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Priority Queues and Sorting CS 244 Brent M. Dingle, Ph.D. Game Design and Development Program Department of Mathematics, Statistics, and Computer Science.

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Presentation on theme: "Priority Queues and Sorting CS 244 Brent M. Dingle, Ph.D. Game Design and Development Program Department of Mathematics, Statistics, and Computer Science."— Presentation transcript:

1 Priority Queues and Sorting CS 244 Brent M. Dingle, Ph.D. Game Design and Development Program Department of Mathematics, Statistics, and Computer Science University of Wisconsin – Stout Content derived from: Data Structures Using C++ (D.S. Malik) and Data Structures and Algorithms in C++ (Goodrich, Tamassia, Mount)c

2 Previously Priority Queues Implemented as Unordered List Ordered List Heap Heap Description

3 Marker Slide General Questions? Next Priority Queues and Sorting

4 Sorting And Priority Queues Didn’t we mention something about sorting using priority queues there at the beginning… Must still be in the future…

5 What do we have so far Priority Queues as unordered lists ordered lists heaps (complete binary trees) What was the algorithm thing for sorting with Priority Queues…

6 Sorting Using a PQ Given a sequence of N items a PQ can be used to sort the sequence: Step 1 Insert N items into the PQ via insertItem(key, data) Step 2 Remove the items by calling removeItem() N times The first remove removes the largest item, the second call the second largest, … the last removes the smallest item

7 Sorting Using a PQ Given a sequence of N items a PQ can be used to sort the sequence: Step 1 Insert N items into the PQ via insertItem(key, data) Step 2 Remove the items by calling removeItem() N times The first remove removes the largest item, the second call the second largest, … the last removes the smallest item Algorithm PriorityQueueSort (S, PQ): Input: Sequence, S, of n items, and empty priority queue, PQ. Output: Sequence S sorted by the total order relation. while ! S.empty() do item := S.removeFirst() PQ.insertItem(item.key, item.data) while ! PQ.empty do item := PQ.removeItem() S.insertLast(item)

8 Example: Sorting Using a PQ Let’s say we had the sequence: (7, 4, 8, 2, 5, 3, 9) Let’s sort it using a PQ implemented as an unordered list Algorithm PriorityQueueSort (S, PQ): while ! S.empty() do item := S.removeFirst() PQ.insertItem(item.key, item.data) while ! PQ.empty do item := PQ.removeItem() S.insertLast(item) Phase 1 (first while loop) List| Priority Queue ================================ 4 8 2 5 3 9| 7 8 2 5 3 9| 7 4 2 5 3 9| 7 4 8 5 3 9| 7 4 8 2 3 9| 7 4 8 2 5 9| 7 4 8 2 5 3 | 7 4 8 2 5 3 9 Phase 2 (second while loop) List| Priority Queue ================================ 2| 7 4 8 5 3 9 2 3| 7 4 8 5 9 2 3 4| 7 8 5 9 2 3 4 5| 7 8 9 2 3 4 5 7| 8 9 2 3 4 5 7 8| 9 2 3 4 5 7 8 9|

9 Class Exercise Apply that PQ sorting algorithm to the sequence of values: (22, 15, 44, 10, 3, 9, 13, 25) Use an unordered list implementation of a PQ Basically do 8 insertItems and then 8 removeItems (or removeMins) Recall this is a LIST not a heap or binary tree Write the state of this PQ List after each insertItem and after each removeItem call 16 lines

10 Next Hold on to that result We need one more…

11 Example: Sorting Using a PQ Let’s say we had the sequence: (7, 4, 8, 2, 5, 3, 9) Let’s sort it using a PQ implemented as an ORDERED list Algorithm PriorityQueueSort (S, PQ): while ! S.empty() do item := S.removeFirst() PQ.insertItem(item.key, item.data) while ! PQ.empty do item := PQ.removeItem() S.insertLast(item) Phase 1 (first while loop) List| Priority Queue ================================ 4 8 2 5 3 9| 7 8 2 5 3 9| 4 7 2 5 3 9| 4 7 8 5 3 9| 2 4 7 8 3 9| 2 4 5 7 8 9| 2 3 4 5 7 8 | 2 3 4 5 7 8 9 Phase 2 (second while loop) List| Priority Queue ================================ 2| 3 4 5 7 8 9 2 3| 4 5 7 8 9 2 3 4| 5 7 8 9 2 3 4 5| 7 8 9 2 3 4 5 7| 8 9 2 3 4 5 7 8| 9 2 3 4 5 7 8 9|

