Implementing 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).

Analyse: Using two stacks: in & out to store the information. IN stack is used to push element while OUT stack is used to pop out element. If two stacks are both empty, then the queue is empty. 

class Queue {
private:
    stack<int> in;
    stack<int> out;
    void move(){//move all elements in the IN stack to the OUT stack
        while(!in.empty()){
            out.push(in.top());
            in.pop();
        }
    }
public:
    // Push element x to the back of queue.
    void push(int x) {
        in.push(x);
    }

    // Removes the element from in front of queue.
    void pop(void) {//be careful about the condition
        if(out.empty()) move(); //if the out stack is empty, then move all elements from IN stack to OUT stack
        if(!out.empty()) out.pop();//if the out stack is not empty, then pop out the top element
    }

    // Get the front element.
    int peek(void) {
        if(out.empty()) move();
        if(!out.empty()) return out.top();
    }

    // Return whether the queue is empty.
    bool empty(void) {
        return in.empty() && out.empty();
    }
};