Is such an algorithm possible?

Question

Algorithms

Recently I was at an interview, they gave a test task in which it was necessary to come up with an algorithm.
The algorithm should suggest a purchase category based on the amount and date of purchase.
You need to rely only on existing operations (!).
Is it possible to come up with something similar? I answered in the negative.

Answer 1

display the average sums by category and compare.

Answer 2

Using binary search in the sorted purchase history, we are looking for the nearest sums Sn1+, Sn1-
We look at their categories:
- k and k --> the category of our sum Sn is k
- k and k+1 --> we set k+1 or calculate the difference of sums by modulo (Sn1+)-Sn and (Sn1-)-Sn. Let's say (Sn1-)-Sn is min, put the category k