Queue • Advanced Architecture

Monotonic Queue

A specialized Double-Ended Queue (Deque) whose elements are strictly strictly increasing or decreasing. Used heavily in Sliding Window optimization problems.

The Core Rule

Before enqueuing a new element at the rear, you must `pop_back` all elements that violate the desired monotonic order (e.g., all elements smaller than the new element). Only then do you `push_back` the new element.

Front Management

Like a standard queue, elements fall out of scope from the front. If the front element's index is no longer within the sliding window, you `pop_front`.

Use Cases

Sliding Window Maximum (Decreasing Deque)
Sliding Window Minimum (Increasing Deque)
Shortest Subarray with Sum at Least K

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Queue • Advanced Architecture

Monotonic Queue

A specialized Double-Ended Queue (Deque) whose elements are strictly strictly increasing or decreasing. Used heavily in Sliding Window optimization problems.

The Core Rule

Front Management

Like a standard queue, elements fall out of scope from the front. If the front element's index is no longer within the sliding window, you `pop_front`.

Use Cases

Sliding Window Maximum (Decreasing Deque)
Sliding Window Minimum (Increasing Deque)
Shortest Subarray with Sum at Least K