232. Implement Queue using Stacks

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).

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第一想法是，ｐｕｓｈ的时候直接把元素放入栈底，栈顶的元素保持为第一次入栈的元素，出栈时相当于出队。这种做法，ｐｕｓｈ的时间复杂度是Ｏ（ｎ），ｐｏｐ是Ｏ（１）。另外还需要一个ｓｔａｃｋ，用来在ｐｕｓｈ时存暂时出栈的元素。

机智的做法是！首先，如果一直在ｐｕｓｈ，早已入栈的元素一直在两个栈之间ｐｕｓｈ和ｐｏｐ，其次，ｓｔａｃｋ把所有元素ｐｏｐ到另一个栈，实际上已经变成了一个ｑｕｅｕｅ

时间复杂度ａｍｏｒｔｉｚｅｄ o(1) 最差情况Ｏ（ｎ）

什么是ａｍｏｒｔｉｚｅｄ o(1), 还有什么是amortized o(1)? 如ＡｒｒａｙＬｉｓｔ的ａｄｄ操作

public class MyQueue {
    Stack<Integer> stack;
    Stack<Integer> queue;
    /** Initialize your data structure here. */
    public MyQueue() {
        stack = new Stack<Integer>();
        queue = new Stack<Integer>();
    }
    
    /** Push element x to the back of queue. */
    public void push(int x) {
        stack.push(x);
    }
    
    /** Removes the element from in front of queue and returns that element. */
    public int pop() {
        if (queue.empty()) {
            while (!stack.empty()) {
                queue.push(stack.pop());
            }
        }
        return queue.pop();
    }
    
    /** Get the front element. */
    public int peek() {
        if (queue.empty()) {
            while (!stack.empty()) {
                queue.push(stack.pop());
            }
        }
        return queue.peek();
    }
    
    /** Returns whether the queue is empty. */
    public boolean empty() {
        if (stack.empty() && queue.empty()) {
            return true;
        } else {
            return false;
        }
    }
}

/**
 * Your MyQueue object will be instantiated and called as such:
 * MyQueue obj = new MyQueue();
 * obj.push(x);
 * int param_2 = obj.pop();
 * int param_3 = obj.peek();
 * boolean param_4 = obj.empty();
 */