Suppose you are given an array A with n entries, with each entry holding a distinct number. You are told that the sequence of values A$[1],$ A$[2],...,$ A$[$n$]$ is unimodal: for some index p between $1$ and n$,$ the values in the array entries increase up to position p in

A and then decrease the remainder of the way until position n$.$ For example, the array A $=$

$[1345678521]$ is unimodal, with the entries increasing up to position A$[7]=8$ and decreasing afterwards. Implement an algorithm that finds the $$peak entry$$ p without having to read the entire array. Your algorithm should run in O$($logn$).$ After designing the algorithm, prove that the running time of the algorithm is O$($logn$).$

$**$ Include the following: $1)$ a listing of your algorithm $($pseudo code$),2)$ prove that the running time of the algorithm is O$($logn$),3)$ Source code $($C$++).$