An LRU cache combines a key lookup table with an ordered list so reads and writes can refresh recency efficiently.
How to reason about it
Start by identifying the state the method maintains and the operation that changes it. Then trace one small input by hand. This separates the invariant that makes the method correct from implementation details such as arrays, pointers, counters, or protocol messages.
Worked example
When a full cache receives a new key, remove the list's least-recently-used tail and insert the new key at the front.
Write down the state before and after each step. For a larger input, repeat the same transition rather than guessing from the final output. That habit makes edge cases visible and gives you a concrete basis for testing.
Trade-offs and common mistakes
LRU is a policy choice, not a guarantee that recently used data will be requested again.'
Choose this technique when its assumptions match the problem. State those assumptions explicitly, test an empty or boundary input, and compare the cost of the operation you perform most often with the memory or setup cost it introduces.
Takeaway
LRU Caches: Evicting the Least Recently Used becomes easier to use once its invariant, input assumptions, and failure cases are clear. A small worked example is a useful first test; measurements and proofs should follow when the system grows.