Example $1$

Robot testing A defense industry firm wants to determine the

highest floor of its $n-$storey building from which a robot can fall

without breaking.

The firm has two identical robots to experiment with. If one of them

gets broken, it cannot be repaired, and the experiment will have to

be completed with the remaining robot.

a$)$ Design an algorithm with $O(n)$ complexity that finds the highest

floor with less than $\frac{n}{2}$ drops in the worst case.

b$)$ Design an algorithm that finds the highest floor with $O(Vn)$

complexity.