Code Golf – Converting seconds to hh:mm:ss.mmm, or reduce() ad absurdam

I’ve had to do some timing using time.clock(), but I like seeing output as hh:mm:ss.000.  divmod is the perfect tool for this, as it does the division and remainder in a single call (rekindling my love for Python’s ease in returning multiple values from a function):

def to_hhmmss(sec):
    min,sec = divmod(sec,60)
    hr,min = divmod(min,60)
    return "%d:%02d:%06.3f" % (hr,min,sec)

Right about the time I wrote that, I happened to see an example using reduce, and thought about using successive calls to divmod to build up the tuple to be passed in to this function’s string interpolation.  That is, I needed to call reduce in such a way to convert 3601.001 to the tuple (1, 0, 1, 1) (1 hour, 0 minutes, 1 second, and 1 millisecond).

reduce() applies a binary operation to a sequence by taking the first two items of the sequence, performing the operation on them and saving the result to a temporary accumulator, then applies the binary operation to the accumulated value and the 3rd item in the sequence, the to the 4th item, etc.  For instance to use reduce to sum up a list of integers [1,5,10,50], we would call reduce with the binary operation:

fn = lambda a,b: a+b

and reduce would work through the list as if running this explicit code:

acc = 1
acc = fn(acc, 5)
acc = fn(acc, 10)
acc = fn(acc, 50)
return acc

I need reduce to build up a tuple, which is a perfectly good thing to do with tuple addition.
Also, I’m going to convert the milliseconds field into its own integer field also, so I’ll need to convert our initial value containing seconds to a value containing milliseconds (also allowing me to round off any decimal portion smaller than 1 msec). And I’ll use divmod with a succession of divisors to get the correct time value for each field.

So the sequence of values that I will pass to reduce will be the succession of divisors for each field in the tuple, working right to left.  To convert to hh, mm, ss, and msec values, these divisors are (1000, 60, 60), and these will be the 2nd thru nth values of the input sequence – the 1st value will be the value in milliseconds to be converted.

The last thing to do is to define our binary function, that will perform the successive divmods, will accumulating our growing tuple of time fields.  Maybe it would be easiest to just map out how our sample conversion of 3601.001 seconds (or 3601001 msec) would work, with some yet-to-be-defined function F.  The last step in the reduce would give us:

(1,0,1,1) = F((0,1,1), 60)
  (0,1,1) = F((1,1), 60)
    (1,1) = F(msec, 1000)

Well, that last line (representing the first binary reduction) looks bad, since all the others are taking a tuple as the first value.  It seems that each successive reduction grows that value by one more term, so the first term should be a 1-value tuple, containing our value in milliseconds:

    (1,1) = F((msec,), 1000)

Also, it’s not really true that this step would have to return (1,1).  Just so long as the final tuple ends with (…,1,1).  So I’ll redo the sequence of steps showing X’s for the unknown intermediate values:

(1,0,1,1) = F((X,1,1), 60)
  (X,1,1) = F((X,1), 60)
    (X,1) = F((msec,), 1000)

The heart of our mystery function F is essentially a call to divmod, using the 0’th element in the current accumulator:

F = lambda a,b : divmod(a[0],b)

But F has to also carry forward (accumulate) the previous divmod remainders, found in the 1-thru-n values in the tuple in a.  So we modify F to include these:

F = lambda a,b : divmod(a[0],b) + a[1:]

Now we have just about all the pieces we need. We have our the binary function F.  The sequence of values to pass to F is composed of the initial accumulator (msec,), followed by the divisors (1000, 60, 60).  We just need to build our call to reduce, and use it to interpolate into a suitable hh:mm:ss-style string:

def to_hhmmss(s):
    return "%d:%02d:%02d.%03d" % \
        reduce(lambda a,b : divmod(a[0],b) + a[1:], [(s*1000,),1000,60,60])

This may not be the most easy-to-read version of to_hhmmss, but it is good to stretch our thinking into some alternative problem-solving approaches once in a while.

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