$.$ Describe the optimal algorithm, the LRU algorithm and the FIFO algorithm for cache block replacement. Given a memory block reference sequence $701203042303142345467650101001122,$ trace the $3$ algorithms for a $2-$way set$-$associative cache with $4$ blocks, calculate the cache hit ratios for the FIFO and LRU. If the sequence of memory accesses are all read operations, and suppose that copying a block of data from memory to cache takes $100$ cycles, calculate the average memory access latency for this sequence of memory references assuming a cache hit takes $10$ cycles.