# Multi-level random selection implementation [closed]

## Structure

I have a structure like this:

• level 1 items represented by a capital letter (A, B, C, D,...)
• level 2 items represented by lower case letter (a, b, c, d,...)
• level 3 items repredented by numbers (1, 2, 3, 4,...)

these items are grouped into "combination" consisting of:
(level 1 item, level 2 item, level 3 item) always in this order.
e.g. (A, c, 5)

Let's say level 1 items are only 4: A, B, C, D
level 2 items are the first 10 letters : a, b, c, d, e, f, g, h, i, j
level 3 items are represented by natural numbers up to 30

Not all possible combinations are considered valid! The suitable combinations are grouped into a list:

(A, f, 3)
(A, f, 8)
(A, f, 10)
(A, j, 23)
(B, h, 1)
(D, d, 30)
(D, g, 18)


The combination list does not allow duplicates, so every combination is unique.

## Process

• Randomly select 1 lvl 1 item from all the possibles (A, B, C, D)
e.g. random selection gives: A
• Retrieve all combinations that have A as lvl 1 item:
(A, a, 12)
(A, f, 3)
(A, f, 8)
(A, f, 10)
(A, j, 23)

• Now from lvl 2 items remained in these 5 combinations (a, f, j), one item is randomly selected. Let's say selection gives f.
Remark: I need to avoid that numerosity of a single lvl 2 item influence the random selection. So in this case the random selection cannot be done simply picking one of the 5 combinations above because it is more likely to pick f (3 of 5) than a or j (1 of 5 each).
Retrieve all combinations that have f as lvl 2 item:
(A, f, 3)
(A, f, 8)
(A, f, 10)

• From lvl 3 items remained in these 3 combinations (3, 8, 10), one item is randomly selected. Let's say 8. identify the unique combination:
(A, f, 8)


Moreover this process is repeated to pick a 2nd random combination. But in this case there is another limitation. The new combination cannot contain the same lvl 1 item. So it has the following form:
(everything but A, lvl 2 item, lvl 3 item) or
(not A, lvl 2 item, lvl 3 item)

All these operation are performed to pass the combination to another application as input.

## Questions

1. What do you think could be the most efficient way to implement such a process?
2. Is it worth using a relational database? (I expect very complex query)
3. Is it better to perform this type of operation using a programming language? e.g. pandas dataframe in Python)

PS: I'm not sure if this questions belongs in this section so please give me feedback on this.

## closed as too broad by gnat, BobDalgleish, Jörg W Mittag, user53019 Jun 18 at 12:08

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Are you really only dealing with a maximum of 1,200 legal combinations ? – High Performance Mark Jun 9 at 11:02
• @HighPerformanceMark yeah I think all possible combinations are exactly 4x10x30 = 1200.. maybe in my real situation lvl3 items are 40/50 instead 30 so we end up with a total of 2000 combinations – basic-ph Jun 9 at 11:29
• I don't have time right now to write an answer, but for such modest sizes of lists I'd suggest simply storing all A,_,_, combinations in one list, all B,_,_, in another, etc. Then you have to select a list at random, and an entry at random, followed by a random selection from one of the other lists. I don't see a role for a DBMS while computing (though you might have reasons to use one for more permanent storage). As for efficiency, I'm not sure that the lists are large enough to warrant anything more advanced than I have already suggested. – High Performance Mark Jun 9 at 12:08
• @HighPerformanceMark thanks for your time. I got the point about splitting into different lists. What do you mean by for more permanent storage speaking about DBMS? – basic-ph Jun 9 at 12:18
• @HighPerformanceMark maybe there is an issue with your strategy. See remarks in the question – basic-ph Jun 9 at 15:06

If I understood your question well, you don't want to pick from a pregenerated list of possible combinations because it will mess up the probabilities per level. One way to deal with that is to make a random pick level-by-level, after you've filtered out disallowed items based on previous picks. Since you've said you're doing this in Python, here's some code to help flesh out the idea (for me, Python is more like an occasional hobby, so the code might not too pythonic; feel free to change and adapt it as you see fit).

import random

level1 = ['A', 'B', 'C', 'D']
level2 = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']
level3 = list(range(1, 31))

possible_combinations = [
('A', 'f', 3),
('A', 'f', 8),
('A', 'f', 10),
('A', 'j', 23),
('B', 'h', 1),
('D', 'd', 30),
('D', 'g', 18)
]

def level1_filter(items_to_ignore, collection_element):
allowed = []
if not items_to_ignore:
allowed = [c[0] for c in possible_combinations]
else:
allowed = [c[0] for c in possible_combinations if c[0] not in items_to_ignore]
return collection_element in allowed

def level2_filter(level1_item, collection_element):
allowed = [c[1] for c in possible_combinations if c[0] == level1_item]
return collection_element in allowed

def level3_filter(level1_item, level2_item, collection_element):
allowed = [c[2] for c in possible_combinations if c[0] == level1_item and c[1] == level2_item]
return collection_element in allowed

def pick_one(collection):
if len(collection) > 0:
return random.choice(collection)
return None

def pick_n_combinations(n):
picked_level1_items = []
for i in range(n):
item1 = pick_one([e for e in level1 if level1_filter(picked_level1_items, e)])
item2 = pick_one([e for e in level2 if level2_filter(item1, e)])
item3 = pick_one([e for e in level3 if level3_filter(item1, item2, e)])
picked_level1_items.append(item1)
yield (item1, item2, item3)

print(list(pick_n_combinations(3)))


Note: the allowed collections in the filter functions will have repeated items, but this doesn't affect the probability since they are not used for picking, just for filtering.

• thanks for your time. Your code works good! In the case possible_combinations list contains 1500-2000 items I can import it from an external plain text file (.txt or .csv). What do you think? – basic-ph Jun 10 at 17:08
• That should work. Try it, see how it goes. – Filip Milovanović Jun 11 at 5:58