Implement Stack using Queues
The code is an implementation of a stack using a single deque, but the problem statement asks for an implementation using two queues. The current code violates the constraints by using a stacklike behavior in the push
method.
Here’s the code that follows the constraints and uses two queues:


The push
operation here will add the element to one queue and then reorganize the elements by moving them between the two queues so that the latest pushed element is at the front of the main queue (queue2). By swapping the names of the two queues, this code ensures that the main queue is always accessible as self.queue2
.
The pop
, top
, and empty
operations are simple and straightforward. The pop
method removes and returns the front element, top
returns the front element without removing it, and empty
checks if the main queue is empty.
This implementation fulfills the constraints of the problem and allows for the correct behavior of a stack.
Identifying Problem Isomorphism
“Implement Stack using Queues” can be approximately mapped to “Implement Queue using Stacks”.
In “Implement Stack using Queues”, you’re required to simulate the functionality of a stack using only instances of a queue. This means that you have to work around the FIFO (First In, First Out) nature of a queue to implement a stack, which operates on a LIFO (Last In, First Out) principle.
In “Implement Queue using Stacks”, you’re given the reverse task: to simulate a queue using only stacks. Here, you have to use the LIFO nature of stacks to implement a queue, which operates on a FIFO principle.
Both problems share the theme of utilizing one data structure to emulate the behavior of another, requiring a deep understanding of both data structures involved.
“Implement Stack using Queues” and “Implement Queue using Stacks” are roughly equivalent in difficulty, as they both involve the similar cognitive task of emulating one data structure with another. It could be argued that one might be slightly easier or more difficult based on the individual’s understanding and comfort level with the data structures involved (stacks and queues), but overall they are on par with each other.


Problem Classification
Data Structures: This problem involves implementing a stack using a queue, which are fundamental data structures. Understanding how stacks and queues work is crucial to this problem.
Stack Operations: The operations that need to be supported are typical of a stack  push (inserting an element), pop (removing the top element), top (accessing the top element), and empty (checking if the stack is empty).
Queue Operations: Given that the stack is implemented using a queue, understanding queue operations is also key.
Design: The problem involves designing a new data structure by manipulating existing ones, which falls into the category of design problems.
Method Overriding: The problem requires defining a class with specific methods, each performing a specific task, which is an example of method overriding in objectoriented programming.
Language Agnostic Coding Drills
Understanding Data Structures: Understanding the usage of different data structures like Stack and Queue is necessary. Stack follows LastInFirstOut (LIFO) principle while Queue follows FirstInFirstOut (FIFO) principle.
Utilizing builtin Data Structures: Familiarity with the builtin queue data structure of a language is required. In Python,
deque
can be used as a queue.Creating a Custom Data Structure: The problem involves creating a Stack using Queue, which is a custom data structure. Hence, understanding how to design such data structures is essential.
Method Overriding: The problem requires creating methods like
push
,pop
,top
andempty
that perform specific operations. Understanding how to define methods and override them if necessary, is required.Manipulating Queues: Basic operations on a queue such as adding an element at the front (
append
orextend
), removing an element from the front (popleft
), and checking the first element ([0]
), must be understood.
In terms of problem solving:
Design a Stack using Queues: The goal is to implement a stack using only instances of queues. This requires understanding of both stack and queue data structures.
Implement Push Operation: On a
push
operation, the new element should be inserted at the front of the queue. This ensures that the last inserted element can be accessed first, to mimic stack behavior.Implement Pop Operation: The
pop
operation removes an element from the front of the queue. This element will be the last one pushed into the stack.Implement Top Operation: The
top
operation returns the front element from the queue without removing it, which is the last inserted element in the stack.Implement Empty Operation: The
empty
operation checks whether the stack (implemented via queue) is empty or not.
The difficulty level increases from understanding and using builtin data structures, to creating a custom data structure (a stack), using another data structure (queue). Finally, implementing the operations of a stack using only the operations of a queue presents a significant challenge.
Targeted Drills in Python
Understanding Data Structures
Learn about Stack and Queue. Here’s a simple example of stack and queue operations in Python using list and deque from collections respectively:
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# Stack using list stack = [] stack.append('a') # Push 'a' stack.append('b') # Push 'b' print(stack.pop()) # Pop, should return 'b' # Queue using deque from collections import deque queue = deque() queue.append('a') # Enqueue 'a' queue.append('b') # Enqueue 'b' print(queue.popleft()) # Dequeue, should return 'a'
Utilizing builtin Data Structures
Python’s deque can be used as a queue. Practice operations on deque.
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from collections import deque q = deque() # Enqueue elements q.append('a') q.append('b') # Dequeue elements print(q.popleft()) print(q.popleft())
Creating a Custom Data Structure
We need to create a stack using queue. For now, let’s just setup the class and methods without implementing the logic.
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from collections import deque class MyStack: def __init__(self): self.queue = deque() def push(self, x: int) > None: pass def pop(self) > int: pass def top(self) > int: pass def empty(self) > bool: pass
Method Overriding
Practice defining methods and overriding them. We’ll implement the logic for our custom stack in this step.
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class MyStack: def __init__(self): self.queue = deque() def push(self, x: int) > None: temp = deque([x]) temp.extend(self.queue) self.queue = temp def pop(self) > int: return self.queue.popleft() def top(self) > int: return self.queue[0] def empty(self) > bool: return len(self.queue) == 0
Manipulating Queues
Practice operations on a queue. In Python, you can use a deque from the collections module. The operations include adding an element at the front, removing an element from the front, and checking the front element.
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from collections import deque q = deque() # Add element at front q.appendleft('a') # Remove element from front q.popleft() # Check front element if q: print(q[0])
After mastering these individual drills, you can combine them to implement the final solution.