Good morning! Here's our prompt for today.
Building a Queue with Two Stacks: A Challenge in Engineering Elegance
The Objective: Queue with Stacks
In this challenge, your task is to implement a queue using two stacks. While many programming languages offer queues through arrays or lists, we're restricting our approach to only utilize stacks.
The end result should behave like this:
JAVASCRIPT
1const tsq = new TwoStackQueue();
2tsq.push(1);
3tsq.push(2);
4tsq.pop(); // Should return 1
5tsq.pop(); // Should return 2
The Blueprint: Visualizing the Mechanics
Imagine having two stacks that work in harmony to simulate a queue. These stacks are like two components of a complex machine, each with its own specific role.

Constraints and Expectations
Let's clarify the rules of the game:
- Number of Operations: The maximum number of operations won't exceed 100,000.
- Value Ranges: The elements you push onto the stack will range between -1,000,000,000 and 1,000,000,000.
- Time Complexity for Push: If the pop operation has a time complexity of
O(n)
, then the push operation should beO(1)
. Otherwise, the time complexity for push should beO(n)
. - Time Complexity for Pop: If the push operation has a time complexity of
O(n)
, then the pop operation should beO(1)
. Otherwise, it should beO(n)
. - Space Complexity: Expected to be
O(n)
.
Try to solve this here or in Interactive Mode.
How do I practice this challenge?
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52
​
class TwoStackQueue:
def __init__(self):
self.inbox = []
self.outbox = []
​
def push():
# fill in
return
​
def pop():
# fill in
return
​
​
import unittest
​
​
class Test(unittest.TestCase):
def test_1(self):
tsq = TwoStackQueue()
tsq.push(1)
tsq.push(2)
tsq.pop()
assert tsq.pop() == 2
print(
"PASSED: Pushing `1` and `2` into a `TwoStackQueue` should pop `1` and then `2`."
)
​
def test_2(self):
OUTPUT
:001 > Cmd/Ctrl-Enter to run, Cmd/Ctrl-/ to comment
Here's how we would solve this problem...
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