Treesarrays

Treesarrays is a term used in computer science to refer to data structures and representations that store hierarchical tree structures within arrays or as collections of arrays. It covers methods that replace or augment pointer-based trees with contiguous memory layouts to improve locality, serialization, or interoperability with low-level systems.

Common representations include:

- Array-based binary trees: used for complete binary trees such as binary heaps, where a node at index i has left and right children at indices 2i and 2i+1 (or 2i+1 and 2i+2 in zero-based indexing).

- Parent array: a single array parent[] stores the index of each node’s parent; the root has a special value like -1. Children are found by scanning the array.

- First-child/next-sibling representation: stores firstChild[i] and nextSibling[i] in arrays to traverse a general tree, effectively encoding a multiway tree in a fixed layout.

- Adjacency arrays: use a head[] array for nodes and an edge array with next[] pointers to enumerate children, similar to adjacency lists but implemented with flat arrays.

Advantages include improved memory locality, simpler serialization, and compact storage for static trees or trees with a known maximum size. Disadvantages involve challenges with dynamic updates, such as insertions or deletions and resizing, which may require reindexing or reallocating large arrays and can waste space for imbalanced structures.

Typical applications are priority queues implemented as heaps, storage of static hierarchical data for efficient traversal, and graph algorithms that benefit from compact, array-based adjacency representations. See also tree data structures, arrays, adjacency lists, and the binary heap.