## 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.

- 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).

### Analysis:

This kind of problem usually requires more than one data structure to implement the other data structure. In this problem, two stacks are enough to implement a queue.

The idea is keep push element into stack 1, then "pop" is called, put all the elements from stack 1 to stack 2. Then pop the top element in stack 2. If "pop" is called again, not stack 2 is not empty, just pop the top element is enough. If stack 2 is empty, put all the elements in stack 1 to stack 2. In short, stack 1 is used for "push", stack 2 is used for "pop" and "peek". We do the "move element from stack1 to stack 2" only when stack 2 is empty and "pop" or "peek" is called.

e.g., We call push(1), push(2), push(3), push(4), and push(5), stack 1 is filled all the five elements, then do pop(), since stack 2 is empty, move elements from stack 1 to stack 2, then pop the top element (now is 1) in stack2:

Then we call push(6), push(7), push(8), push(9), and pop(), pop(), pop(), stack 1 is used for pushing, and stack 2 is used for popping :

Again, we call pop() (now 5 is popped out and no element in stack 2), and a peek() operation is called, stack 2 is empty, so push elements from stack 1 to stack 2, and return the top element as the peek:

### Code(C++):

class Queue { stack<int> st1; stack<int> st2; public: // Push element x to the back of queue. void push(int x) { st1.push(x); } // Removes the element from in front of queue. void pop(void) { if (!st2.empty()){ st2.pop(); }else{ while (!st1.empty()){ st2.push(st1.top()); st1.pop(); } st2.pop(); } } // Get the front element. int peek(void) { if (!st2.empty()){ return st2.top(); }else{ while (!st1.empty()){ st2.push(st1.top()); st1.pop(); } return st2.top(); } } // Return whether the queue is empty. bool empty(void) { return (st1.empty() && st2.empty()); } };

### Code(Python):

class Queue(object): def __init__(self): """ initialize your data structure here. """ self.st1 = [] self.st2 = [] def push(self, x): """ :type x: int :rtype: nothing """ self.st1.append(x) def pop(self): """ :rtype: nothing """ if len(self.st2) == 0: while len(self.st1) != 0: self.st2.append(self.st1.pop()) self.st2.pop() def peek(self): """ :rtype: int """ if len(self.st2) == 0: while len(self.st1) != 0: self.st2.append(self.st1.pop()) return self.st2[-1] def empty(self): """ :rtype: bool """ return not self.st1 and not self.st2

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