This trace follows the actual state transitions behind the companion Hash Tables: From Keys to Buckets. It describes a common execution path; implementation details can vary, so keep the contract separate from the mechanism.
Step 1: Compute a hash from the key
A hash table transforms a key into a hash value and uses part of that value to select a bucket or slot. The table then checks key equality because hashes can collide: equal hashes do not prove equal keys. Correctness therefore depends on both a stable hash/equality contract and collision handling.
Step 2: Select a bucket or slot
With separate chaining, each bucket holds a collection of entries. With open addressing, collisions probe other slots according to a rule. As occupancy rises, probe sequences or bucket chains tend to grow, so implementations resize around a chosen load factor. Resizing reassigns entries because bucket positions depend on table capacity.
Step 3: Check key equality
After selecting a candidate bucket, compare the original key for equality; a hash match narrows the search but cannot establish that two keys are the same.
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: Resolve collisions or resize
Expected constant-time lookup relies on assumptions about hash distribution and workload; adversarial keys can create long chains or probe clusters. Mutable keys are dangerous when their hash changes after insertion. Hash tables also do not inherently preserve sorted order and may use more memory than a compact array.
Step 5: Return the value or absence
Explain why a map must compare the original key after a hash match. Then describe what goes wrong if a key object changes a field used by its hash after insertion.
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.