Question $4$:$30$ points

Consider your path to success, which is pretty much like climbing a ladder. Very frequently in

life, as it is strictly the case for this problem, there are two choices in front of you: you either

step to the next step of the ladder, or skip the middle one and step on the second step. And

each step comes with a certain level of success $($or failure$),$ which is quantified by an integer

for this problem.

More formally, you are given an array of integers that represents the ladder and the values

stored in the array represents the contribution of landing on this step to your success.

Considering the costs of each step of the ladder, you are expected to suggest a strategy $($i$.$e$.,$

an algorithm$)$ that will provide the optimal steps to be taken to maximize the success by the

time you reach the pinnacle of your career. $($Disclaimer: once they reach the pinnacle, human

beings either die and conclude their success story in dust, or fall from there before they die

and still end their story in dust!!! Moral of the story: Success in career shouldn't be the end

goal...$)$

$($a$)[15$ points$]$ Suggest an algorithm for this problem $($in bullet points$)$ that utilizes binary

trees as part of its solution. Explain the runtime of your algorithm.

$($b$)[15$ points$]$ Suggest a more efficient algorithm that uses graphs instead of binary trees.

explain the runtime of your algorithm.