How to divide a set of overlapping ranges into non-overlapping ranges?

Question

Let\'s say you have a set of ranges:

• 0 - 100: \'a\'
• 0 - 75: \'b\'
• 95 - 150: \'c\'
• 120 - 130: \'d\'

Obviously, these range

Answer 1

I had the same question when writing a program to mix (partly overlapping) audio samples.

What I did was add an "start event" and "stop event" (for each item) to a list, sort the list by time point, and then process it in order. You could do the same, except using an integer point instead of a time, and instead of mixing sounds you'd be adding symbols to the set corresponding to a range. Whether you'd generate empty ranges or just omit them would be optional.

Edit Perhaps some code...

# input = list of (start, stop, symbol) tuples
points = [] # list of (offset, plus/minus, symbol) tuples
for start,stop,symbol in input:
    points.append((start,'+',symbol))
    points.append((stop,'-',symbol))
points.sort()

ranges = [] # output list of (start, stop, symbol_set) tuples
current_set = set()
last_start = None
for offset,pm,symbol in points:
    if pm == '+':
         if last_start is not None:
             #TODO avoid outputting empty or trivial ranges
             ranges.append((last_start,offset-1,current_set))
         current_set.add(symbol)
         last_start = offset
    elif pm == '-':
         # Getting a minus without a last_start is unpossible here, so not handled
         ranges.append((last_start,offset-1,current_set))
         current_set.remove(symbol)
         last_start = offset

# Finish off
if last_start is not None:
    ranges.append((last_start,offset-1,current_set))

Totally untested, obviously.