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Summer Final Solutions to last three problems

Summer Final Solutions to last three problems. Bryce Boe CS24 , Fall 2013. Problem 11. Draw the contents of the array that represents the following max-heap after calling dequeue 3 times. The following are the initial contents of the array. 60 40 10 25 0 3 1 4. Problem 11: Suggestions.

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Summer Final Solutions to last three problems

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  1. Summer FinalSolutions to last three problems Bryce Boe CS24, Fall 2013

  2. Problem 11 Draw the contents of the array that represents the following max-heap after calling dequeue 3 times. The following are the initial contents of the array. 60 40 10 25 0 3 1 4

  3. Problem 11: Suggestions • Convert the array into a tree representation • No required, but makes it more likely for you to receive partial credit if you make a mistake • Show the resulting tree after each removal • Convert the final tree back into the array form

  4. Problem 11: Initial Heap

  5. Problem 11: First Dequeue

  6. Problem 11: Second Dequeue

  7. Problem 11: Third Dequeue

  8. Problem 11: Solution

  9. Problem 12 Draw the contents of a hash table of size 8 with a linear probing constant of 3 after inserting the following items. Hash function: h(x) = x % 8 7 2 15 5 12 4

  10. Problem 12: Suggestions • Again it might be useful to show the complete contents after each insertion in the event you make a mistake.

  11. Problem 12: Insert 7

  12. Problem 12: Insert 2

  13. Problem 12: Insert 15 (2) Second position occupied, try again (1) Initial position occupied, try again

  14. Problem 12: Insert 5 (1) Initial position occupied, try again

  15. Problem 12: Insert 12

  16. Problem 12: Insert 4 (3) Third position occupied, try again (1) Initial position occupied, try again (2) Second position occupied, try again (5) Fifth position occupied, try again (4) Fourth position occupied, try again

  17. Problem 12: Solution

  18. Problem 13 Assume we have a poorly implemented hash table of size 8 with a linear probing constant of 1 that does not properly record deletions. Beginning with the following filled hash table, which elements (numbers) are no longer accessible after removing both 10 and 14? Hash function: h(x) = x % 8

  19. Problem 13: Suggestions • Remove elements 10 and 14 • For each element test if it’s reachable

  20. Problem 13: Remove elements

  21. Problem 13: contains(8)? (1) 8 % 8 == 0 PASS

  22. Problem 13: contains(7)? (2) (7 + 1) % 8 == 0 occupied -- next 7 % 8 == 7 occupied -- next (3) (0 + 1) % 8 == 1 PASS

  23. Problem 13: contains(1)? (1) 1 % 8 == 1 occupied -- next (2) (1 + 1) % 8 == 2 unoccupied -- FAIL

  24. Problem 13: contains(12)? (1) 12 % 8 == 4 PASS

  25. Problem 13: contains(2)? (1) 2 % 8 == 2 unoccupied -- FAIL

  26. Problem 13: contains(6)? (1) 6 % 8 == 6 unoccupied -- FAIL

  27. Problem 13: Solution • Items 1, 2, and 6 are no longer reachble

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