1. Alyce Brady CS 470: Data Structures CS 510: Computer Algorithms Breadth-First Binary Tree Traversal Algorithm

2. Reminder: Breadth-First Traversal A BC DEFG A B C D E F G

3. Pseudo-Code for Breadth-First Traversal breadth-first-traversal put root node onto a queue while the queue is not empty dequeue the next node visit the node e.g., print value enqueue the left child node enqueue the right child node

4. Breadth-First Search A BC DEFG A B C D E F G Queue: Current:

5. Breadth-First Search A BC DEFG Queue: Current: A

6. Breadth-First Search A BC DEFG Queue: Current: A A

7. Breadth-First Search A BC DEFG Queue: Current: A A A

8. Breadth-First Search A BC DEFG Queue: Current: B A A A

9. Breadth-First Search A BC DEFG Queue: Current: CBCB A A A

10. Breadth-First Search A BC DEFG Queue: Current: B A A CBCB

11. Breadth-First Search A BC DEFG Queue: Current: B C A B

12. Breadth-First Search A BC DEFG Queue: Current: DCDC B A B

13. Breadth-First Search A BC DEFG Queue: Current: EDCEDC B A B

14. Breadth-First Search A BC DEFG Queue: Current: C EDCEDC A B

15. Breadth-First Search A BC DEFG Queue: Current: C A B C EDED

16. Breadth-First Search A BC DEFG Queue: Current: C A B C FEDFED

17. Breadth-First Search A BC DEFG Queue: Current: C A B C GFEDGFED

18. Breadth-First Search A BC DEFG Queue: Current: D A B C GFEDGFED

19. A B C D Breadth-First Search A BC DEFG Queue: Current: D GFEGFE

20. Breadth-First Search A BC DEFG A B C D Queue: Current: E GFEGFE

21. Breadth-First Search A BC DEFG Queue: Current: E GFGF A B C D E

22. Breadth-First Search A BC DEFG Queue: Current: F GFGF A B C D E

23. Breadth-First Search A BC DEFG Queue: Current: F G A B C D E F

24. Breadth-First Search A BC DEFG Queue: Current: G G A B C D E F

25. Breadth-First Search A BC DEFG Queue: Current: G A B C D E F G

26. Breadth-First Search A BC DEFG A B C D E F G

27. Time and Space Complexity for Breadth-First Search Alg. Time Complexity Time Complexity –Consider each node twiceO(n) when put on queue when put on queue when taken from queue when taken from queue

28. Space Complexity Space Complexity –Queue to handle unexplored nodes Queue length = width of lowest level(n/2) Queue length = width of lowest level(n/2) O(n) O(n) Time and Space Complexity for Breadth-First Search Alg.