algorithm to determine whether a value is within a range of a multiple
algorithm, python
Solution
I find this solution easier to understand:
remainder = (value % cycle)
(remainder <= range) || (cycle - remainder) <= range
Basically I find the remainder of the `value` I search for in respect of the modulo (`cycle`) and then check if it is within the expected range.
Alternative:
An alternative solution (doing essentially the same) will be:
remainder = (value % cycle)
min(remainder, cycle - remainder) <= range
You are free to choose whichever of the two solutions you like better.
NOTE This algorithm works verbatim if `range` < `cycle`. In the other cases answer is always true.
Problem
Algorithm question: Let's say I want to determine whether a value is within a range (eg 2) of a tens multiple -- so, 8-12, 18-22, 28-32, etc. My current solution is to add the range to the value, mod by 10, then re-subtract the range -- thus leaving me with something from -2 to 8 -- and then check whether the absolute value is less than the desired range. ``` value = 38 range = 2 cycle = 10 tweaked_mod = ((value + range) % cycle) - range # tweaked_mod = -2 within_range = (abs(tweaked_mod) <= range) # within_range = True ``` versus: ``` value = 37 range = 2 cycle = 10 tweaked_mod = ((value + range) % cycle) - range # tweaked_mod = 7 within_range = (abs(tweaked_mod) <= range) # within_range = False ``` It works, but it's awkward. Am I missing a more intuitive / succinct algorithm here?