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Caching With Invalidation Rules

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Problem

SimSpace Cyber frequently retrieves values that change only occasionally. Implement a cache simulator that supports time-based expiration, least-recently-used eviction, direct key invalidation, and dependency-based tag invalidation.

A cached value is valid only when it has not exceeded the TTL, its key version is unchanged, and every dependency tag version matches the snapshot stored when the value was cached. Updating a source value invalidates that key and every cached entry sharing one of its tags.

Formal Specification

Implement simulate_cache(initial, tags, operations, capacity, ttl). initial maps each key to its current integer value. tags maps each key to a list of dependency-tag strings. operations contains arrays in chronological order:

  • ["get", key, timestamp]
  • ["set", key, value, timestamp]
  • ["invalidate_key", key, timestamp]
  • ["invalidate_tag", tag, timestamp]

Return an object with results, containing values returned by get operations in order, plus hits, misses, and evictions counters. A miss loads the current value from initial and stores it if capacity > 0. A timestamp exactly ttl units after insertion is expired. Assume all requested keys exist.

Constraints

  • 1 <= len(initial) <= 10^5
  • 1 <= len(operations) <= 2 * 10^5
  • 1 <= capacity <= 10^5
  • 1 <= ttl <= 10^9
  • Timestamps are nondecreasing integers
  • Each key has at most 10 dependency tags

Function Signature

def simulate_cache(initial, tags, operations, capacity, ttl):
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