LRU Page Cache for B-Tree Nodes

Write a C program that implements an LRU page cache for B-tree nodes.

Requirements:

• Define a CacheEntry struct: page_id, is_dirty, last_access_time, data (a simple int representing the page)
• Define a PageCache struct: entries array, capacity, count, current_time
• Implement cache_get(cache, page_id): return the page data or -1 if miss. On hit, update last_access_time.
• Implement cache_put(cache, page_id, data, is_dirty): add to cache, evict LRU if full
• Implement cache_evict_lru(cache): remove the entry with smallest last_access_time
• Simulate a workload:
  1. Access pages: 1, 2, 3, 4, 5 (all miss, cache capacity=3, so pages 1,2,3 loaded, then 4 evicts 1, 5 evicts 2)
  2. Access page 3 (hit)
  3. Access page 1 (miss, evicts LRU)
  4. Write page 6 (dirty)
• After each access, print cache state: page IDs in cache, hits/misses so far
• Print final dirty pages that need flush
• Calculate and print the hit rate
• Include a note about why write-back caching is used with WAL for durability