Question

I’m looking for algorithm with an average case performance of O(log(N)), to extract the elements are between (or equal to) a min and a max value from a sorted list.

The issue being that since the the min and max values may not actually be in the list, or perhaps even repeated, a binary search won’t do. Ternary search seems to be closer to what I seek, but I haven’t been able to create a function that does what I see based on ternary search so far.

For example, the input:

list=[1,2,3,4,5,6,7], min=3, max=6

Should return [3,4,5,6]. Likewise,

list=[500,757,2412,10000,123123], min = 600, max = 5000

Should return [757,2412].

This could also be done in python less efficiently using:

def withinRange(values,min,max):
   return [val for val in sorted(values) if val <= max and val >= min]

The operation is called enough that a O(log(N)) is very much preferred, and the sorting will only be done once.

Answer 1

This seems to work:

>>> import bisect
>>> def bin_slice(L, min, max):
...     i = bisect.bisect_left(L, min)
...     j = bisect.bisect(L, max)
...     return L[i:j]
... 
>>> bin_slice([1,2,3,4,5,6,7,8,9], 3, 6)
[3, 4, 5, 6]
>>> bin_slice([500,757,2412,10000,123123], 600, 5000)
[757, 2412]

The complexity is something like 2log(N) which is O(log(N)). Also note that bisect may use a C implementation for bisect which will be faster than anything you can write in pure-python, so a pure-python solution will probably be slower even if doing a bit less comparisons.

You could optimize slightly the search for j passing the lo parameter to bisect:

j = bisect.bisect(L, max, i)