Choosing mutually exclusive pairs efficiently

Question

This is a problem that could be done with some type of brute-force algorithm, but I was wondering if there are some efficient ways of doing this.

Let\'s assume that

Answer 1

Edit: This won't work as user98235 points out in the comments. I will leave this here however in case anyone else has the same idea.

I think this will work if I have understood the problem correctly.

Pseudocode:

resultList = new List of Pair
elementSet = new Set of int

for pair in inputPairs:

    if not elementSet.Contains(pair.First) and not elementSet.Contains(pair.Second):
        elementSet.Add(pair.First)
        elementSet.Add(pair.Second)
        resultList.Add(pair)

The time complexity will be O(N).