[Leetcode] 225. Implement Stack using Queues 解题报告

题目：

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 must use only standard operations of a queue -- which means only push to back, peek/pop from front, size, and is empty operations are valid.
• 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.
• You may assume that all operations are valid (for example, no pop or top operations will be called on an empty stack).

思路：

我们首先看看队列和栈的区别：队列是先进先出，而栈是后进先出。可以看出算法实现的关键就在于在队列中存储元素的时候，将最近push进来的元素放在队列首位还是末尾了。根据这个区别，就可以有两种实现方法：

1、懒惰实现：顾名思义，就是新加入一个元素之后，我们懒惰第将它放在队列末尾。这就导致一个问题，当需要pop的时候，我们此时需要pop掉的是队列中的最后一个元素，而这个操作是队列这种数据结构所不支持的。所以在懒惰实现的pop中，我们需要首先把除队末元素之外的所有队列元素都移出队列，然后重新添加，这样就可以保证原来的队末元素此时位于队列头部了，可以直接pop。

2、勤奋实现：顾名思义，就是新push一个元素进来的时候，我们想办法把它置于队列头部，这样当需要pop的时候直接pop出来队列头部就可以了。所以这种“勤奋实现”的关键在于push函数的实现。事实上它和“懒惰实现”的pop函数完全一样：先把新元素加在队列元素的末尾，然后把所有除此之外的元素顺次移除，并添加到队列的末尾。

代码：

1、懒惰实现：

class MyStack {
public:
    /** Initialize your data structure here. */
    MyStack() {
        
    }
    
    /** Push element x onto stack. */
    void push(int x) {
        que.push(x);
    }
    
    /** Removes the element on top of the stack and returns that element. */
    int pop() {
        int size = que.size();
        for (int i = 0; i < size - 1; ++i) {
            que.push(que.front());
            que.pop();
        }
        int ret = que.front();
        que.pop();
        return ret;
    }
    
    /** Get the top element. */
    int top() {
        return que.back();
    }
    
    /** Returns whether the stack is empty. */
    bool empty() {
        return que.empty();
    }
private:
    queue<int> que;
};

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

2、勤奋实现：

class MyStack {
public:
    /** Initialize your data structure here. */
    MyStack() {
        
    }
    
    /** Push element x onto stack. */
    void push(int x) {
        que.push(x);
        for (int i = 0; i < que.size() - 1; ++i) {
            que.push(que.front());
            que.pop();
        }
    }
    
    /** Removes the element on top of the stack and returns that element. */
    int pop() {
        int ret = que.front();
        que.pop();
        return ret;
    }
    
    /** Get the top element. */
    int top() {
        return que.front();
    }
    
    /** Returns whether the stack is empty. */
    bool empty() {
        return que.empty();
    }
private:
    queue<int> que;
};

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