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Invariants you can prove
Caches, heaps, tries, filters and balanced trees, each with explicit invariants and complexity targets.
Build constant-time lookup and eviction with a hash map and a doubly linked list.
Evict by access frequency with an LRU tie-break and constant-time bookkeeping.
Combine exact expiry checks with generation-safe cleanup and bounded capacity.
Maintain a heap plus identity index for efficient priority changes and removal.
Implement a fixed-capacity FIFO with wraparound and explicit overflow behavior.
Build a bounded probabilistic membership structure with compatible serialization.
Implement exact lookup, prefix enumeration and deletion using compressed edge labels.
Implement deterministic virtual-node placement and immutable membership snapshots.
Track connected components with path compression, union by size and stable API rules.
Build an ordered map with randomized towers, range scans and injectable randomness.
Maintain deterministic logarithmic map operations with rotations and deletion rebalancing.
Build an insertion-only ordered index with leaf splits, separator propagation and range scans.