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Comp 352 – Fall 2012

Comp 352 – Fall 2012. Tutorial Session 3. Session Outline. Quick Overview on Stacks: Definition Methods Quick Overview on Queues : Definition Methods Implementation General Overview Highlights on Queue Implementation Using a Circular Array Problem Solving.

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Comp 352 – Fall 2012

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  1. Comp 352 – Fall 2012 Tutorial Session 3

  2. Session Outline • Quick Overview on Stacks: • Definition • Methods • Quick Overview on Queues: • Definition • Methods • Implementation • General Overview • Highlights on Queue Implementation Using a Circular Array • Problem Solving

  3. The Stack ADT -Definition A stack is a collection of objects that are inserted and removed according to the last-in first-out (LIFO) principle. Objects can be inserted into a stack at any time, but only the most recently inserted (that is, "last") object can be removed at any time.

  4. The Stack ADT -Methods • push(e): Insert element e, to be the top of the stack. • pop(): Remove from the stack and return the top element on the stack; an error occurs if the stack is empty. • size(): Return the number of elements in the stack. • isEmpty(): Return a Boolean indicating if the stack is empty. • top(): Return the top element in the stack, without removing it; an error occurs if the stack is empty.

  5. The Queue ADT -Definition • A queue, a close "cousin" of the stack, is a collection of objects that are inserted and removed according to the first-in first-out (FIFO) principle. That is, elements can be inserted at any time, but only the element that has been in the queue the longest can be removed at any time. • We usually say that elements enter a queue at the rear and are removed from the front.

  6. The Queue ADT -Methods • enqueue(e): Insert element e at the rear of the queue. • dequeue(): Remove and return from the queue the object at the front; an error occurs if the queue is empty. • size(): Return the number of objects in the queue. • isEmpty(): Return a Boolean value that indicates whether the queue is empty. • front(): Return, but do not remove, the front object in the queue; an error occurs if the queue is empty.

  7. The Stack & Queue ADT -Implementations • The methods of both the Stack and Queue ADTs can be implemented via: • An array-based implementation • A generic linked list-based implementation • A circular array is used for the implementation of a Queue to avoid an O(n) performance for its Dequeue() operation, as well as an array-out-of-bounds error.

  8. Highlights on a Queue Implementation Using a Circular Array • The following variables are defined: • f: index to the cell storing the first element in the queue (candidate to be removed) • r: index to the next available cell • Operations: • size()  (N – f + r) modN • isEmpty()  f = r • enqueue(x)  r = (r + 1) modN • dequeue()  f = (f + 1) modN

  9. Problem Solving -R-5.3 Suppose an initially empty stack S has performed a total of 25 push operations, 12 top operations, and 10 pop operations, 3 of which generated StackEmptyExceptions, which were caught and ignored. What is the current size of S?

  10. Problem Solving -R-5.5 Describe the output of the following series of stack operations: push(5), push(3), pop(), push(2), push(8), pop(), pop(), push(9), push(1), pop(), push(7), push(6), pop(), pop(), push(4), pop(), pop().

  11. Problem Solving -R-5.6 Give a recursive method for removing all the elements in a stack.

  12. Problem Solving -R-5.8 Describe the output for the following sequence of queue operations: enqueue(5), enqueue(3), dequeue(), enqueue(2), enqueue(8), dequeue(), dequeue(), enqueue(9), enqueue(1), dequeue(), enqueue(7), enqueue(6), dequeue(), dequeue(), enqueue(4), dequeue(), dequeue().

  13. Problem Solving -R-5.9 Suppose an initially-empty queue Q has performed a total of 32 enqueueoperations, 10 front operations, and 15 dequeue operations, 5 of which generated QueueEmptyExceptions, which were caught and ignored. What is the current size of Q?

  14. Problem Solving -R-5.10 If the queue of the previous problem was implemented with an array of capacity N = 30, as described in the chapter, and it never generated a FullQueueException, what would be the current values of f and r?

  15. Problem Solving -C-5.4 Suppose Alice has picked three distinct integers and placed them into a stack S in random order. Write a short, straight line 0piece of pseudo-code (with no loops or recursion) that uses only one comparison and only one variable x, yet guarantees with probability 2/3 that at the end of this code the variable x will store the largest of Alice's three integers. Argue why your method is correct.

  16. Problem Solving -C-5.5 Describe how to implement the stack ADT using two queues. What is the running time of the push() and pop() methods in this case?

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