CS 206 Introduction to Computer Science II

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1 CS 206 Introduction to Computer Science II 07 / 26 / 2016 Instructor: Michael Eckmann

2 Today s Topics Comments/Questions? Stacks and Queues Applications of both Priority Queues Michael Eckmann - Skidmore College - CS Summer 2016

3 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 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 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 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 Method calls A new call to a method causes its 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, its local data & state is popped off the stack You've seen me write information about method calls on the board in stack format.

8 Could we implement a Queue with a linked list an array Could we implement a Stack with a linked list an array

9 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 Let's implement a queue with an array what will be our instance variables?

11 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 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 Let's use that Queue class in an interesting sorting method called Radix Sort.

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

16 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

17 Applications of stacks postfix expressions (reverse Polish notation) infix (what we're used to) is like: 1.07* *8.75 postfix is like: 1.07, 8.75, *, 14.05, +, 1.07, 3.85, *, + infix result requires us to do the multiplies first and then store the intermediate values and then do the 2 adds. postfix operates in the following way: when see a number, push it when see an operator, perform it to the two top numbers on the stack and push the result final result in our example is:

18 Applications of stacks converting from infix (with only +, *, (, ) ) to postfix expressions infix example (assume normal precedence): a + b*c + ( d*e + f ) * g postfix for our example could be: a b c * + d e * f + g * + let's look at the algorithm to do this using a stack

19 converting infix to postfix when an operand (a, b, c, etc.) is read, write it to the output if we see a ) then we pop the stack and write to output until a ( is on top of the stack --- at which point we pop ( but do not output it. when a + or * is read, examine the top of the stack if it is empty or if top is of lower precedence than the one just read, or if top is (, then push the operator when a + or * is read if top is of the stack does not have lower precedence than the one just read, then pop the operator and write to output when a ( is read push it When finished reading input, pop stack, write to output until stack is empty Let's try this algorithm with our example: infix: a + b*c + ( d*e + f ) * g postfix (expected output): a b c * + d e * f + g * +

20 Another application of Stack Determining if curly braces are balanced Ideas on the board

21 Priority Queues The main difference between a Queue and a Priority Queue is that In a Queue, an item will be dequeued based ONLY on the order in which it was enqueued In a Priority Queue, an item can be dequeued BEFORE some other item that was enqueued earlier Every item is enqueued with a priority value Higher priority items have preference when dequeuing Items with the same priority can be enqueued / dequeued like a Queue

22 Priority Queues Priority queues have the following characteristics Each item placed into a priority queue has a priority value associated with it When a dequeue is requested from a priority queue, we dequeue the highest priority item We need a way to determine if the priority queue is empty We can also have a peek to see what item has the highest priority without removing it It is best to limit priority values to be integers (reason to be seen shortly).

23 Priority Queues It is also wise to maintain the following values for a priority queue current size (how many items are in the whole priority queue) the priority of the highest priority item in the queue to make dequeue efficient however it causes (some) additional work after the dequeue happens we need to possibly change this value after an enqueue we just need to check if the one we added is higher than the highest, if so, change it.

24 Priority Queues Implementation of a priority queue could be an array of queues. The index of the array is the priority value (see how we want our priority values to be integers?) The range of priority values (all integers) determines how many queues we're storing --- that is, how many elements of the array there will be. Let's implement a priority queue in this way now.

25 Deques Deque (or Dequeue) stands for double-ended queue. It is pronounced deck. Allows adding to and removing from both the front and rear. Since this allows adding and removing from both ends what kind of linked list would be best to implement this data structure?

CS 206 Introduction to Computer Science II

CS 206 Introduction to Computer Science II 03 / 31 / 2017 Instructor: Michael Eckmann Today s Topics Questions? Comments? finish RadixSort implementation some applications of stack Priority Queues Michael