Sorted data is a gift

A sorted list gives you information for free: equal values sit side by side, and everything smaller than an element is to its left. A solution that does not use that is a solution written for an unsorted list.

1count = 0
2previous = None
3for v in values:
4    if v != previous:
5        count += 1
6        previous = v
7return count

Looking for a value in a sorted list you do not look at it all either. Look at the middle element: if what you want is larger, throw away the whole left half; if smaller, the right half. Each step halves what is left; a million elements take twenty steps. This is binary search.