This trace follows the actual state transitions behind the companion Choosing a Search or Sorting Strategy. It describes a common execution path; implementation details can vary, so keep the contract separate from the mechanism.
Step 1: Check ordering and update needs
Search and sorting choices depend on what is already known about the data and what operations the product needs. A sorted array supports binary search because its order lets each comparison eliminate half the remaining candidates. An unsorted collection cannot safely use that shortcut.
Step 2: Choose a search or sort plan
If a dataset is queried once, sorting solely to run one binary search may cost more than a linear scan. If it will serve thousands of lookups, paying the sort cost once can be worthwhile. Merge sort preserves equal-key order when implemented stably; quicksort often has strong locality but can have quadratic worst-case behavior without safeguards.
Step 3: Narrow or partition the range
For binary search, compare at the midpoint and discard only the half the ordering proves cannot contain the target; for one-off lookups, account for the cost of sorting first.
At this point, record the state that changed and check the invariant before advancing. If the operation repeats, make clear which values persist and which are recomputed.
Step 4: Handle duplicates and bounds
Sorting is not free metadata: updates can invalidate order, and duplicate handling affects semantics. Binary search also requires a precise boundary convention; off-by-one errors often appear when the target is absent or repeated. For large data, external sorting must account for disk reads and writes.
Step 5: Return the ordered result
Given repeated lookup, frequent insertion, and duplicate keys, compare a sorted array, balanced search tree, and hash table. Explain which requirement changes your choice.
The trace is complete when the result satisfies the stated contract. Compare this model with the concrete runtime or system you are studying before making a performance claim.