This is the problem:
An art gallery hired you to put guards so they can monitor artworks in a hallway. The goal is to minimize the amount of guards needed in this hallway. Each guard has a range of 10 meters (5m on the right, 5m on the left with him being in the middle).
No matter where the artworks are put in the hallway we want the minimal amount of guards as possible.
My Greedy Algorithm:
Start at the beginning of the hallway. Find the position of the closest artwork from the entrance. Put the guard at position closest artwork + 5m ahead. Eliminate all the artworks covered by the guard. Re-do the process but this time start where the range of the previous guard ended
Now how do I write a proof for this? How do I prove that my algorithm is indeed optimal? Which mathematical proof techniques can I use?