# 232. Implement Queue using Stacks

# Problem

Implement a first in first out (FIFO) queue using only two stacks. The implemented queue should support all the functions of a normal queue (`push`

, `peek`

, `pop`

, and `empty`

).

Implement the `MyQueue`

class:

`void push(int x)`

Pushes element x to the back of the queue.`int pop()`

Removes the element from the front of the queue and returns it.`int peek()`

Returns the element at the front of the queue.`boolean empty()`

Returns`true`

if the queue is empty,`false`

otherwise.

**Notes:**

- You must use
**only**standard operations of a stack, which means only`push to top`

,`peek/pop from top`

,`size`

, and`is empty`

operations are valid. - Depending on your language, the stack may not be supported natively. You may simulate a stack using a list or deque (double-ended queue) as long as you use only a stack's standard operations.

# Solution

Stack is where we add to the top and pop from the top, like a stack of plates.

Queue is where we add to the back and pop from the top, like a queue at a shop being served.

The question gives us a hint to use two stacks.

## Append

If we want to append, say to S1 (our main stack), let's say we append `a`

.

`a`

Then we add B to the queue:

```
b
a
```

We want to pop the queue, in theory `a`

should be popped and not `b`

as it's first-in-first-out.

With the second stack we can add the values in the opposite way. We can do something like this:

- Add A to stack:

`a`

- We want to add B, so move A to the second stack.

```
stack1:
stack2:
a
```

- Add B to stack1

```
stack1:
b
stack2:
a
```

- Add A back to stack 1

```
stack1:
a
b
stack2:
```

If we `pop()`

`a`

will be popped, in a queue `a`

was put in first so it's meant to be popped out first.

Here's a solution:

```
class MyQueue:
def __init__(self):
self.inStack, self.outStack = [], []
def push(self, x: int) -> None:
self.inStack.append(x)
def pop(self) -> int:
self.move()
return self.outStack.pop()
def peek(self) -> int:
self.move()
return self.outStack[-1]
def empty(self) -> bool:
return (not self.inStack) and (not self.outStack)
def move(self):
# moves all elements of the "inStack" to the "outStack" when the "outStack" is empty.
if not self.outStack:
while self.inStack:
# While our instack has items in it, pop them and append them to the outstack
self.outStack.append(self.inStack.pop())
# Your MyQueue object will be instantiated and called as such:
# obj = MyQueue()
# obj.push(x)
# param_2 = obj.pop()
# param_3 = obj.peek()
# param_4 = obj.empty()
```