Sorted Array¶
A sorted array keeps comparable keys in contiguous index order, enabling binary-search lookup and contiguous ranges while making middle updates costly.
Core Idea¶
A sorted array is an indexable contiguous sequence whose keys follow a comparison order. Midpoint access and monotone keys support O(log n) binary search. Middle insertions/deletions can require O(n) shifts even after a fast search for their position.[ref-5e648c6537fe][ref-0a5e7abdf3a7]
Scope of Application¶
GNU gprof constructs a contiguous symbol array, sorts it by address and binary-searches it for symbol lookup. MIT's one-dimensional range-search example uses two binary searches to bound an interval and then reports its k points in O(log n+k). Both benefit from maintained order, though their keys and queries differ.[ref-5409d4da09b8][ref-5e648c6537fe]
Clarity¶
The structure is neither a sorting algorithm nor merely a sorted linked list. Both indexed storage and the order invariant matter. Searching for a duplicate needs a stated first/last convention; finding an insertion position does not make the subsequent insertion cheap.[^ref-0a5e7abdf3a7]
Manages Complexity¶
An array can be sorted once and then searched repeatedly. The query advantage should be weighed against the linear movement needed for frequent middle updates. No universal superiority over hash tables, trees or disk-sorted files follows from the simple array's complexity bounds.
Abstract Reasoning¶
For sorted A, a midpoint comparison eliminates one half of candidate indices. Two lower/upper boundary searches isolate all keys in [a,b] as an adjacent slice. To insert at the middle while preserving both order and contiguity, the later suffix must move.[ref-5e648c6537fe][ref-0a5e7abdf3a7]
Knowledge Transfer¶
The address-keyed gprof table and coordinate-keyed range array share indexed-order search. Their exact operations, comparators and update schedules differ. Live Data Structure is the strict arrangement-for-use parent; the sorted key order and indexed layout are this child's differentia.
[^ref-5409d4da09b8]: GNU Binutils, gprof manual.
[^ref-5e648c6537fe]: MIT OpenCourseWare, 6.046J Lecture 9.
[^ref-0a5e7abdf3a7]: Python Software Foundation, bisect documentation.
Relationships to Other Abstractions¶
Current abstraction Sorted Array Domain-specific
Parents (1) — more general patterns this builds on
-
Sorted Array is a kind of Data Structure Prime
A sorted array is a concrete data structure combining indexable storage with maintained key order.
Hierarchy path (1) — routes to 1 parentless root
- Sorted Array → Data Structure → Trade-offs → Constraint
Neighborhood in Abstraction Space¶
Sorted Array sits in a moderately populated region (59th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Storage & Lookup Data Structures (21 abstractions)
Nearest neighbors
- K-d Tree — 0.87
- Multimap — 0.85
- Parallel Array — 0.85
- Queap — 0.85
- Queue (FIFO Abstract Data Type) — 0.84
Computed from structural-signature embeddings · 2026-10-08