1. CS 206 Introduction to Computer Science II 10 / 26 / 2009 Instructor: Michael Eckmann

2. Michael Eckmann - Skidmore College - CS 206 - Fall 2009 Today’s Topics Questions? Comments? Queue Stack

3. Queues and Stacks A queue is a data structure that has the following characteristics – It is linear – Uses FIFO (first in, first out) processing Queue operations – Enqueue – add an item to the rear of the queue – Dequeue – remove an item from the front of the queue – Empty – returns true if the queue is empty What's significant about a queue is that there are no insert in anywhere or remove from anywhere in the queue. The only place to add something to the queue is the rear, and the only place to remove something from the queue is the front.

4. Queues and Stacks A stack is a data structure that has the following characteristics – It is linear – Uses LIFO (last in, first out) processing Stack operations – Push – add an item to the top of the stack – Pop – remove an item from the top of the stack – Empty – returns true if the stack is empty – Peek – retrieve information about the item on top of the stack without removing it The only allowable ways to put an item into and to get an item from the stack is via push and pop. There are no insert in anywhere or remove from anywhere in the stack. What if there was no peek? Is it redundant --- could a series of the existing operations achieve the same functionality.

5. Queues and Stacks Can anyone think of real world examples that are naturally modeled by queues? Can anyone think of a real world example that is naturally modeled by a stack? Let's see visual representations of a queue and a stack on the board.

6. Queues and Stacks Can anyone think of real world examples that are naturally modeled by queues? – Line of people at grocery store checkout – Line of airplanes waiting for takeoff Can anyone think of a real world example that is naturally modeled by a stack? – Plates at a salad bar A customer takes the top plate (pop)‏ When new plates come out, they are “pushed” to the top of the stack. – Why is this example not a queue?

7. Queues and Stacks Method calls A new call to a method causes it's local data and other state information (where in the method does it return to, etc.) to be pushed onto the stack The method calls finish in reverse order, so when a method call ends, it's local data & state is popped off the stack –You've seen me write information about method calls on the board in stack format.

8. Queues and Stacks Could we implement a Queue with – a linked list – an array Could we implement a Stack with – a linked list – an array

9. Queues and Stacks Let's implement a stack with an array –what will be our instance variables? Let's implement a queue with an array –what will be our instance variables?

10. Queues and Stacks Let's implement a queue with an array –what will be our instance variables?

11. Queues and Stacks Let's implement a queue with an array –what will be our instance variables? –if we want to keep a fixed sized array and we don't want to keep shifting the values around in the array we can use a scheme that stores an index to the front, an index to the rear –if we want the front to be the index that we would dequeue from and rear to be the index of the last element (so that we would enqueue to rear+1) then we should do the following: –front and rear being the same value means we have 1 element in the queue, so for an empty queue we would want front and rear start off at 0 and -1 –when enqueue first one, front stays 0 and rear becomes 0 –also, when rear goes off the end of the array we can wrap it around to 0, only if front is not still 0. Make sense?

12. Queues and Stacks Let's implement a queue with an array –how would we tell if the queue is full? when front is 0 and rear is maxindex or when...

13. Queues and Stacks Let's use that Queue class in an interesting sorting method called Radix Sort.

14. Queues and Stacks Radix Sort. –consider the job of sorting (base 10) integers let's limit them to 0-99 for now (all >=0 and <= 100)‏ –we handled this in several ways already –a totally different way is the following way start with an unsorted list separate the numbers to be sorted into 10 different bins based on their 1's digit then, get the numbers out of the bins and make a new list (take numbers from bin 0, then add on to the end of the list the numbers in bin 1,... and so on, finally adding to the end of the list the numbers from bin 9)‏ then separate this list into 10 bins based on the 10's digit. get the numbers out of the bins like before to get a sorted list.

15. Queues and Stacks Radix Sort. –example on board with the following: { 12, 15, 88, 76, 63, 21, 22, 1, 52, 2, 23, 5 }

16. Queues and Stacks Radix Sort. –example on board with the following: { 12, 15, 88, 76, 63, 21, 22, 1, 52, 2, 23, 5 } –each of the 10 bins were queues –also if you want to sort numbers that have a maximum of n digits in them, then you need n passes through the sort and each pass is a higher place in the number –we could use an array of 10 queues each index to the array corresponds to the digit in whatever place we're working on