• A stack can be implemented using two queues. We know that a queue supports enqueue and dequeue operations. Using these operations, we need to develop push, pop operations.


• Let stack be ‘s’ and queues used to implement be ‘q1’ and ‘q2’. Then, stack ‘s’ can be implemented in two ways:

1. By making push operation costly:

• This method ensures that the newly entered element is always at the front of ‘q1’ so that pop operation just dequeues from ‘q1’.


• ‘q2’ is used as auxillary queue to put every new element in front of ‘q1’ while ensuring pop happens in O(1) complexity.


• 
  Pseudocode:
  • Push element to stack s: Here push takes O(n) time complexity.
  
  

• Pop element from stack s: Takes O(1) time complexity.

2. By making pop operation costly:

• In push operation, the element is enqueued to q1.


• In pop operation, all the elements from q1 except the last remaining element, are pushed to q2 if it is empty. That last element remaining of q1 is dequeued and returned.


• 
  Pseudocode:
  • Push element to stack s: Here push takes O(1) time complexity.
  
  

• Pop element from stack s: Takes O(n) time complexity.