$1.$ Describe the problem.

$2.$ Design an algorithm as a pseudo code to solve this problem.

$3.$ Describe the type of your algorithm $($dynamic programming, greedy, $...)$ and

analyze the time complexity for this algorithm.

$4.$ The output obtained as a result of executing your implemented algorithm in

Java.

$1$: $($Elevator Optimization$)$ Assume that you work in a very tall building with a

slow elevator. The elevator is frustratingly interrupted when people press buttons

for many neighboring floors during a trip. Encountering interruptions during an

upward journey becomes especially frustrating when individuals press buttons for

several neighboring floors, like $13,14,$ and $15.$ The ascent is repeatedly

interrupted three times, once at each of these floors. A more considerate

approach would be for those passengers to collectively agree to press only the

button for floor $14.$ Subsequently, individuals on floors $13$ and $15$ could opt to use

the stairs for a single floor, taking advantage of the opportunity to walk. We

presume that the cost of ascending a flight of stairs is equivalent to descending $$

considering the health benefits of exercise. To resolve ties between solutions with

equal costs, management suggests prioritizing elevator stops at the lowest floor

possible, as this consumes less electricity. Importantly, the elevator is not

obligated to stop precisely at the floors specified by riders; for instance, if riders

indicate floors $27$ and $29,$ the elevator can choose to stop at floor $28$ instead. Your

task is to optimize the elevator's stops to minimize the total walking distance for

the riders.