How efficient is binary search?

In each iteration, we are **cutting the list in half.** The time complexity is `O(log N)`

.

A sorted list of `64`

elements will take **at most** `log`

_{2}`(64) = 6`

comparisons.

In the worst case:

Comparison 1: We look at the middle of all

`64`

elementsComparison 2: If the middle is not equal to our search value, we would look at

`32`

elementsComparison 3: If the new middle is not equal to our search value, we would look at

`16`

elementsComparison 4: If the new middle is not equal to our search value, we would look at

`8`

elementsComparison 5: If the new middle is not equal to our search value, we would look at

`4`

elementsComparison 6: If the new middle is not equal to our search value, we would look at

`2`

elements

When there’s `2`

elements, the search value is either one or the other, and thus, there is at most `6`

comparisons in a sorted list of size `64`

.

### Instructions

A sorted data-set speeds up searching by a significant amount!

Without any knowledge about the ordering, we would resort to a linear search taking `O(N)`

time.

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