 # 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:

a
• We want to add B, so move A to the second stack.
stack1:

stack2:
a
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()