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

If you don't assume arbitrary content (as in Oli's answer) and you can encode each row as an unsigned integer with binary flags, then you can do it in O(n) and O(1) by just repeatedely performing a logical AND of each row with the latest result.

The final set of flags will only have ones where the relevant column was also one.