You are studying a searching algorithm used to find a specific value in a sorted array. This

algorithm operates by dividing the search interval in half at each step, comparing the target value

to the midpoint value, and then discarding one half of the search interval based on the

comparison, continuing with the remaining half.

a$.$ Based on this description, identify the algorithm used.

b$.$ Simulate the algorithm with the sorted array $,$

$80,90,100$ and the target value $70.$ Show how the target value $70$ is located

step$-$by$-$step, providing the midpoints and search intervals for each iteration until the

target is found.

c$.$ Consider a rotated sorted array $,$

$20$ and find the value $70$ using the modified version of the binary search algorithm.

Explain how the algorithm adapts to handle the rotation and describe the steps taken to

locate the target value $70.$