The first improvement we can make to our program is to take advantage of an
operator Python (and most programming languges) provides to calculate
remainders. Everyday arithmetic gets by with addition, +, subtraction, -,
multiplication, *, and division /, but remainders occur in a host of common
algorithms so programming languages provide a fifth arithmetic operator in
addition to the common four. The fifth operation is named modulo and is
denoted in Python by the symbol %. It returns the remainder of a division. For
example 17 / 5 is 3 because 5 goes into 17 three
times, but what if we need to know how much was "left over"? We use the modulo
operator like this: 17 % 5 to get 2, the remainder when 17 is
divided by 5.
We wrote instructions of our own to calculate the remainder above but using modulo will be more compact, i.e. make our program shorter, and may well be more efficient (because the language writers will have implemented it as efficiently as possible), and will at any rate not be less efficient.
Using modulo we can rewrite the processing portion of our program like this:
days = tot_seconds / (24*60*60)
remainder = tot_seconds % (24*60*60)
hours = remainder / (60*60)
remainder = remainder % (60*60)
minutes = remainder / 60
remainder = remainder % 60%. This operation is useful for packaging a large quantity
into smaller packages, e.g. a large number of seconds into packages of
days, hours, minutes and seconds. This sort of packaging turns out to be a
common operation in many kinds of problems.