Implement the following operations of a stack using queues.

• push(x) -- Push element x onto stack.
• pop() -- Removes the element on top of the stack.
• top() -- Get the top element.
• empty() -- Return whether the stack is empty.

Notes:

• You may assume that all operations are valid (for example, no pop or top operations will be called on an empty stack).
• Depending on your language, queue may not be supported natively. You may simulate a queue by using a list or deque (double-ended queue), as long as you use only standard operations of a queue -- which means only push to back, pop from front, size, and is empty operations are valid.

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and all test cases.

用隊列Queues的基本操作來實現棧Stack，隊列和棧都是重要的數據結構，區別主要是，隊列是先進先出，而棧是先進後出。

解法1: 在隊列push進來新元素時，就把其它元素pop出來排到新元素的後面，新元素就在前面了，就可以後進先出。就好像大家都在排隊，來了個重要客人，要讓他第一，其他人從前面按順序跑到他後面。

解法2: push的時候，其他元素不動只是用一個變量記住這個新元素。當top的時候直接給這個變量的值。當pop時，在調整順序，把最後一個排到前面，彈出。變量記住目前在最尾部的值。

Python: Time: push: O(n), pop: O(1), top: O(1)， Space： O(n)

class Queue:
    def __init__(self):
        self.data = collections.deque()
        
    def push(self, x):
        self.data.append(x)
    
    def peek(self):
        return self.data[0]
    
    def pop(self):
        return self.data.popleft()
    
    def size(self):
        return len(self.data)
    
    def empty(self):
        return len(self.data) == 0


class Stack:
    # initialize your data structure here.
    def __init__(self):
        self.q_ = Queue()

    # @param x, an integer
    # @return nothing
    def push(self, x):
        self.q_.push(x)
        for _ in xrange(self.q_.size() - 1):
            self.q_.push(self.q_.pop())

    # @return nothing
    def pop(self):
        self.q_.pop()

    # @return an integer
    def top(self):
        return self.q_.peek()

    # @return an boolean
    def empty(self):
        return self.q_.empty()

Python: Time: push: O(1), pop: O(n), top: O(1)，Space: O(n)

class Stack:
    # initialize your data structure here.
    def __init__(self):
        self.q_ = Queue()
        self.top_ = None

    # @param x, an integer
    # @return nothing
    def push(self, x):
        self.q_.push(x)
        self.top_ = x

    # @return nothing
    def pop(self):
        for _ in xrange(self.q_.size() - 1):
            self.top_ = self.q_.pop()
            self.q_.push(self.top_)
        self.q_.pop()

    # @return an integer
    def top(self):
        return self.top_

    # @return an boolean
    def empty(self):
        return self.q_.empty()

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