Find the year with the most number of people alive in Python

Question

Given a list of people with their birth and end years (all between 1900 and 2000), find the year with the most number of people alive.

Here

Answer 1

I would go like this:

• Sort persons by birth year (unborn list)
• Starting from the first born
  • Put that person in the alive list
  • Using an insertion sort by date of death (the list stays sorted, so use a binary search)
  • Until you reach a person that was not born that year
• Then, starting from the person in the alive list that dies first, remove it from the list.
• Put the size of the alive list in a dict
• Increment the year
• Loop until the unborn and alive lists are empty

Complexity should be around O((m + n) * log(m)) (each year is considered only once, and each person only twice, multiplied by the insertion cost in the alive list)

Implementation

from bisect import insort

def most_populated(population, single=True):
    years = dict()
    unborn = sorted(population, key=lambda x: -x[0])
    alive = []
    dead = []
    for year in range(unborn[-1][0], max(population, key=lambda x: x[1])[1] + 1):
        while unborn and unborn[-1][0] == year:
            insort(alive, -unborn.pop()[1])
        while alive and alive[-1] == -(year - 1):
            dead.append(-alive.pop())
        years[year] = len(alive)
    return max(years, key=years.get) if single else \
           [key for key, val in years.iteritems() if val == max(years.values())]