Nanheaps

Nanheaps are a data structure that combines features of heaps and arrays. They are typically used in scenarios where efficient insertion, deletion, and retrieval of minimum or maximum elements are required, while also allowing for direct access to elements based on their index. Unlike traditional heaps, nanheaps maintain an underlying array structure, enabling O(1) access to any element. However, maintaining the heap property requires operations that are similar in complexity to standard heaps. Insertion into a nanheap usually involves adding the element to the end of the array and then "bubbling" it up to its correct position to satisfy the heap invariant. Deletion of the minimum or maximum element typically involves replacing the root with the last element of the array and then "bubbling" it down. The exact implementation details and performance characteristics can vary depending on the specific design, but the core idea is to offer both array-like random access and heap-like priority queue functionality. They find applications in algorithms that require both sorted order and direct element referencing, such as certain graph algorithms or specialized scheduling systems.