Stacks and Queues

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Stacks and Queues

Objectives

Describe arrays in the context of lower-level languages (C++, Java)
Memorize the acronyms LIFO and FIFO and how they apply to stacks and queues
Use data structures to implement stacks and queues

Memory and Arrays

So far, we've used arrays in JavaScript, which act as flexible containers for storing data. However, arrays in many lower-level languages (C++, Java) do not act like this. They are fixed in length, and we need to explicitly define the size on creation.

To understand why this is the case, let's look at how memory is stored in a computer.

Memory is stored in a block-like fashion, similar to city blocks. Each block has buildings with "addresses", and each block has a fixed length that can't be changed unless destroyed.

Memory in a computer is similar. When we allocate memory, we allocate "blocks". Each block has a fixed size, generally enough to store the type of data we're using. Each block has an address. And note that since the blocks are fixed and uniform, we can only have arrays of a specific data type in C++ and Java (no combining strings and integers in the same array).

Does JavaScript do this?

Stack

Arrays are the foundation for implementing a container called a stack. Stacks are special arrays where items can only be added and removed from the end. This is a LIFO (last in, first out) procedure.

Adding the constraint that items are only added and removed from the end of the array guarantees that adding and removing items is always an O(1) operation. Adding a constraint on how data can exist becomes an optimization!

Consider what it means to have an array that represents a list of things that allows you to add or remove things from the middle of the list. If things are added and removed in the middle, then things have to be scooted around to make room for new things, and things need to be condensed together when something is removed. A list that supports adding and removing elements in the middle has a complexity of O(N) because you could potentially have to move every single item in the list to make room for a new item, or to condense the list after an item has been removed.

Again, the whole idea of a Stack is that it takes a list and tells people that they're only allowed to either add something to the end, or take something off of the end. Since these operations are constrained to the end of the list the rest of the items never have to scoot over, or condense. Adding and removing off of the end is guaranteed to always be a constant O(1) operation.

Stacks traditionally have special names for the add and remove methods: push and pop. Stacks are often visualized vertically, like a stack of cafeteria trays, to indicate that the only item accessible is what's on top of the stack.

push - push something on top of the stack
pop - pop something off the top of the stack

Stacks in JavaScript

Whenever we talk about data structures there's always two things:

the idea and formal definition of the data structure.
the implementation of the data structure.

The idea and formal definition of a data structure is an idea that can be applied across all programming languages. The implementation of a data structure refers to how the idea of the data structure actually exists in a given language.

In JavaScript, you can represent a Stack using an array and only using the .push() and .pop() methods. If you ever accessed the array using a[index] or a.splice() or anything then you're cheating and you're not really following the idea of a Stack.

In Python, you can represent a Stack using a list and restricting yourself to only using the .append() and .pop() methods.

You can also create your own simple class in Python to implement the behaviour of a Stack yourself, and guarantee people using your program only use Stack-like methods.

class Stack:
  def __init__(self):
    self.data = []

  def push(self, value):
    self.data.append(value)

  def pop(self):
    if len(self.data) > 0:
      return self.data.pop()
    return None

  def size(self):
    return len(self.data)

  def __len__(self):
    return self.size()

ss = Stack()
ss.push(42)
ss.push(91)
ss.push(32)

ss.pop() # 32
ss.pop() # 91
ss.pop() # 42
ss.pop() # None

Practical Applications for Stacks

Different data structures are good at different things. It can be beneficial to confine oneself to using a specific data structure while solving a problem because it may naturally lead to more efficient code, or it may make our code less prone to errors. Becoming familiar with different data structures and learning when they're useful will make you a better programmer.

Also, there's lot of algorithms designed specifically for data structures. If you study data structures and algorithms you may find well-tested answers for a wide variety of problems you want to solve.

Here's some problems Stacks are especially good at solving:

Bracket matching
Keeping track of undo/redo operations

Queue

A queue is another type of container generally implemented with a linked list, but can be implemented with arrays. Items are only added to the end of a queue, and only removed from the beginning of the queue. This is a FIFO (first in, first out) procedure.

Queues normally support these two operations:

enqueue - add something at the back of the line.
dequeue - remove something from the front of the line.

