# Time:  O(1), amortized
# Space: O(n)
#
# Implement the following operations of a queue using stacks.
#
# push(x) -- Push element x to the back of queue.
# pop() -- Removes the element from in front of queue.
# peek() -- Get the front element.
# empty() -- Return whether the queue is empty.
#
# 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, stack may not be supported natively.
# You may simulate a stack by using a list or deque (double-ended queue),
# as long as you use only standard operations of a stack.
# You may assume that all operations are valid
# (for example, no pop or peek operations will be called on an empty queue).
#

class Queue:
    # initialize your data structure here.
    def __init__(self):
        self.A, self.B = [], []

    # @param x, an integer
    # @return nothing
    def push(self, x):
        self.A.append(x)

    # @return nothing
    def pop(self):
        self.peek()
        self.B.pop()
        
    # @return an integer
    def peek(self):
        if not self.B:
            while self.A:
                self.B.append(self.A.pop())
        return self.B[-1]
        
    # @return an boolean
    def empty(self):
        return not self.A and not self.B

# Time:  O(1), amortized
# Space: O(n)
#
# Implement the following operations of a queue using stacks.
#
# push(x) -- Push element x to the back of queue.
# pop() -- Removes the element from in front of queue.
# peek() -- Get the front element.
# empty() -- Return whether the queue is empty.
#
# 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, stack may not be supported natively.
# You may simulate a stack by using a list or deque (double-ended queue),
# as long as you use only standard operations of a stack.
# You may assume that all operations are valid
# (for example, no pop or peek operations will be called on an empty queue).
#

class Queue:
    # initialize your data structure here.
    def __init__(self):
        self.A, self.B = [], []

    # @param x, an integer
    # @return nothing
    def push(self, x):
        self.A.append(x)

    # @return an integer
    def pop(self):
        self.peek()
        return self.B.pop()
        
    # @return an integer
    def peek(self):
        if not self.B:
            while self.A:
                self.B.append(self.A.pop())
        return self.B[-1]
        
    # @return an boolean
    def empty(self):
        return not self.A and not self.B

Update implement-queue-using-stacks.py