Question

I am looking for an algorithm to calculate the next set of operations in a sequence. Here is the simple definition of the sequence.

1. Task 1A will be done every 500 hours
2. Task 2A will be done every 1000 hours
3. Task 3A will be done every 1500 hours

So at t=500, do 1A. At t=1000, do both 1A and 2A, at t=1500 do 1A and 3A, but not 2A as 1500 is not a multiple of 1000. You get the idea.

It would be quite easy if I had the actual time, but I don’t. What I have is the history of tasks (eg last time a [1A+2A] was done).

Knowing last time (eg [1A+2A]) is not enough to decide:

• [1A+2A] could be at t=1000: next is [1A+3A] at t=1500
• [1A+2A] could be at t=5000: next is [1A] at t=5500

Is there an algorithm for this? It looks like a familiar problem (some sort of sieve?) but I can’t seem to find a solution.

Also it must ‘scale’ as I actually have more than 3 tasks.

Answer 1

Bill the Lizard is right. Here is how to determine the task intervals from the history (in Python):

history = [list of tuples like (timestamp, (A, B, ...)), ordered by timestamp] lastTaskTime = {} taskIntervals = {}  for timestamp, tasks in history:     for task in tasks:         if task not in lastTaskTime:             lastTaskTime[task] = timestamp         else:             lastTimestamp = lastTaskTime[task]             interval = abs(timestamp - lastTimestamp)             if task not in taskIntervals or interval < taskIntervals[task]:                 taskIntervals[task] = interval  # Found a shorter interval              # Always remember the last timestamp             lastTaskTime[task] = timestamp  # taskIntervals contains the shortest time intervals of each tasks executed at least twice in the past # lastTaskTime contains the last time each task was executed 

To get the set of tasks, which will be executed next:

nextTime = None nextTasks = []  for task in lastTaskTime:     lastTime = lastTaskTime[task]     interval = taskIntervals[task]      if not nextTime or lastTime + interval < nextTime:         nextTime = lastTime + interval         nextTasks = [task]     elif lastTime + interval == nextTime:         nextTasks.append(task)  # nextTime contains the time when the next set of tasks will be executed # nextTasks contains the set of tasks to be executed