Stacks, Queues, Deques

2
Stacks, Queues, and Deques
 A stack is a last in, first out (LIFO) data structure
 Items are removed from a stack in the reverse order from the
way they were inserted
 A queue is a first in, first out (FIFO) data structure
 Items are removed from a queue in the same order as they
were inserted
 A deque is a double-ended queue—items can be
inserted and removed at either end

3
Array implementation of stacks
 To implement a stack, items are inserted and removed at
the same end (called the top)
 Efficient array implementation requires that the top of
the stack be towards the center of the array, not fixed at
one end
 To use an array to implement a stack, you need both the
array itself and an integer
 The integer tells you either:

Which location is currently the top of the stack, or

How many elements are in the stack

4
Pushing and popping
 If the bottom of the stack is at location 0, then an empty
stack is represented by top = -1 or count = 0
 To add (push) an element, either:
 Increment top and store the element in stk[top], or
 Store the element in stk[count] and increment count
 To remove (pop) an element, either:
 Get the element from stk[top] and decrement top, or
 Decrement count and get the element in stk[count]
top = 3 or count = 4
0 1 2 3 4 5 6 7 8 9
17 23 97 44stk:

5
After popping
 When you pop an element, do you just leave the “deleted”
element sitting in the array?
 The surprising answer is, “it depends”
 If this is an array of primitives, or if you are programming in C or C++,
then doing anything more is just a waste of time
 If you are programming in Java, and the array contains objects, you should
set the “deleted” array element to null
 Why? To allow it to be garbage collected!
0 1 2 3 4 5 6 7 8 9
17 23 97 44stk:

6
Sharing space
 Of course, the bottom of the stack could be at the other end
17239744
0 1 2 3 4 5 6 7 8 9
stk:
 Sometimes this is done to allow two stacks to share the same
storage area
topStk2 = 6
1723974449 57 3
0 1 2 3 4 5 6 7 8 9
stks:
topStk1 = 2

7
Error checking
 There are two stack errors that can occur:
 Underflow: trying to pop (or peek at) an empty stack
 Overflow: trying to push onto an already full stack
 For underflow, you should throw an exception
 If you don’t catch it yourself, Java will throw an
ArrayIndexOutOfBounds exception
 You could create your own, more informative exception
 For overflow, you could do the same things
 Or, you could check for the problem, and copy
everything into a new, larger array

8
Pointers and references
 In C and C++ we have “pointers,” while in Java
we have “references”
 These are essentially the same thing

The difference is that C and C++ allow you to modify pointers
in arbitrary ways, and to point to anything
 In Java, a reference is more of a “black box,” or ADT

Available operations are:
 dereference (“follow”)
 copy
 compare for equality

There are constraints on what kind of thing is referenced: for
example, a reference to an array of int can only refer to an
array of int

9
Creating references
 The keyword new creates a new object, but also returns
a reference to that object
 For example, Person p = new Person("John")
 new Person("John") creates the object and returns a
reference to it
 We can assign this reference to p, or use it in other ways

10
Creating links in Java
class Cell { int value; Cell next;
Cell (int v, Cell n) { value = v; next = n; }
}
Cell temp = new Cell(17, null);
temp = new Cell(23, temp);
temp = new Cell(97, temp);
Cell myStack = new Cell(44, temp);
44 97 23 17
myStack:

11
Linked-list implementation of stacks
 Since all the action happens at the top of a stack, a singly-
linked list (SLL) is a fine way to implement it
 The header of the list points to the top of the stack
44 97 23 17
myStack:
 Pushing is inserting an element at the front of the list
 Popping is removing an element from the front of the list

12
Linked-list implementation details
 With a linked-list representation, overflow will not
happen (unless you exhaust memory, which is
another kind of problem)
 Underflow can happen, and should be handled the
same way as for an array implementation
 When a node is popped from a list, and the node
references an object, the reference (the pointer in
the node) does not need to be set to null
 Unlike an array implementation, it really is removed--
you can no longer get to it from the linked list
 Hence, garbage collection can occur as appropriate

13
Array implementation of queues
 A queue is a first in, first out (FIFO) data structure
 This is accomplished by inserting at one end (the rear) and
deleting from the other (the front)
 To insert: put new element in location 4, and set rear to 4
 To delete: take element from location 0, and set front to 1
17 23 97 44
0 1 2 3 4 5 6 7
myQueue:
rear = 3front = 0

