Ordering without sorting algorithm

Hello guys, I've got a question related to my data structures class.

I have file in which data is unordered. Say:

hello program

red apple

blue sky

new phone

old number

I have to search a string using Binary Search. But since we cannot apply Binary Search to unordered list, we should make an ordered list using some sorting algorithms.

However, main point of my assignment is making an ordered list without using any sorting algorithms and then apply Binary Search.

Any ideas how to do that?

Any help will be highly appreciated!