Algorithm: how to find a column in matrix filled with all 1, time complexity O(n)?

Question

I have a matrix which looks like this:

| 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 | 1 |
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Answer 1

Let me take a very wild guess on what you are trying to do. Hint from the mention of:

1. The array represent relation on people
2. You are finding a column with all 1s
3. You are trying to find an O(n) algorithm

Well, you can not do that in O(n) and I can prove that it is O(n^2) only.

But my wild guess is that you doing a classic celebrity identification problem, and that you misunderstood the problem.

A celebrity is person that is known by every other person, but doesn't know any [other people].

I celebrity identification problem, you are trying to find something like:

Find the number i where
a[i][x] = 1 for all x            -> every one knows the celebrity
a[x][i] = 0 for all x != i       -> the celebrity doesn't know anyone else

And indeed with this extra constrain on what you are trying to find, there is an O(n) solution.