How to count the presence of a set of numbers in a set of intervals efficiently

Question

The input parameters are a list of tuples representing the intervals and a list of integers. The goal is to write a function that counts the number of intervals each integer

Answer 1

You can presort the integers and then use bisect_left on the lower bound. Sorting has O(M*log(M)) complexity while bisect has O(log(M)). So effectively you have O(max(M, N) * log(M)).

import bisect
from collections import defaultdict

result = defaultdict(int)
integers = sorted(integers)
for low, high in intervals:
    index = bisect.bisect_left(integers, low)
    while index < len(integers) and integers[index] <= high:
        result[integers[index]] += 1
        index += 1