12 Class Exercise Apply that PQ sorting algorithm to the sequence of values: (6, 5, 3, 1, 8, 7, 2, 4) Use an ordered list implementation of a PQ Basically do 8 insertItems and then 8 removeItems (or removeMins) Recall this is a LIST not a heap or binary tree Write the state of this PQ List after each insertItem and after each removeItem call 16 lines

13 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version

14 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version The relation between the two sorts is a little tricky to see because of the SWAPs done It’s the selection of the smallest value that makes them connected. So X out the red numbers 1 at a time – use line 1

15 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version The relation between the two sorts is a little tricky to see because of the SWAPs done It’s the selection of the smallest value that makes them connected. So X out the red numbers 1 at a time – use line 1

16 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version The relation between the two sorts is a little tricky to see because of the SWAPs done It’s the selection of the smallest value that makes them connected. So X out the red numbers 1 at a time – use line 1

17 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version The relation between the two sorts is a little tricky to see because of the SWAPs done It’s the selection of the smallest value that makes them connected. So X out the red numbers 1 at a time – use line 1

18 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version The relation between the two sorts is a little tricky to see because of the SWAPs done It’s the selection of the smallest value that makes them connected. So X out the red numbers 1 at a time – use line 1

19 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version The relation between the two sorts is a little tricky to see because of the SWAPs done It’s the selection of the smallest value that makes them connected. So X out the red numbers 1 at a time – use line 1

20 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version The relation between the two sorts is a little tricky to see because of the SWAPs done It’s the selection of the smallest value that makes them connected. So X out the red numbers 1 at a time – use line 1

21 Similar? Selection Sort versus Unordered List PQ Sort 22 15 44 10 3 9 13 25 3 15 44 10 22 9 13 25 3 9 44 10 22 15 13 25 3 9 10 44 22 15 13 25 3 9 10 13 22 15 44 25 3 9 10 13 15 22 44 25 3 9 10 13 15 22 25 44 3 | 22 15 44 10 9 13 25 3 9 | 22 15 44 10 13 25 3 9 10 | 22 15 44 13 25 3 9 10 13 | 22 15 44 25 3 9 10 13 15 | 22 44 25 3 9 10 13 15 22 | 44 25 3 9 10 13 15 22 25 | 44 3 9 10 13 15 22 25 44 | Phase 2 (second while loop) List | Priority Queue ================================================ enhanced version The relation between the two sorts is a little tricky to see because of the SWAPs done It’s the selection of the smallest value that makes them connected. So X out the red numbers 1 at a time – use line 1

22 Similar comparison for Insertion Next Slide enhanced version

23 Similar? Insertion Sort versus Ordered List PQ Sort Phase 1 (first while loop) List | Priority Queue ================================================ 5 3 1 8 7 2 4 | 6 3 1 8 7 2 4 | 5 6 1 8 7 2 4 | 3 5 6 8 7 2 4 | 1 3 5 6 7 2 4 | 1 3 5 6 8 2 4 | 1 3 5 6 7 8 4 | 1 2 3 5 6 7 8 | 1 2 3 4 5 6 7 8 enhanced version 6 5 3 1 8 7 2 4 5 6 3 1 8 7 2 4 3 5 6 1 8 7 2 4 1 3 5 6 8 7 2 4 1 3 5 6 7 8 2 4 1 2 3 5 6 7 8 4 1 2 3 4 5 6 7 8

24 Similar? Insertion Sort versus Ordered List PQ Sort Phase 1 (first while loop) List | Priority Queue ================================================ 5 3 1 8 7 2 4 | 6 3 1 8 7 2 4 | 5 6 1 8 7 2 4 | 3 5 6 8 7 2 4 | 1 3 5 6 7 2 4 | 1 3 5 6 8 2 4 | 1 3 5 6 7 8 4 | 1 2 3 5 6 7 8 | 1 2 3 4 5 6 7 8 enhanced version 6 5 3 1 8 7 2 4 5 6 3 1 8 7 2 4 3 5 6 1 8 7 2 4 1 3 5 6 8 7 2 4 1 3 5 6 7 8 2 4 1 2 3 5 6 7 8 4 1 2 3 4 5 6 7 8 This one is a little easier to see

25 Why the comparisons? We defined a sorting algorithm generically for a priority queue Using 2 different implementations of a PQ data structure we arrived at 2 different implementations of the sorting algorithm Or rather the Priority Queue algorithm unified the 2 “already existing” sorting algorithms into 1 generic description Sadly, in these cases both were O(n 2 ) However, that O(n 2 ) is NOT inherent in the PQ algorithm… just the implementation We will see this when we apply the same algorithm but using the Heap implementation

26 The End of This Part End

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