Queues can be implemented in JavaScript with an array by using only the push and shift functions to push (enqueue) something at the end of the list, and shift (dequeue) something from the front of the list.

Python has a class in it's collections library called deque that stands for "double ended queue." It has an .append() method to enqueue something to end of the line and a .popleft() method to dequeue something off the front of the line.

The Python docs say that deque is "A list-like sequence optimized for data accesses near its endpoints." It's called a double ended queue because it actually supports adding and removing elements to just the front and back of itself. Since it doesn't involve rearranging things in the middle, this is still able to maintain an efficiency of O(1).

Here's a small Python class that wraps around the deque object to create enqueue and dequeue method names around the provided Python object.

from collections import deque

qq = deque()
qq.append(1)
qq.append(2)
qq.append(3)

# First in, first out.
qq.popleft() # 1
qq.popleft() # 2
qq.popleft() # 3

Practical Applications for Queues

Representing a line
Buffers for print jobs, or other tasks

Using Stacks and Queues Together

Stacks and queues often appear together. Check this out. You can reverse everything in a stack by running it through a queue!

Stacks and queues normally use while loops that run until the size of the stack or queue is zero when they're all emptied out.

from collections import deque

stack = []
stack.append(1)
stack.append(2)
stack.append(3)
stack.append(4)
stack.append(5)

qq = deque()
while len(stack) > 0:
  qq.append(stack.pop())

while len(qq) > 0:
  stack.append(qq.popleft())

while len(stack) > 0:
  print(stack.pop()) # prints 5, 4, 3, 2, 1

Challenge: Bracket Matching

Define a function called test_brackets that takes a string and determines if all brackets are correctly matching / nested (returns True or False). This is code could be used as part of a system to detect syntax errors in code.

It should check for the following: [ ],{ },( )

Use a Stack data structure
Opening characters are left-parens, left-brackets, left-curly-braces
Closing characters are right-parens, right-brackets, right-curly-braces
Push opening characters onto the stack when you see them
When you see a closing character see if it matches what's popped off the stack.
Ignore any character that's not an opening character or a closing character.

Usage Examples

# True
test_brackets('abc(123)')

#returns True
test_brackets('a[bc(123)]')

#returns True
test_brackets('a{b}{c(1[2]3)}')

#returns True
test_brackets('()')

#returns True -- no brackets = correctly matched
test_brackets('abc123yay')

#returns False -- missing closing bracket
test_brackets('abc(123')

#returns False -- improperly nested
test_brackets('a[bc(12]3)')

#returns False -- improperly nested
test_brackets('a{b}{c(1}[2]3)')

Challenge: Josephus problem

In the Josephus problem from antiquity, n people are in dire straits and agree to the following strategy to reduce the population. They arrange themselves in a circle (at positions numbered from 0 to n−1) and proceed around the circle, eliminating every Mth person until only one person is left. Legend has it that Josephus figured out where to sit to avoid being eliminated.

Define a function called josephus that accepts a list of people's names, and a number M. Your function should simulate the population reduction strategy, going around in a circle and eliminating every Mth person and finally returning the name of the final person left.

Start counting with 1 at index zero so josephus(["Jack", "John"], 1) returns "John" because "Jack" was eliminated on the first count.

Hint: put all of the names in a queue. Cycle through the names by dequeueing names and immediately enqueueing them, unless they should be eliminated.

It may help you to start out your program printing out something like this, so you can see what's going on:

josephus(["James", "John", "Mike", "Josephus"], 1)
1 James is eliminated
1 John is eliminated
1 Mike is eliminated
Josephus is the only one left.

josephus(["James", "John", "Mike", "Josephus"], 2) # returns "James"
1 James is skipped
2 John is eliminated
1 Mike is skipped
2 Josephus is eliminated
1 James is skipped
2 Mike is eiliminated
James is the only one left.

josephus(["James", "John", "Mike", "Josephus"], 3) # returns "James"
1 James is skipped
2 John is skipped
3 Mike is eliminated
1 Josephus is skipped
2 James is skipped
3 John is eliminated
1 Joshephus is skipped
2 James is skipped
3 Joshephus is eliminated
James is the only one left.

This long one should return "Mary".

josephus(["Peter", "Paul", "Mary", "Abba", "Prince", "Sting", "Beck"], 57)

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