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

複選題40. Which of the following statem ents are true? (A) An insertion in AVL tree requires Ω(logn) single- and double-rotations in the worst case. (B) An insertion in AVL trce requires O(1) single- and double-rotations in the worst case. (C) A deletion in AVL tree requires Ω(logn) single- and double-rotations in the worst case. (D) Adeletion in AVL tree requires O(1) singie- and double-rotations in the worst case. (E) There is no red left child in AA tree.

複選題41. Consider an AVL tree that results from successively inserting keys 2, 4, 5, 3, 8, 7, 1, 6, 9 into an initially empty tree. Which of the following statements are true? (A) The tree height is 4. (B) Key 3 and key 5 have the same depth. (C) Key 2 and key 8 have the same height. (D) Key 6 is a leaf. (E) Key 7 is the parent ofkey 9.

複選題42. Consider the splay tree in Figure 1. Which of the following statements are true? (Assume bottom-up splay, also assume the Join0 operation splays on the maximum element in the left tree, which then attaches the right tree.) (A) In Figure I, after deleting key 26, then key 33 is a child of key 48. (B) In Figure I , after deleting key 26, then key 17 is the root. (C) In Figure I, after inserting key 75, then key 64 is an ancestor of key 99. (D) In Figure I, after inserting key 75, then key 33 is a descendant of key 55. (E) In Figure I, after inserting key 75, then key 75 is the root.

複選題43. Consider the red-black tree in Figure 2, which of the following statements are true? (Assume bottom-up insertion/deletion) (A) In Figure 2, after inserting key 14, then there are 6 red nodes. (B) In Figure 2, after inserting key 54, then key 49 and key 54 are siblings. (C) In Figure 2, after deleting key 22, then key 25 and key 73 are siblings. (D) In Figure 2, after deleting key 66, then key 35 is red. (E) In Figure 2, after deleting key 83, then key 89 is red.

複選題44.Consider an AA tree that results from suc ccessively inserting keys 96, 49, 79, 14, 41, 87, 75, 90, 61 into an initially empty tree. Which of the following statements are true? (A) The root is key 61. (B) There is less than 3 horizontal links. (C) Key 41 and key 49 are in the same level. (D) Key 87 and key 96 are siblings. (E) Key 14 is the parent of key 4 1.

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