Implement Queue Using Stacks

To solve this coding challenge, the fundamental idea is to implement a queue using two stacks. A stack is a LIFO (Last In First Out) data structure, but a queue requires FIFO (First In First Out) functionality. Thus, we need to use two stacks to simulate the behavior of a queue.

Explanation

Let's break down the implementation step-by-step to understand how we can simulate a queue using two stacks:
  1. Stack Basics :
    • A stack allows operations at the top (push, pop, peek).
    • We will use two stacks (
      stack1
      and
      stack2
      ) to implement the queue.
  2. Pushing an Element :
    • When we want to push an element to the queue, we need to ensure that the order of the elements in
      stack1
      remains such that the first element pushed into
      stack1
      remains at the bottom.
    • We achieve this by temporarily moving all existing elements in
      stack1
      to
      stack2
      , pushing the new element to
      stack1
      , and then moving all elements back from
      stack2
      to
      stack1
      .
  3. Popping an Element :
    • The
      pop
      operation simply pops the top element from
      stack1
      because we have already ensured that
      stack1
      is maintaining the correct order for a queue.
  4. Peeking at the Front Element :
    • For the
      peek
      operation, we return the top element of
      stack1
      since the top of
      stack1
      represents the front of the queue.
  5. Checking if the Queue is Empty :
    • To check if the queue is empty, we simply check if
      stack1
      is empty.
    Here is the detailed step-by-step explanation:
  6. Initialization :
    • Create a class
      MyQueue
      .
    • Within the constructor, initialize two empty stacks (
      stack1
      and
      stack2
      ).
  7. Push Operation :
    • When pushing an element
      x
      :
      • Transfer all elements from
        stack1
        to
        stack2
        .
      • Push
        x
        onto
        stack1
        .
      • Transfer all elements back from
        stack2
        to
        stack1
        .
  8. Pop Operation :
    • Perform a pop operation on
      stack1
      and return the popped element.
  9. Peek Operation :
    • Return the top element of
      stack1
      .
  10. Empty Check :
    • Return
      True
      if
      stack1
      is empty, otherwise return
      False
      .

    Pseudocode with Comments

                                                
    // Definition of the MyQueue class
    Class MyQueue:
    // Constructor to initialize the stacks
    def __init__():
    stack1 = []   // Stack to hold elements in queue order
    stack2 = []   // Temporary stack used for reordering
    
    // Method to push an element x into the queue
    def push(x):
    // Transfer all elements from stack1 to stack2
    while stack1 is not empty:
    stack2.push(stack1.pop())
    
    // Push the new element onto stack1
    stack1.push(x)
    
    // Transfer all elements back from stack2 to stack1
    while stack2 is not empty:
    stack1.push(stack2.pop())
    
    // Method to remove and return the front element of the queue
    def pop():
    // Pop the top element from stack1 (front of the queue)
    return stack1.pop()
    
    // Method to return the front element of the queue without removing it
    def peek():
    // Return the top element of stack1
    return stack1.peek()
    
    // Method to check if the queue is empty
    def empty():
    // Return True if stack1 is empty, else False
    return stack1 is empty
    
                                            

    Detailed Steps in Pseudocode

  11. Initialization :
    • def __init__():
      • Initialize
        stack1
        as an empty list.
      • Initialize
        stack2
        as an empty list.
  12. Push :
    • def push(x):
      • While
        stack1
        is not empty, pop elements from
        stack1
        and push them onto
        stack2
        .
      • Push
        x
        onto
        stack1
        .
      • While
        stack2
        is not empty, pop elements from
        stack2
        and push them onto
        stack1
        .
  13. Pop :
    • def pop():
      • Pop the top element from
        stack1
        .
      • Return the popped element.
  14. Peek :
    • def peek():
      • Return the top element of
        stack1
        .
  15. Empty :
    • def empty():
      • Return
        True
        if
        stack1
        is empty, otherwise return
        False
        .
This pseudocode provides a clear framework to implement a queue using stacks, ensuring that all operations maintain the FIFO order proper to a queue by leveraging the LIFO nature of stacks effectively.