An algorithm is a finite procedure that turns an input into an output. Choosing one means deciding which costs matter for the workload: running time, memory, implementation risk, or behavior on hostile input.
Complexity analysis (Big O) compares growth rates before any code is benchmarked. An O(n log n) sort can remain practical at input sizes where O(n²) work does not. Big O says nothing about constant factors or cache behavior, though, and it cannot predict the data a production system will receive. The final choice still needs measurements on representative inputs.
Consider membership checks against a large list of IDs. Repeated queries can justify sorting once and using binary search. A single query usually cannot: the preprocessing costs more than a plain linear scan saves.
Algorithms Inside Systems
System-design diagrams hide algorithms inside boxes labelled “cache,” “scheduler,” or “database.” Naming the mechanism makes its cost and failure boundary visible.
| Mechanism | System use | Cost or failure boundary |
|---|---|---|
| Hashing | Cache keys, partition selection, deduplication | Collisions require equality checks. Changing a naive modulo shard count remaps most keys |
| Consistent hashing | Distributing keys across changing node sets | Reduces remapping. Virtual nodes or another weighted ownership scheme can reduce skew, which still requires load observation |
| Trees and prefix search | Database indexes, routing tables, autocomplete | Shape and storage model determine update cost and range behavior |
| Graph traversal | Dependency analysis, routing, recommendations | Cycles require visited-state. Dense graphs can dominate memory |
| Heap-backed priority queues | Scheduling, timers, top-k selection | Efficient best-item access does not provide sorted iteration |
| Bloom filters | Skipping absent database or object-store reads | False positives perform unnecessary work. False negatives are forbidden by construction |
| Token buckets | Rate limiting with bounded bursts | A shared bucket needs atomic coordination. Per-node buckets only approximate a global limit |
| Consensus | Replicated metadata and leader election | Safety requires quorum communication. A partition that cannot form a quorum loses progress while the quorum side can continue |
The visual is a topic inventory, not a universal priority ranking. A design decision depends on the mechanism’s invariant and where it fails under the actual workload.