Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

Solutions to Chapter 16 | Low Level
16.8 A device boots with an empty FIFO queue. In the first 400 ns period after startup,
and in each subsequent 400 ns period, a maximum of 80 words will be written to the
queue. Each write takes 4 ns. A worker thread requires 3 ns to read a word, and 2 ns to
process it before reading the next word. What is the shortest depth of the FIFO such
that no data is lost?
SOLUTION
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While a perfectly optimal solution is complex, an interviewer is most interested in how you
approach the problem.
THEORY
First, note that writes do not have to be evenly distributed within a period. Thus a likely worst
case is 80 words are written at the end of the first period, followed by 80 more at the start of
the next.
Note that the maximum write rate for a full period is exactly matched by a full period of processing
(400 ns / ((3 ns + 2 ns)/process) = 80 processed words/period).
As the 2nd period in our example is fully saturated, adding writes from a 3rd period would
not add additional stress, and this example is a true worst case for the conditions.
A SAFE QUEUE DEPTH
For an estimate of maximum queue size, notice that these 160 writes take 640 ns (160 writes
* 4 ns / write = 640 ns), during which time only 128 words have been read (640 ns / ((3 ns + 2
ns) / word) = 128 words). However, the first read cannot start until the first write has finished,
which fills an extra slot in the queue.
Also, depending on the interactions between read and write timing, a second additional slot
may be necessary to ensure a write does not trash the contents of a concurrently occurring
read. Thus, a safe estimate is that the queue must be at least 34 words deep (160 - 128 + 1 +
1 = 34) to accommodate the unread words.
FINDING AN OPTIMAL (MINIMAL) QUEUE DEPTH
Depending on the specifics of the problem, it’s possible that the final queue spot could be
safely removed. In many cases, the time required to do an edge case analysis to determine
safety is not worth the effort. However, if the interviewer is interested, the full analysis follows.
We are interested in the exact queue load during the final (160th) consecutive write to the
queue. We can approach this by graphing the queue load from time = 0 ns, observing the
pattern, and extending it to time = 716 ns, the time of the final consecutive write.
The graph below shows that the queue load increases as each write begins, and decreases
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Cracking the Coding Interview | Knowledge Based