Write-back vs. write-through cache

Simulate a block cache with LRU replacement.

Input: policy (through or back), capacity (blocks), then operations: read b, write b, sync, crash.

• read b: hit if cached; on a miss, read the block from disk (disk read) and insert it.
• write b: a miss inserts the block without reading it (full-block write). With through, the block is written to disk immediately (disk write) and stays clean; with back, it becomes dirty.
• Eviction (when inserting into a full cache): remove the least recently used block; if it is dirty, write it to disk (disk write).
• Print read 3: miss / write 1: hit for each read/write.
• sync: write all dirty blocks, mark them clean: sync: 2 dirty blocks written (singular block for 1).
• crash: print CRASH: lost updates to blocks [4, 5] (sorted dirty blocks, or none) and empty the cache.

At the end: Operations: n, hits: h, disk reads: r, disk writes: w (reads and writes only count as operations).