Question

Given a set integers, the problem consists of finding the number of possible arithmetic series of length 3. The set of integers may or may not be sorted.

I could implement a simple bruteforce algorithm taking time O(n^3) but time efficiency is important and the set of integers can be as large as 10^5. This means bruteforce obviously won’t work. Can anyone suggest some algorithm/pseudocode/code in c++?

An example: there are 4 numbers 5,2,7,8 . Clearly there is only one such possibility – (2,5,8) in which the common difference is 3, so our answer is 1.

EDIT:I forgot to mention one important property – each number of set given is between 1 to 30000 (inclusive).

Answer 1

You can do it in O(N^2) as follows: create a hash set of your integers so that you could check a presence or absence of an element in O(1). After that, make two nested loops over all pairs of set elements {X, Y}. This is done in O(N^2).

For each pair {X, Y}, assume that X < Y, and calculate two numbers:

Z1 = X - (Y-X)
Z2 = Y + (Y-X)

A triple {X, Y, Zi} form an arithmetic sequence if Zi != X && Zi != Y && set.contains(Zi)

Check both triples {X, Y, Z1} and {X, Y, Z2}. You can do it in O(1) using a hash set, for a total running time of the algorithm of O(N^2).