Firework Festival

// This one seems pretty abstract and probably depends a lot from interview to interview 
// but here's my interpretation without any feedback from the interviewer 
// and trying to do it in 15 mins

public class Firework
{
    public int StartTime {get;set;}
    public int Duration {get;set;}
}

public bool WereFireworksAlwaysPresent(List<Firework> fireworks)
{
    //general check stuff here
    
    // sort fireworks based on start time (probably a better way)
    fireworks = fireworks.OrderBy(x => x.StartTime).ToList();
    
    int farthestEndTime = 0;
    
    // start at the second firework since the festival starts with the first one
    for(int i = 1; i < fireworks.Length; i++)
    {
        // logic here might be a little iffy
        // we're seeing what is the latest end time for fireworks so far
        int previousEndTime = fireworks[i-1].StartTime + Duration;
        if(previousEndTime > farthestEndTime)
            farthestEndTime = previousEndTime;
        
        // check if by the time the firework ended if the next one started or if a previous one already went off
        if(farthestEndTime < fireworks[i].StartTime)
            return false;
    }
    
    return true;
}

public int MaxNumOfFireworksPresent(List<Firework> fireworks)
{
    // general check stuff here
    
    //this is pretty much a "find the max number of intervals overlapping" question
    var start = fireworks.OrderBy(x => x.StartTime).ToList();
    var end = fireworks.OrderBy(x => x.StartTime + Duration).ToList();
    
    int currentOverlap = 0;
    int maxOverlap = 0;
    int startIndex = 0;
    int endIndex = 0;
    
    while(startIndex < start.Length && endIndex < end.Length)
    {
        if(start[startIndex] < end[endIndex])
        {
            currentOverlap++;
            if(currentOverlap > maxOverlap)
                maxOverlap = currentOverlap;
                
            startIndex++;
        }
        else
        {
            currentOverlap--;
            endIndex++;
        }
    }
    
    return maxOverlap;
}