Look for a specific number in a sorted list by repeatedly cutting the search area in half.
Find the leftmost position where you could insert a number into a sorted list and keep it sorted.
Find where a number first and last appears in a sorted list that may have duplicates.
Find the largest integer whose square is less than or equal to x.
Find any element in an array that is bigger than both its neighbors.
Find the smallest number in a sorted array that has been rotated (e.g., [4,5,6,7,0,1,2]).