29. For a binary heap of height 2021, let x be the minimumn possible size, y be the maximum possible size, then (3xty) mod 5
(A) 0
(B) 1
(C)2
(D)
(E) 4

30. Consider a binary heap that results from successively inserting keys 6, 3, 7, 8, 5, 1, 2, 4, 9 into an initially empty heap. Then the depth of key 5 is (A)0 (B)1 (C) 2 (D) 3(E) None of above

31. A binomial heap contains 2021 items. How many among them have depth 7? (A) 165 (B) 170 (C) 175 (D) 180 (E) 185

32. If Dijkstra algorithm is implemented with Binomial heap as priority qucue, then the complexity is (A) O(|V|2+|E| log|V|) (B) O(|V|2) (C) O(|E| log|V|) (D) O(|E|  ||+|V| log|V|)(E) O(|E|)

33. If Dijkstra algorithm is implemented with Fibonacci heap as priority queue, then the complexity is (A) O(|V|2+|E| log |V|) (B) O(|V|2) (C) O(|E| log|V|) (D) O(|E|+I|V| log(|V|) (E) O(|E|)

34. If Dijkstra algorithn is implemented with binary heap as priority queue, then the complexity is (A) O(|V|2+[IEl log|V|) (B) O(|V|2) (C) O(|E|log|V|) (D)O(|E|+|V|logIV|) (E) O(|E|)

35. If Dijkstra algorithm is implemented with doubly-linked Iist as prionity qucue, then the complexity is (A) O(|V|2+1Ellog|V|) (B) O(|V|2) (C) O(|E|log|V|) (D) O(|E|+|V| log|V|) (E) O(|E|)

複選題36. Which of the following statements are true? (A) [logn]! = 0(n2) (B) (logn)n = 0(n!) (C) log(n!) = O(nlogn) (D) log* n = O(log *logn) (E)

複選題37. Which of the following statements are true? (A) Stack implements a FIFO (first-in-first-out) policy. (B) Queue implements a LIFO (last-in-first-out) policy. (C) Stack can be realized by deque (double-ended qucue). (D) The Find() operation in a doubly linked list takes O(n) time. (E) The EnqueueO operation in a queue takes O(1) time.

複選題38. Consider a binary scarch tree that results from successively inserting keys 2, 8, 9, 1, 5. 7, 6, 3, 4 into an initially empty tree. Which of the following statements are true? (A) The tree height is 4. (B) Key 8 is prior to key 3 in terms of pre-order traversal. (C) Key 2 is prior to key 7 in terns of post-order traversal. (D) Key 4 is prior to key 5 in terms of in-order traversal. (E) Key 3 and key 9 are siblings.

複選題39. Which of the following are balanced search trees? (A) Binary search tree (B) Red-black trec (C) AVL tree (D) 2-3-4 tree (E) Splay tree

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