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Not sure if this is the right place get help with this kind of problem, but I am trying to solve this by coding so I'll try. If anyone knows about some better suited forum/place for this kind of problem, let me know.

I have a data frame that looks like this:

import pandas as pd


data = {
    "ID": [1, 2, 3, 4, 5, 6, 7....],
    "NAME": ["male_1", "male_2", "male_3", "male_4", "female_1", "female_2", "female_3"...],
    "M_F": ["M", "M", "M", "M", "F", "F", "F"...],
    "AGE": [9, 5, 8, 6, 10, 11, 9...],
    "GROUP": ["1,2,3", "1,2,3", "1,2,3", pd.NA, "5,6", "5,6", pd.NA...]
}


df = pd.DataFrame(data)

In r it can be written as

df <- data.frame(
  ID = c(1, 2, 3, 4, 5, 6, 7...),
  NAME = c("male_1", "male_2", "male_3", "male_4", "female_1", "female_2", "female_3"...),
  M_F = c("M", "M", "M", "M", "F", "F", "F"...),
  AGE = c(9, 5, 8, 6, 10, 11, 9..),
  GROUP = c("1,2,3", "1,2,3", "1,2,3", NA, "5,6", "5,6", NA...),
  stringsAsFactors = FALSE
)

And it something like this

| ID | NAME | M_F | AGE | GROUP |
| -- | ---- | --- | --- | ----- |
| 1  |male_1 | M| 9 | 1,2,3|
| 2  |male_2 | M| 5 | 1,2,3|
| 3  |male_3 | M| 8 | 1,2,3|
| 4  |male_4 | M| 6 | NA |
| 5  |female_1 |F|10|5,6|
| 6  |female_2 |F|11|5,6|
| 7  |female_3 |F|9|NA|
| . | . | . | . | .|

I have about 100 people in this data frame(length of DataFrame) , grouped as indicated by GROUP category in groups of up to 7 and some have no group (NAs). I need to place these people into huts/houses which can house 3, 4, 7 or 8 people. Number of these huts are as follows:

  • 4x hut with size 3
  • 13x hut with size 4
  • 4x hut with size 7
  • 4x hut with size 8

So I have a total housing capacity of 124(4 * 3 + 13 * 4 + 4 * 7 + 4 * 8) people for about 100 people, so there is some spare space. Criteria for placing people in these huts are as follows:

  1. Males and females have to be in separate huts
  2. Groups have to be respected, people with group = NA can be placed with any group, in any hut
  3. Difference in age between youngest and oldest in hut should be 4 years maximum

I am working on this problem in R, but I have little experience with Python as well, if that would be more comfortable for someone. Any help or ideas are appreciated. It is a passion project of mine, I am just trying to help out with some tedious task of manualy sorting these kids into huts on a summer camp :D
Cheers!

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The following script uses the assign_huts function, which primarily uses a greedy algorithm with heuristics to assign people to huts. It works as follows *Picks a hut size from the available capacities.

  • Iterates over remaining people, selecting those who fit the age constraint and belong to the same group.
  • Adds them to the hut until full.
  • Assign person jwth group= NA to hit first found.

Complexity is O(n log n)


from itertools import combinations

huts = dict(3=4 , 4=13 , 7=4 , 8=4) # {capacity: number of huts}

def parse_groups(x):
    return set(map(int, x.split(","))) if pd.notna(x) else set()

df["GROUP_SET"] = df["GROUP"].apply(parse_groups)

df.sort_values(by=["GROUP", "AGE"], inplace=True)

def assign_huts(df, huts):
    assigned_hut = []
    remaining_p = df.to_dict(orient="records")
    
    while remaining_p:
        for hut_size, count in huts.items():
            for _ in range(count):
                if not remaining_p:
                    break

                hut = []
                available_people = remaining_p[:]

                # Prioritize keeping groups together
                while available_people and len(hut) < hut_size:
                    for p in available_people[:]:
                        if not hut or (max(x["AGE"] for x in hut) - min(x["AGE"] for x in hut) <= 4): # xhecing the difference between minimum and Maximun age 
                            hut.append(p)
                            available_people.remove(p)
                            remaining_p.remove(p)
                            if len(hut) == hut_size:
                                break
                
                assigned_hut.append(hut)

    return assigned_hut

males = df[df["M_F"] == "M"].copy()
females = df[df["M_F"] == "F"].copy()

male_huts = assign_huts(males, huts)
female_huts = assign_huts(females, huts)

You can use knapsack, which ensures huts are filled more efficiently than a greedy approach, and it works efficiently in large inputs. But has a complexity of O(n * W) where W is the Hut capacity. [Hut capacity is not necessary, as stated by you

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