Comparablemerge

Comparablemerge is a generic data-processing operation that merges two or more sorted sequences using a provided comparator to determine ordering. The term is used informally in algorithm discussions and library documentation to emphasize the role of a custom comparison function rather than a fixed natural order.

In the common two-sequence case, comparablemerge repeatedly selects the next element with the smallest key according to the comparator from the heads of the input sequences and appends it to the output. If elements compare equal, a policy may be used to decide which input to take first, in order to preserve stability or to balance inputs.

Complexity for a standard two-sequence merge is linear in the total number of elements: O(n + m) time, with space usage depending on the variant. In in-place implementations, additional space can be O(1); in other variants, such as when producing a new merged array, space is O(n + m). Variants include multi-way merge and external (disk-based) merge for large data sets, often implemented with data structures like priority queues or tournament trees to manage candidate elements.

Applications of comparablemerge include sorting (as a component of merge sort and k-way merge), database query processing, and data pipelines that combine multiple sorted streams. It is also used in programming language libraries that support custom comparators for sorting and merging.

Example: merging A = [1, 4, 7] and B = [2, 5, 6] with a numeric comparator yields [1, 2, 4, 5, 6, 7].

See also: merge sort, k-way merge, comparator, stable sort. Note: comparablemerge is not a formal standard term; it describes a pattern of merging based on a comparator.