1. Use strong induction to prove that the algorithm below correctly returns the maximum value for every array of size 1 or more. \begin{tabular}{1} \begin{tabular}{[1]} \hline Input: data: array with $n$ integers W Input: $n: $ size of data Output: the maximum of data; that is, an element " data[m] such that data[m] is greater than or W equal to every element of data \end{tabular} \ \begin{tabular}{1[1] 1 & Algorithm: RecursiveMax 1 2 & if $n=1$ then 3 & return data[1] 4 & else 5 & $\operatorname{mid}=\lfloor n / 2 floor$ 6 & \ellmax $=$ RecursiveMax $( $ data $[1.. mi d])$ \\ 7 & rmax $=$ RecursiveMax $($ data $[\operatorname{mid}+1..n])$ 8 & if $\ell max \geq \operatorname{rmax} \operatorname{then} $ 9 & return $\ell \max $ 10 & else 11 & return $\operatorname{rmax}$ 12 & end 13 & end \end{tabular} \ \hline \end{tabular} CS.VS. 1104