(a) Show the bracket notation for the list of Figure 12.19(a). (b) Show the bracket notation for the list of Figure 12.19(b). (c) Show the bracket notation for the list of Figure 12.19(c).

(a) Show the BST that results from inserting the values 15, 20, 25, 18, 16, 5, and 7 (in that order). (b) Show the enumerations for the tree of (a) that result from doing a preorder traversal, an inorder traversal, and a postorder traversal.

(a) Show the heap that results from deleting the maximum value from the max-heap of Figure 5.20b. (b) Show the heap that results from deleting the element with value 5 from the max-heap of Figure 5.20b.

(a) Show the result (including appropriate rotations) of inserting the value 39 into the AVL tree on the left in Figure 13.4. (b) Show the result (including appropriate rotations) of inserting the value 300 into the AVL tree on the left in Figure 13.4. (c) Show the result (including appropriate rotations) of inserting the value 50 into the AVL tree on the left in Figure 13.4. (d) Show the result...

(a) Show the result of building a bintree from the following points (inserted in the order given). Assume the tree is representing a space of 64 by 64 units. A (20, 20), B (10, 30), C (25, 50), D (35, 25), E (30, 45), F (30, 35), G (45, 25), H (45, 30), I (50, 30). (b) Show the result of deleting point C from the tree you built in part (a). (c) Show the result of deleting point F from the...

(a) Show the result of building a k-d tree from the following points (inserted in the order given). A (20, 20), B (10, 30), C (25, 50), D (35, 25), E (30, 45), F (30, 35), G (55, 40), H (45, 35), I (50, 30). (b) Show the result of deleting point A from the tree you built in part (a).

(a) Show the result of building a PR quadtree from the following points (inserted in the order given). Assume the tree is representing a space of 64 by 64 units. A (20, 20), B (10, 30), C (25, 50), D (35, 25), E (30, 45), F (30, 35), G (45, 25), H (45, 30), I (50, 30). (b) Show the result of deleting point C from the tree you built in part (a). (c) Show the result of deleting point F from the...

(a) Show the result of deleting F from the PR quadtree of Figure 13.16. (b) Show the result of deleting records E and F from the PR quadtree of Figure 13.16.

(a) Suppose that a particular algorithm has time complexity T(n) = 3 × 2n, and that executing an implementation of it on a particular machine takes t seconds for n inputs. Now suppose that we are presented with a machine that is 64 times as fast. How many inputs could we process on the new machine in t seconds? (b) Suppose that another algorithm has time complexity T(n) = n2, and that executing...

(a) Use induction to show that n2 - n is always even. (b) Give a direct proof in one or two sentences that n2 - n is always even. (c) Show that n3 - n is always divisible by three. (d) Is n5 - n a ways divisible by 5? Explain your answer.