Data Type

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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.

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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.

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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.

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Sorting with a Priority Queue

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Methods of a Priority Queue

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Items in a Priority Queue

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The Comparator Abstract Data Type

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Class Lexicographic

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Data Structure Exercises 14.1

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Implementing a Priority Queue with a Sequence

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O(n)

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Class SortedSequencePriorityQueue

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Selection Sort and Insertion Sort

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

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Data Structure Exercises 15.1

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Implementing a Priority Queue with a Sequence

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Class SortedSequencePriorityQueue

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Selection Sort and Insertion Sort

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Data Structure Exercises 15.1

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THE WELL ORDERING PROPERTY Definition: Let B be a set of integers. An integer m is called a least element of B if m is an element of B, and for every x.

THE WELL ORDERING PROPERTY Definition: Let B be a set of integers. An integer m is called a least element of B if m is an element of B, and for every x.

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