Chapter 13: Data structures

Transcription

1 Chapter 13: Data structures ANSWERS TO QUESTIONS IN THE STUDENT S BOOK Page Explain what is meant by the following terms: (a) list (b) stack (c) queue (d) array (a) A list organises data by index so there is no need to set up a structure in advance. Data in these structures can be modified, added or deleted at any stage. (b) A stack is a Last In First Out data structure; that is, the last item placed in the stack is the first one to be removed. (c) A queue is a First In First Out structure where the data that has been in the queue longest is the first to be removed. (d) Arrays are data structures that store data under a single identifier by index. Arrays may be multi-dimensional, for example a two-dimensional list is like a table of data with rows and columns. 2. Using a suitable pseudocode language, devise algorithms to implement: (a) an LIFO stack (b) a queue. Adding and removing data from stacks and queues is covered on pages 158 and Using a suitable high-level language, implement these algorithms and test them with suitable data. Allow for a maximum of 10 data items. Coding task is language dependent so no answer supplied. 1. In pseudocode, write a program to store a value input by the user into the first available space in a 5 by 5 two-dimensional array.

2 The answer should include a check for each space in turn (nested loop) to locate the first empty location to store the input data. Coded solutions should be accepted. 2. A stack contains the values 3,4,5, with 3 being the first value stored and 5 the last. Show how the stack changes when the following sequence of commands is used: Pop Push 7 Pop Push 8 Push A queue contains the values 3,4,5, with 3 being the first value stored and 5 the last. Show how the queue changes when the following sequence of commands is used: Pop Push 7 Pop Push 8 Push Using pseudocode and the data 6,18,21,34,61, devise suitable algorithms to implement a: (a) stack (b) queue. This is test data to be used with question 3 above.

3 Page 164 The data items Mouse, Cat, Apple, Horse and Fox are stored in a list in that order. The list is sorted alphabetically. 1. Represent this as a linked list using a diagram. 2. Show the linked list after the data item Donkey has been added to the first free space. 3. Show the list when Cat is removed from the linked list. 4. Write an algorithm in pseudocode to delete an item from the list. 5. Write an algorithm in pseudocode to add an item to the list Solution outlines are in the Student s Book on page Solution outlines are in the Student s Book on pages Page Create a tree from the data Melon, Pear, Banana, Apple, Orange, Rhubarb, Damson. Where the left pointer means precedes alphabetically and the right pointer means follows alphabetically.

4 2. For this tree, list the nodes in the order visited for: (a) preorder traversal (b) inorder traversal (c) postorder traversal. (a) ABCDEFGH (b) CBDAEGFH (c) CDBGHFEA s 3. Write an algorithm in pseudocode for inorder traversal of a tree. 4. Write an algorithm in pseudocode for postorder traversal of a tree. 5. Write an algorithm in pseudocode for preorder traversal of a tree. s Pages of the Student s Book give the basis for these algorithms.

5 6. Convert the following reverse Polish expressions into infix notation: (a) AB+C* (b) ABC/D*T+- (a) (A + B) * C (b) A (B/C * D) + T 7. Convert the following infix notation expressions into reverse Polish notation: (a) A*B-(C+D)*E (b) A+B*C/D (a) AB*CD+E* (b) ABC*D/+ 8. Show how the following would be carried out using a stack: (a) / (b) * (a) Push(9) Push(3) Pop Pop Push(6)Push(2)/Pop Pop Push(3) (b) Push(9) Push(3) Push(1) Pop Pop Push(2) *Pop Pop Push(18) Page Write an algorithm to locate a node in an undirected graph and report if not found.

6 The algorithm is outlined in the Student s Book: the depth-first approach on page 169 and breadth first on page 170. Modify the conditions slightly to stop when node found or report when not found. Further discussion and algorithms for graphs can be found in chapter Draw the adjacency matrix for the following graph. A B C D E F A 6 5 B C 3 D 7 E 3 7 F For the following graph, show the traversal of the tree using: (a) depth-first traversal (b) breadth-first traversal.

7 (a) Stack E D C C F F B B B B B B A A A A A A A Visited A B C E F D (b) Queue B B D D D C F F E D C C F E F B Visited A B D C F E Current node A A A B B B D C C F E Page 172 Use the hashing function address =k(k+3)mod m, where k is the key field and m the bucket size, select a suitable bucket size to hold at least 250 data items to calculate an address for the following values: (a) 101 (b) 232 (c) ANN 251 is a prime number larger than 250 so we can use this as a value for m: (a) (101*101)MOD251 = 161 (b) (232*232)MOD251 = 110 (c) ANN replaced by could be (657979*657979)MOD251 = 118 Alternatively = 223 (223*223)MOD 251 = 31 Page The items 12, 3, 8 and 17 are stored in a linked list. (a) Draw a diagram showing these items in a linked list sorted numerically. (b) Draw a diagram showing the value 5 inserted into the list. (c) Draw a diagram showing the value 8 removed from the list.

8 (a) (b) (c) 2. Draw a diagram for the tree with the data items Harry, Ben, Daisy, Mohammed, Peter, Afshin, where the left pointer means precedes alphabetically and the right pointer means follows alphabetically. List the items in the order they are retrieved by postorder traversal of the tree. 3. Using a tree, convert the expression (A+B/C)/(D E) into reverse Polish.

9 ABC/+DE / 4. Convert the reverse Polish expression AB+CD EF/** into infix algebraic notation. (A+B)*(C D)*E/F 5. Draw the graph represented by the edges: {(A,B,5),(A,D,4),(A,E,3),(B,A,5),(C,D,3),(D,B,2),(D,C,3),(D,F,4), (E,F,6),(F,D,4)} Something like this; nodes may be arranged differently:

10 6. Show the traversal of the following tree using depth-first traversal: Stack C C B B E E E F F F D D D D D D D A A A A A A A A Visited A D E C F B 7. Where k is the key value and m the number of locations required, use the hashing function k(k+3)mod m to find an address for the data with key value 121 where m is (121+4)MOD 113 = 96