Union of multiple ranges

Question

I have these ranges:

7,10
11,13
11,15
14,20
23,39

I need to perform a union of the overlapping ranges to give ranges that are not overlappi

Answer 1

I tried with particular cases of presence of (45, 46) and (45, 45)
and also test cases that are unlikely to happen in your application: presence of (11,6), presence of (-1, -5), presence of (-9, 5), presence of (-3, 10).
Anyway the results are right for all these cases, it's a point.

The algorithm:

def yi(li):
    gen = (x for a,b in li for x in xrange(a,b+1))
    start = p = gen.next()
    for x in gen:
        if x>p+2:
            yield (start,p)
            start = p = x
        else:
            p = x
    yield (start,x)

If aff in the following code is set to True, the steps of the execution are displayed.

def yi(li):
    aff = 0
    gen = (x for a,b in li for x in xrange(a,b+1))
    start = p = gen.next()
    for x in gen:
        if aff:
            print ('start %s     p %d  p+2 %d     '
                   'x==%s' % (start,p,p+2,x))
        if x>p+2:
            if aff:
                print 'yield range(%d,%d)' % (start,p+1)
            yield (start,p)
            start = p = x
        else:
            p = x
    if aff:
        print 'yield range(%d,%d)' % (start,x+1)
    yield (start,x)



for li in ([(7,10),(23,39),(11,13),(11,15),(14,20),(45,46)],
           [(7,10),(23,39),(11,13),(11,15),(14,20),(45,46),(45,45)],
           [(7,10),(23,39),(11,13),(11,15),(14,20),(45,45)],

           [(7,10),(23,39),(11,13),(11,6),(14,20),(45,46)], 
           #1 presence of (11, 6)
           [(7,10),(23,39),(11,13),(-1,-5),(14,20),(45,45)], 
           #2  presence of (-1,-5)
           [(7,10),(23,39),(11,13),(-9,-5),(14,20),(45,45)], 
           #3  presence of (-9, -5)
           [(7,10),(23,39),(11,13),(-3,10),(14,20),(45,45)]): 
           #4  presence of (-3, 10)

    li.sort()
    print 'sorted li    %s'%li
    print '\n'.join('  (%d,%d)   %r' % (a,b,range(a,b)) 
                     for a,b in li)
    print 'list(yi(li)) %s\n' % list(yi(li))

result

sorted li    [(7, 10), (11, 13), (11, 15), (14, 20),
              (23, 39), (45, 46)]
  (7,10)   [7, 8, 9]
  (11,13)   [11, 12]
  (11,15)   [11, 12, 13, 14]
  (14,20)   [14, 15, 16, 17, 18, 19]
  (23,39)   [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 
             35, 36, 37, 38]
  (45,46)   [45]
list(yi(li)) [(7, 20), (23, 39), (45, 46)]

sorted li    [(7, 10), (11, 13), (11, 15), (14, 20), 
              (23, 39), (45, 45), (45, 46)]
  (7,10)   [7, 8, 9]
  (11,13)   [11, 12]
  (11,15)   [11, 12, 13, 14]
  (14,20)   [14, 15, 16, 17, 18, 19]
  (23,39)   [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
             35, 36, 37, 38]
  (45,45)   []
  (45,46)   [45]
list(yi(li)) [(7, 20), (23, 39), (45, 46)]

sorted li    [(7, 10), (11, 13), (11, 15), (14, 20), 
              (23, 39), (45, 45)]
  (7,10)   [7, 8, 9]
  (11,13)   [11, 12]
  (11,15)   [11, 12, 13, 14]
  (14,20)   [14, 15, 16, 17, 18, 19]
  (23,39)   [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
             35, 36, 37, 38]
  (45,45)   []
list(yi(li)) [(7, 20), (23, 39), (45, 45)]

sorted li    [(7, 10), (11, 6), (11, 13), (14, 20), 
              (23, 39), (45, 46)]
  (7,10)   [7, 8, 9]
  (11,6)   []
  (11,13)   [11, 12]
  (14,20)   [14, 15, 16, 17, 18, 19]
  (23,39)   [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 
             35, 36, 37, 38]
  (45,46)   [45]
list(yi(li)) [(7, 20), (23, 39), (45, 46)]

sorted li    [(-1, -5), (7, 10), (11, 13), (14, 20), 
              (23, 39), (45, 45)]
  (-1,-5)   []
  (7,10)   [7, 8, 9]
  (11,13)   [11, 12]
  (14,20)   [14, 15, 16, 17, 18, 19]
  (23,39)   [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
             35, 36, 37, 38]
  (45,45)   []
list(yi(li)) [(7, 20), (23, 39), (45, 45)]

sorted li    [(-9, -5), (7, 10), (11, 13), (14, 20), 
              (23, 39), (45, 45)]
  (-9,-5)   [-9, -8, -7, -6]
  (7,10)   [7, 8, 9]
  (11,13)   [11, 12]
  (14,20)   [14, 15, 16, 17, 18, 19]
  (23,39)   [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
             35, 36, 37, 38]
  (45,45)   []
list(yi(li)) [(-9, -5), (7, 20), (23, 39), (45, 45)]

sorted li    [(-3, 10), (7, 10), (11, 13), (14, 20), 
              (23, 39), (45, 45)]
  (-3,10)   [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
  (7,10)   [7, 8, 9]
  (11,13)   [11, 12]
  (14,20)   [14, 15, 16, 17, 18, 19]
  (23,39)   [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 
             35, 36, 37, 38]
  (45,45)   []
list(yi(li)) [(-3, 20), (23, 39), (45, 45)]