14
Array implementation of queues
 Notice how the array contents “crawl” to the right as elements are
inserted and deleted
 This will be a problem after a while!
17 23 97 44 333After insertion:
23 97 44 333After deletion:
rear = 4front = 1
17 23 97 44Initial queue:
rear = 3front = 0

15
Circular arrays
 We can treat the array holding the queue elements as
circular (joined at the ends)
44 55 11 22 33
0 1 2 3 4 5 6 7
myQueue:
rear = 1 front = 5
 Elements were added to this queue in the order 11, 22,
33, 44, 55, and will be removed in the same order
 Use: front = (front + 1) % myQueue.length;
and: rear = (rear + 1) % myQueue.length;

16
Full and empty queues
 If the queue were to become completely full, it would look
like this:
 If we were then to remove all eight elements, making the queue
completely empty, it would look like this:
44 55 66 77 88 11 22 33
0 1 2 3 4 5 6 7
myQueue:
rear = 4 front = 5
0 1 2 3 4 5 6 7
myQueue:
rear = 4 front = 5
This is a problem!

17
Full and empty queues: solutions
 Solution #1: Keep an additional variable
 Solution #2: (Slightly more efficient) Keep a gap between
elements: consider the queue full when it has n-1 elements
44 55 66 77 88 11 22 33
0 1 2 3 4 5 6 7
myQueue:
rear = 4 front = 5count = 8
44 55 66 77 11 22 33
0 1 2 3 4 5 6 7
myQueue:
rear = 3 front = 5

18
Linked-list implementation of queues
 In a queue, insertions occur at one end, deletions at
the other end
 Operations at the front of a singly-linked list (SLL)
are O(1), but at the other end they are O(n)
 Because you have to find the last element each time
 BUT: there is a simple way to use a singly-linked
list to implement both insertions and deletions in
O(1) time
 You always need a pointer to the first thing in the list
 You can keep an additional pointer to the last thing in the
list

19
SLL implementation of queues
 In an SLL you can easily find the successor of a
node, but not its predecessor
 Remember, pointers (references) are one-way
 If you know where the last node in a list is, it’s
hard to remove that node, but it’s easy to add a
node after it
 Hence,
 Use the first element in an SLL as the front of the queue
 Use the last element in an SLL as the rear of the queue
 Keep pointers to both the front and the rear of the SLL

20
Enqueueing a node
17
Node to be
enqueued
To enqueue (add) a node:
Find the current last node
Change it to point to the new last node
Change the last pointer in the list header
2344
last
first
97

21
Dequeueing a node
 To dequeue (remove) a node:
 Copy the pointer from the first node into the header
44 97 23 17
last
first

22
Queue implementation details
 With an array implementation:
 you can have both overflow and underflow
 you should set deleted elements to null
 With a linked-list implementation:
 you can have underflow
 overflow is a global out-of-memory condition
 there is no reason to set deleted elements to null

23
Deques
 A deque is a double-ended queue
 Insertions and deletions can occur at either end
 Implementation is similar to that for queues
 Deques are not heavily used
 You should know what a deque is, but we won’t
explore them much further

24
Stack ADT
 The Stack ADT, as provided in java.util.Stack:
 Stack(): the constructor
 boolean empty() (but also inherits isEmpty())
 Object push(Object item)
 Object peek()
 Object pop()
 int search(Object o): Returns the 1-based position of the
object on this stack

25
A queue ADT
 Java provides a queue interface
 Here are the usual operations on a queue:
 Queue(): the constructor
 boolean isEmpty()
 Object enqueue(Object item): add at element at the rear
 Object dequeue(): remove an element from the front
 Object peek(): look at the front element
 int search(Object o): Returns the 1-based position from the
front of the queue
 Java’s interface uses goofy names:
 enqueue(Object)  offer(Object)
 dequeue()  poll()

26
A deque ADT
 Java does not provide a deque class
 Here is a possible deque ADT:
 Deque(): the constructor
 boolean isEmpty()
 Object addAtFront(Object item)
 Object addAtRear(Object item)
 Object getFromFront()
 Object getFromRear()
 Object peekAtFront()
 Object peekAtRear()
 int search(Object o): Returns the 1-based position from the
front of the deque

27
Using ArrayLists
 You could implement a deque with
java.util.ArrayList:
 addAtFront(Object)  add(0, Object)
 addAtRear(Object item)  add(Object)
 getFromFront()  remove(0)
 getFromRear()  remove(size() – 1)
 If you did this, should you extend ArrayList or use it as
a field in your Deque class?
 Would this be a good implementation?
 Why or why not?

28
The End
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