12. Consider the Red-Black tree resulting from sequentially inserting the following numbers into an empty Red-Blacktree:40 60 55 15 20 5 25 30
What is the sum of the numbers in the red nodes in the Red-Black tree?
(A)90
(B) 130
(C) 155
(D) 160
(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

13. Consider the B-tree, say T', resulting from sequentially inserting the following numbers into the following B-tree T with order 3:  15 20  5  25 30 What is the sum of the keys in the non-leaf nodes in T'? (A) 95 (B) 100 (C) 110 (D) 120 (E) none of the above

14. Consider the B+-tree, say T', resulting from sequentially inserting the following numbers into the following B+-tree T with order 3:  15 20 5 25 30 What is the sum of the keys in the non-leaf nodes in T'? (A) 95(B) 100 (C) 110(D) 120(E) none of the above

15. Consider the given directed graph. Let dist(i, j) be the length of the shortest path from node i to node j. What is dist(A,C)+dist(A,E)+dist(A,F)?(A) 10 (B) 12 (C) 13 (D) 15 (E) None of the above.

16. Consider the graph in the previous problem. Let dist(i, j) be the length of the shortest path from node i to node j. What is dist(A,F)+dist(B,F) +dist(C,F)+dist(D,F)+dist(E,F)? (A)7 (B)8 (C)9 (D)10 (E) none of the above

17. Consider the following activity network. What is the length of the critical path?(A)14 (B) 16 (C) 18(D) 20(E) none of the above

18. Consider six nodes with weights 2, 4, 6, 8, 10 and 12, respectively. Give the weighted external path length of the Hufiman tree with the above six nodes as external nodes. (A)95 (B) 100(C) 102 (D)104 (E) none of the above