Graphing algorithm?

Question

Algorithms

Hello
There is a task to build an appointment
schedule, there is a schedule, divided into 30 minutes,
i.e. 9.00 9.30 10.00 and so on
there are 3 doctors (there can be as many as you like),
each doctor can be both busy and free at each interval
, the appointment takes 1 hour.
those. if one of the doctors is free at 9.00 and 10.00 and 9.30 is busy, then we cannot sign up for 9.00
, as a result, we must get a grid of time with each of the cells active or not.
those. for example, if 9.00 is active, then we mean that there is at least 1 doctor to whom you can make an appointment at 9.00 and he will be able to take 1 hour. (Free intervals are 9:00 and 9:30)
(i.e., in fact, it may turn out that, for example, at 9, everyone has free time, and at 9.30, the cell at 9.00 is busy, respectively)
I understand that this cannot be solved without any algorithm.
Unless it's a brute force for all options in all ways, which, it seems to me, is not effective

Answer 1

not an algorithm, but in javascript I would do something like this

doc1 = [850, 950, 1100]   // для удобства счета 800 = 8:00 850 = 8:30 итд
doc2 = [1100, 1200]
doc3 = [1000]
docs = [doc1, doc2, doc3]

STEP = 50 // 0.5 часа

for (let i = 800; i < 1400; i += STEP){
  console.log(i)
  const found = docs.filter(d => !d.some(time => [i - STEP, i, i + STEP].includes(time)))
  console.log(found)   // выводит доступных врачей на время i, или пустой массив, если никого нет
}