However, binary search is only valid if the list is in sorted order.

They've figured out how they can do a binary search in order to narrow it down.

However, a binary search can only be performed if the list is in sorted order.

Also, using a binary search within a sorting method is debatable.

Several algorithms closely related to or extending binary search exist.

Many standard libraries provide a way to do a binary search:

If not, you can do a binary search on .

Vale had sat through twenty minutes of the binary search without complaint.

For example, one may sort the list and use binary search, or build any efficient search data structure from it.

The second problem can also be solved in O(log n) time by binary search.