LeetCode Notes: Implement Queue using Stacks


Implement a first in first out (FIFO) queue using only two stacks. The implemented queue should support all the functions of a normal queue (push, peek, pop, and empty).

Implement the MyQueue class:

  • void push(int x) Pushes element x to the back of the queue.
  • int pop() Removes the element from the front of the queue and returns it.
  • int peek() Returns the element at the front of the queue.
  • boolean empty() Returns true if the queue is empty, false otherwise.


  • 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, the stack may not be supported natively. You may simulate a stack using a list or deque (double-ended queue) as long as you use only a stack's standard operations.

Example 1:


["MyQueue", "push", "push", "peek", "pop", "empty"]

[[], [1], [2], [], [], []]


[null, null, null, 1, 1, false]


MyQueue myQueue = new MyQueue();

myQueue.push(1); // queue is: [1]

myQueue.push(2); // queue is: [1, 2] (leftmost is front of the queue)

myQueue.peek(); // return 1

myQueue.pop(); // return 1, queue is [2]

myQueue.empty(); // return false


  • 1 <= x <= 9
  • At most 100 calls will be made to push, pop, peek, and empty.
  • All the calls to pop and peek are valid.

Follow-up: Can you implement the queue such that each operation is amortized O(1) time complexity? In other words, performing n operations will take overall O(n) time even if one of those operations may take longer.

For questions of the same type, please refer to

225. Implement Stack using Queues



Take advantage of the characteristics of the js array, where the top of the stack is at the head of the array.


 * Initialize your data structure here.
var MyQueue = function() {
    this.queue = []

 * Push element x to the back of queue. 
 * @param {number} x
 * @return {void}
MyQueue.prototype.push = function(x) {

 * Removes the element from in front of queue and returns that element.
 * @return {number}
MyQueue.prototype.pop = function() {
    return this.queue.shift()

 * Get the front element.
 * @return {number}
MyQueue.prototype.peek = function() {
    return this.queue[0]

 * Returns whether the queue is empty.
 * @return {boolean}
MyQueue.prototype.empty = function() {
    return this.queue.length === 0

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