In which case will the linear search return the lowest value faster than the
binary search?

A linear search is one that scans every record/file until it discovers the value being searched for.

Binary search, on the other hand, is also known as Logarithmic search. It is used to locate the position of a value inside an array that has already been sorted.  

The linear search will return the lowest value faster than the binary search when small arrays are involved.

This will only be feasible when the array is sorted prior.

Cheers!

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