• A double-ended Queue (deque) allows you to push and pop elements from both ends

Monotonic Queue

  • A Queue that ensures elements inside are either monotonically increasing or monotonically decreasing, implemented with a Deque
  • Below is a monotonic queue implementation using Java
class MonotonicQueue {
  Deque<Integer> deque;
  public MonotonicQueue() {
    this.deque = new ArrayDeque<>();
  public void offer(int val) {
    // ensure we have a monotonic decreasing queue, need poll from back, thus
    // deque needed
    while (!deque.isEmpty() && deque.peekLast() < val) deque.pollLast();
  public void poll() {
  public int peek() {
    return deque.peekFirst();
  public String toString() {
    return deque.toString();

How does it work?

If we are adding an element that is larger than the element at the end of the queue, and we want to ensure the values in the queue are in decreasing order, we will pop elements from the back until the last element of the queue is larger than the element we want to add.

This is also why we need to use a deque, as we need to pop elements from the back.

How is this useful?

Monotonic queues are commonly used in problems related to Dynamic Programming, sliding window algorithms, and Combinatorial Optimisation tasks where you need to efficiently find maximum or minimum values over a range of elements.

We can use monotonic queue to solve Sliding Window Maximum which requires us to find the biggest element in a sliding window.