exchangereplace

Exchangereplace is a term used in data structures and algorithm design to describe a composite operation that combines exchanging two elements with a subsequent replacement or update of one or both elements. The exact interpretation of the replacement varies by context, but the overarching idea is to swap positions and then apply an update to preserve an invariant, improve a metric, or reflect a computed change.

In formal terms, given a collection A and indices i and j, an exchangereplace may proceed as follows: swap A[i] and A[j], then apply a replacement function r to one or both of the involved elements, such as A[i] <- r(A[i]) and/or A[j] <- r(A[j]). The replacement step may depend on a constraint, a priority value, or a local optimization objective. Some variants perform a single swap followed by a single replacement on one of the elements, while others apply different updates to both positions.

Applications of exchangereplace appear in various domains, including in-place sorting optimizations, priority queue maintenance, and dynamic data structures where maintaining a property (such as order, heap-structure, or balance) is as important as moving elements. It can also be used in reconciliation tasks within collaborative editing or cache replacement strategies that require both repositioning and value adjustment.

Variants and terminology differ across literature; some authors refer to the operation as a swap followed by an update, while others describe it as a single atomic action. See also swap, replace, update, and related in-place mutation techniques.