CS350 - Exam 1 (100 Points)

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1 Spring 2013 Name CS350 - Exam 1 (100 Points) 1.(25 points) Stacks and Queues (a) (5) For the values 4, 8, 2, 5, 7, 3, 9 in that order, give a sequence of push() and pop() operations that produce the following stack configuration - all the values must be used, but each value may only be pushed/popped once. Be sure to indicate the order in which the operations are performed. (b) (10) Assume a queue is implemented with a fixed size array shown below. Under each operation, indicate the array index accessed for that operation. Also give the final configuration after the sequence of operations and indicate the head and tail elements. enqueue(3), enqueue(2), enqueue(1), dequeue() 0 enqueue(3), enqueue(2), enqueue(1), dequeue(), enqueue(4), dequeue(), enqueue(5), enqueue(2),dequeue(), dequeue(), enqueue(7)

2 (c) (7) Assume a queue is implemented with a circularly doubly linked list (with a sentinel node) where elements are inserted at the beginning of the list. Sketch the configuration (starting with the provided node) after the following sequence of operations in the figures below - be sure to indicate the sentinel node. (i) enqueue(3), enqueue(2), enqueue(1) (ii) enqueue(3), enqueue(2), enqueue(1), dequeue(), enqueue(4), dequeue(), enqueue(5) (d) (3) Briefly explain when it is advantageous for a queue to use an array backing structure that can be dynamically resized and when it is advantageous to use a linked list backing structure: Array: Linked list:

3 2.(25 points) Linked Lists (a) (4) For the following (non-circular) singly linked list, indicate on the diagram the order in which the pointers are accessed for the operation find(5) (b) (7) For a non-circular singly linked list, sketch an efficient insert operation for an element X and (using C++ish pseudocode) list the steps of the implementation. Assume the list contains a head pointer (note this is not a node but rather a pointer to a node) and each node contains a next pointer and a data field. Assume duplicate values are not allowed to exist in the list but the list implementation provides a find() method which takes a value x as an argument and returns a bool indicating whether or not x exists in the list. (c) (7) For a circular doubly linked list, give a (C++ish) pseudocode implementation for a remove() method which takes a value x as a parameter. Assume the list contains a sentinel node named dummy and each node contains next and prev pointers along with a data field. Additionally, you may assume the list implementation contains a findnode() method which takes a value x as an argument and returns a pointer to a node containing the value (or the dummy node if the value is not present).

4 (d) (7) Give (C++ish) pseudocode for a circularly singly linked list method listsum() to compute the sum of all the elements currently in the list. Assume the list contains a sentinel node named dummy and each node contains a next pointer and an int data field (hence the method will return an int). int listsum() {

3.(25 points) Skip Lists (a) (5) Show the final constructed skip list after inserting the following values in the given order at the specified levels (assume level 1 is the bottom level): 7 at

5 3.(25 points) Skip Lists (a) (5) Show the final constructed skip list after inserting the following values in the given order at the specified levels (assume level 1 is the bottom level): 7 at level 2, 4 at level 3, 10 at level 1, 1 at level 1 (b) (7) For the following skip list, enumerate the order in which pointers are touched or array levels are changed for the operation find(19)

6 (c) (5) For the following skip list, fill in the update[] array for the operation based on Pugh s implementation insert(6) at level 4 (d) (5) For the following skip list, fill in the update[] array for the operation based on Pugh s implementation remove(10) (e) (3) According to Pugh s article Skip Lists: A Probabilistic Alternative to Balanced Trees, briefly describe how the maximum number of levels for a skip list should be chosen?

7 4.(25 points) Runtimes (a) (21) Fill in the following table with asymptotic run times, i.e. O() notation, of the operations for each of the data structures (ignoring any memory allocation or array resizing costs) find(x) avg case find(x) worst case insert(x) avg case insert(x) worst case remove(x) avg case remove(x) worst case Stack (array backed) Queue (circular list backed) Singly Linked List (non-circular) Doubly Linked List (circular) Skip List (b) (2) Briefly explain when it is advantageous to use a skip list compared to a standard linked list. (c) (2) Briefly explain when it is advantageous to use a standard linked list compared to a skip list.

8. Fundamental Data Structures

172 8. Fundamental Data Structures Abstract data types stack, queue, implementation variants for linked lists, [Ottman/Widmayer, Kap. 1.5.1-1.5.2, Cormen et al, Kap. 10.1.-10.2] Abstract Data Types 173