Count how many people are alive per year, based on their birthyear and deathyear, aims for simplicity.

count_living_per_year.py

import collections
import random
import timeit

pop = [
    (b := random.randint(1900, 2000), random.randint(b + 1, b + 100))
    for _ in range(10000)
]


# 5.049 s (with 10000 people [1,100] years old)
def count_living_per_year(population: list[tuple[int, int]]) -> dict[int, int]:
    living_per_year = {}
    for birth, death in population:
        for year in range(birth, death):
            if year in living_per_year:
                living_per_year[year] += 1
            else:
                living_per_year[year] = 1
    return living_per_year


print(sorted(tuple(count_living_per_year(pop).items())))
print(
    timeit.timeit(
        "count_living_per_year(pop)",
        globals=globals(),
        number=100,
    )
)


# 3.697 s (with 10000 people [1,100] years old)
def count_living_per_year(population: list[tuple[int, int]]) -> dict[int, int]:
    living_per_year = {}
    for birth, death in population:
        for year in range(birth, death):
            living_per_year[year] = living_per_year.get(year, 0) + 1
    return living_per_year


print(sorted(tuple(count_living_per_year(pop).items())))
print(
    timeit.timeit(
        "count_living_per_year(pop)",
        globals=globals(),
        number=100,
    )
)


# 3.929 s (with 10000 people [1,100] years old)
def count_living_per_year(population: list[tuple[int, int]]) -> dict[int, int]:
    living_per_year = collections.defaultdict(int)
    for birth, death in population:
        for year in range(birth, death):
            living_per_year[year] += 1
    return living_per_year


print(sorted(tuple(count_living_per_year(pop).items())))

print(
    timeit.timeit(
        "count_living_per_year(pop)",
        globals=globals(),
        number=100,
    )
)


# 4.084 s (with 10000 people [1,100] years old)
def count_living_per_year(population: list[tuple[int, int]]) -> dict[int, int]:
    return collections.Counter(
        year for birth, death in population for year in range(birth, death)
    )


print(sorted(tuple(count_living_per_year(pop).items())))

print(
    timeit.timeit(
        "count_living_per_year(pop)",
        globals=globals(),
        number=100,
    )
)

Here's a faster numpy implementation:

def count_living_per_year(population: list[tuple[int, int]]) -> dict[int, int]:
    return dict(np.stack(np.unique(np.concatenate([np.arange(*item) for item in population]), return_counts=True), axis=1))

Having to return a dict slows it down a bit.

Here's an updated numpy method, but it's not as quick as the optimized collections.Counter method:

def count_living_per_year(population: list[tuple[int, int]]) -> dict[int, int]:
    births, deaths = np.array(population).T

    def counter(arr, min, max):
        temp = np.zeros(((max - min) + 1))
        counter = np.unique(np.array(arr), return_counts=True)
        temp[counter[0] - min] = counter[1]

        return temp

    min, max = births.min(), deaths.max()
    births_count = counter(births, min, max)
    deaths_count = counter(deaths, min, max)
    delta_living = births_count - deaths_count
    living_per_year = np.cumsum(delta_living)

    return dict(np.stack((np.arange(min, max + 1), living_per_year), axis=1))

Looks like the numpy.unique method is not quite as efficient.

ChatGPT helped speed it up a little more using bincount instead of unique.:

def count_living_per_year(population: list[tuple[int, int]]) -> dict[int, int]:
    births, deaths = np.array(population).T
    min_year = births.min()
    max_year = deaths.max()
    years = np.arange(min_year, max_year + 1)

    birth_counts = np.bincount(births - min_year, minlength=max_year - min_year + 1)
    death_counts = np.bincount(deaths - min_year, minlength=max_year - min_year + 1)

    living_per_year = np.cumsum(birth_counts - death_counts)

    return dict(zip(years, living_per_year))

I looked at bincount but wasn't sure how to set the minlength - looks obvious now!