Captain Algos needs your help analyzing the flight path of her drone over a mountain range. The

drone$$s altitude at different points is recorded in an array, and it forms a peak.

A peaked array has the property that the subarray A$[1..$i$]$ has the property that the altitude increases steadily,

i$.$e$.$ A$[$j$]<$ A$[$j $+1]$ for $1$ j A$[$j $+1]$ for i $$ j $<$ n$.$ Using a flight simulator, she notes the

following peaked array A $=[7,8,10,15,16,23,19,17,4,1],$ as an example.

$1.$ She needs to find the highest point to ensure the drone has enough battery and can handle the pressure

changes. Write a recursive algorithm $($pseudocode$)$ that takes asymptotically sub$-$linear time to find the

maximum element of A$.$ Please write the complete pseudocode in algorithmic style. Use algortihm package

in latex. Please give a brief explanation of different aspects of your code.

$2.$ Prove that your algorithm is correct. $($Hint: can we use induction$/$ Loop invariance$)$