# Implement Queue using Stacks

## # Solution

Solve using two stacks.

### # Vanilla Two Stacks

Code is omitted but here is the explanation:

`__init__`

: initialize`s1`

as the main stack and`s2`

as auxiliary`push`

: add the newly pushed element to the bottom of`s1`

- move all
`s1`

to`s2`

- push the new element to
`s1`

- move back old elements from
`s2`

to`s1`

- move all

All other operations are quite straightforward and have constant time and space complexities.

Complexity for `push`

:

- time:
- space:
due to additional space taken by `s2`

### # Improved Two Stacks

The new element is always pushed to `s1`

. Pop elements from `s2`

. If `s2`

is empty, `_move`

all elements from `s1`

to `s2`

.

Complexity for `pop`

:

- time: amortized
, worst case - normal case: if
`s2`

is not empty,`pop`

from`s2`

- worst case: if
`s2`

is empty,`_move`

doesn't pop`s1`

and append to`s2`

- normal case: if
- space:
due to additional space taken by `s2`

All other operations are quite straightforward and have constant time and space complexities.

```
class MyQueue:
def __init__(self):
"""
Initialize your data structure here.
"""
self.s1 = []
self.s2 = []
def push(self, x: int) -> None:
"""
Push element x to the back of queue.
"""
self.s1.append(x)
def pop(self) -> int:
"""
Removes the element from in front of queue and returns that element.
"""
self._move()
return self.s2.pop()
def peek(self) -> int:
"""
Get the front element.
"""
self._move()
return self.s2[-1]
def empty(self) -> bool:
"""
Returns whether the queue is empty.
"""
return not self.s1 and not self.s2
def _move(self) -> None:
if not self.s2:
while self.s1:
self.s2.append(self.s1.pop())
```