LRU Cache

mediumTests passed 2026-11-11v1.0.0
TC: O(1)|SC: O(C)
Linked ListsDesignOriginal Statement (leetcode).md

1. Core Invariant / The Trick

Combine a HashMap (`key -> Node`) for O(1) lookup with an insertion/recency doubly-linked list (with dummy `head`/`tail` sentinels) so promotion to MRU and eviction from LRU both run in O(1).

2. Complexity Bounds & Proof

Hash lookup + pointer splice at head/tail executes fixed instructions per `get`/`put`; memory is bounded by capacity C.

3. Minimal Idiomatic Code

from collections import OrderedDict
class LRUCache:
    def __init__(self, capacity: int):
        self.cap = capacity
        self.cache = OrderedDict()

    def get(self, key: int) -> int:
        if key not in self.cache:
            return -1
        self.cache.move_to_end(key)
        return self.cache[key]

    def put(self, key: int, value: int) -> None:
        if key in self.cache:
            self.cache.move_to_end(key)
        self.cache[key] = value
        if len(self.cache) > self.cap:
            self.cache.popitem(last=False)

4. Failure Modes & Interview Follow-ups

Pitfalls:- Updating an existing key in `put` must promote it to MRU and NOT trigger capacity eviction if already present. - Built-in Map iteration order in JS/Python `OrderedDict` works cleanly too, but interviewers often ask for the manual DLL.
Follow-ups:- LFU Cache uses frequency buckets (Map of frequency -> doubly-linked list) plus `minFreq` tracking.

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Related Invariants

Reorder List (O(N))
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