The stack is a collection of items that follows the
last-in, first-out concept.
For the addition of new items, the stack only allows it to push the new item to the top. When it comes to removing items, it only allows us to remove the last added item, or commonly known as the top item.
The main API methods are
push (add) and
pop (remove). But we can also add other methods as part
of the API implementation:
We can create a
Stack class as a wrapper and use the
Python list to store the stack data. This class will have the
implementation of the
The first step is to create a class definition and how we are gone store our items.
class Stack: def __init__(self): self.items = 
This is basically what we need for now. Just a class and its
constructor. When the instance is created, it will have the
items list to store the stack items.
push method, we just need to use the list
append method to add new items. The new items will be
placed in the last index of this
items list. So the top
item from the stack will always be the last item.
def push(self, item): self.items.append(item)
It receives the new item and appends it to the list.
size method only counts the number of the stack items
by using the
def size(self): return len(self.items)
The idea of the
is_empty method is to verify if the list
has or not items in it. If it has, returns
True. To count the number of items in the
stack, we can simply use the
size method already
def is_empty(self): return self.size() == 0
pop method from the list data structure can also be
used to pop the item from the stack. It pops the last element as it is
expected for the stack. The last added item.
def pop(self): return self.items.pop()
But we need to handle the stack emptiness. For an empty list, the
pop method raises an exception
IndexError: pop from empty list. So we can create an
exception class to handle this issue.
class Emptiness(Exception): pass
And uses it when the list is empty:
def pop(self): if self.is_empty(): raise Emptiness('The Stack is empty') return self.items.pop()
If it is empty, we raise this exception. Otherwise, we can pop the top item from the stack.
We use this same emptiness strategy for the
def top(self): if self.is_empty(): raise Emptiness('The Stack is empty') return self.items[-1]
If it has at least one item, we get the top, the last added item in the stack.
The usage would be something like:
stack = Stack() stack.is_empty() # True stack.push(1) #  stack.push(2) # [1, 2] stack.push(3) # [1, 2, 3] stack.push(4) # [1, 2, 3, 4] stack.push(5) # [1, 2, 3, 4, 5] stack.is_empty() # False stack.top() # 5 stack.pop() # 5 stack.pop() # 4 stack.pop() # 3 stack.pop() # 2 stack.is_empty() # False stack.pop() # 1 stack.is_empty() # True
We first instantiate a new stack from the
- Verify emptiness: yes, it is!
- Add 5 new items to the stack:
[1, 2, 3, 4, 5].
- Verify emptiness: not anymore!
- Get the top element: 5 because it was the last added item.
- Remove 4 items: 5, 4, 3, and 2.
- Verify emptiness: empty yet!
- Remove the remaining item.
- Verify emptiness: it is empty now!
Runtime and Space complexities
Now about space and runtime complexities for each method implemented.
The space is pretty simple. It's a list, so it's
n is the current number of items
in the stack.
The runtime for each method is
O(1), constant time.
Reversing a list
We can use the stack data structure for a diverse number of algorithms. An example is to reverse the items from a list.
We want to reverse a list of books, a bookshelf.
def reverse(bookshelf): stack = Stack() for book in bookshelf: stack.push(book) reversed_bookshelf =  while not stack.is_empty(): reversed_bookshelf.append(stack.pop()) return reversed_bookshelf
- Create a stack instance
- Push each list item to the stack
- Create an empty reversed list
- Pop each item until the stack is empty
- For each popped item, append it to the reversed list
- Return the reversed list
The idea is to make the last list item the first to be popped from the stack.
The function usage would be something like:
bookshelf = [ 'Harry Potter', 'Atomic Habits', 'Leonardo da Vinci', 'Sapiens', 'Peak' ] reversed_bookshelf = reverse(bookshelf) print(reversed_bookshelf) # ['Peak', 'Sapiens', 'Leonardo da Vinci', 'Atomic Habits', 'Harry Potter']
We can also implement the stack concept in a
undo command. Imagine our text editor. For each document
change, we store the new document in the stack. If we want to
undo the change, we just need to pop the last change and
stay with the previous state of the document.
Web Browsers can also use stacks to store the visited website. When the user visits a new website, it pushes the new URL to the stack. When the user goes back, using the "back" button, it pops the last visited website and uses the previous URL.