1. The transitive closure matrix of the given directed graph have k elements that are 1's. What is true about k?

(A)k≤6
(B)7≤k≤10
(C)11≤k≤14
(D)15≤k≤18
(E)k≥19

2. Consider a pair of corresponding infix and postfix arithmetic expressions. Which of the following statements is true? (A) In a postfix expression, the order of operators is from high to low precedence.(B) The infix and postfix expressions always have the same number of parentheses. (C) The infix and postfix expressions always have the same order of operands. (D) A priority queue for the operators is required when evaluating a postfix expression. (E) All of the above.

3. Below is the C++ implementation of ADTX, an unknown abstract data type. For clarity, exception handling codes are omitted. Which of the following is the most likely abstract data type implemented here? (A) stack(B) first-in-first-out queue (C) priority queue (D) linked list (E) none of the above

4. For the ADTX implementation in the previous question, after the following C++ code is executed, what is the value in adtx. x[1]? (A)6(B)9(C)3(D)7 (E)5 

5. For the postorder traversal sequence of the binary tree below, which of these statements is true?(A) Node B appears at the second position. (B) Node M appears after node D. (C) Node H appears immediately before node J. (D) The first four nodes in the sequence are all leaf nodes in the tree. (E) Node A appears between node B and node D.

6. If we make the binary tree in the previous question a threaded binary tree, which node is pointed to by a thread of node B? (A) node A (B)nodeE (C) nodeD (D)nodeF (E) node

7. For a certain binary tree, its inorder traversal sequence is EKHDAGBJFC and its level-order traversal sequence is GKBEAFHJCD. Here each letter represents a node of the tree. Which of the following statements about this binary tree is incorrect? (A) Node D is a descendent of node K. (B) There are exactly four leaf nodes. (C) Node G is the root and has two children. (D) The parent of node H is node A. (E) None of the above.

8. Starting with an empty binary search tree, what is the maximum level of the nodes in the tree after this series of insertions: 3. 9, 1, 2, 7, 6, 5, 4, 8, 0? Note: the level of the root is one. No balancing operation occurs at insertions. (A)3 or less (B)4 (C) 5 (D) 6 (E) 7 or more

9. A max-heap is given below； the numbers at the nodes are their keys. Now after one insertion operation (the number inserted is 14) and then one deletion operation, which of the following statements is false regarding the resulting heap? Here node (n) represents the node with key n. (A) The parent of node (4) is node (11). (B) node (13) has two children. (C) The position of node (10) in the tree does not change. (D) node (17) is the root. (E) The number of leaf nodes does not change.

10. For a doubly-linked list class, each of its nodes has two links left and right to its two neighboring nodes. Assume that we want to implement a member function ShiftRight, which takes an input x, a pointer to a node, and swaps that node with the node to its right. Let us further assume that neither xx nor the node to its right is the first or the last node of the list. There are six pointers to be set, and the statements, labeled s1 to s6, are listed in the box below. Which of the following ordering of these statements will produce the correct behavior? (A)s5→s2→s6→s1→s4→s3 (B)s2→s5→s4→s3→s1→s6 (C)s4→s3→s6→s1→s2→s5 (D)s1→s2→s3→s6→s5→s4 (E)s4→s5→s3→s6→s1→s2

11. Consider the AVL tree resulting from sequentially inserting the following numbers into an empty AVL tree: 40 60 55 15 20 5 25 30What is the sum of the numbers in the leaf nodes in the AVL tree? (A)90 (B) 130 (C) 155(D) 160 (E) none of the above

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