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

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Presentation on theme: "Priority Queues - Ed. 2. and 3.: Chapter 7 – - Ed. 4.: Chapter 8 -"— Presentation transcript:

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

2 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

3 The Priority Queue Abstract Data Type

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7 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.

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

9 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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12 Sorting with a Priority Queue

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18 Methods of a Priority Queue

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21 Items in a Priority Queue

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23 The Comparator Abstract Data Type

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25 Class Lexicographic

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31 Data Structure Exercises 14.1

32 Implementing a Priority Queue with a Sequence

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38 O(n)

39 Class SortedSequencePriorityQueue

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42 Selection Sort and Insertion Sort

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

46 Data Structure Exercises 15.1

47 Implementing a Priority Queue with a Sequence

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54 Class SortedSequencePriorityQueue

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57 Selection Sort and Insertion Sort

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61 Data Structure Exercises 15.1


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