Question $1$

Optimization problems arise frequently in applications, and computer scientists aim to find the best solutions.

An example of such a problem is the Activity Scheduling Problem. A simple case of this problem is problem number $435$ on Leetcode $($here is a link Es$)$

Here is the problem description for your convenience:

Given an array of intervals intervals where intervals $,$ end $[$:${?}_i\},$ return the minimum number of intervals you need to remove to make the rest of the

intervals non$-$overlapping.

Note that intervals which only touch at a point are non$-$overlapping. For example, $1,2$ and $2,3$ are non$-$overlapping.

You can solve this problem by solving its dual, which is trying to return the maximum number of intervals that do not overlap. The maximum number of

intervals is the size of what we call an optimal schedule.

As a primary test of understanding, select the true sentences from the ones below:

Choose all correct answers

There is only one optimal schedule $($unique$)$

There could be more than one optimal schedule

The problem above is always solvable

There are cases in which this problem is not solvable