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

Here is a one-liner using functools.reduce (assuming (x, 10) and (11, y) overlap):

reduce(
    lambda acc, el: acc[:-1:] + [(min(*acc[-1], *el), max(*acc[-1], *el))]
        if acc[-1][1] >= el[0] - 1
        else acc + [el],
    ranges[1::],
    ranges[0:1]
)

This begins with the first range and uses reduce to go through the rest of the ranges. It compares the last element (acc[-1]) with the next range (el). If they overlap, it replaces the last element with the min and max of the two ranges (acc[:-1:] + [min, max]). If they don't overlap, it simply puts this new range at the end of the list (acc + [el]).

Example:

from functools import reduce

example_ranges = [(7, 10), (11, 13), (11, 15), (14, 20), (23, 39)]

def combine_overlaps(ranges):
    return reduce(
        lambda acc, el: acc[:-1:] + [(min(*acc[-1], *el), max(*acc[-1], *el))]
            if acc[-1][1] >= el[0] - 1
            else acc + [el],
        ranges[1::],
        ranges[0:1],
    )

print(combine_overlaps(example_ranges))

Output:

[(7, 20), (23, 39)]

Answer 2

The following function works well for the given example data:

def range_overlap_adjust(list_ranges):
    overlap_corrected = []
    for start, stop in sorted(list_ranges):
        if overlap_corrected and start-1 <= overlap_corrected[-1][1] and stop >= overlap_corrected[-1][1]:
            overlap_corrected[-1] = min(overlap_corrected[-1][0], start), stop
        elif overlap_corrected and start <= overlap_corrected[-1][1] and stop <= overlap_corrected[-1][1]:
            break
        else:
            overlap_corrected.append((start, stop))
    return overlap_corrected

Usage

list_ranges = [(7, 10), (11, 13), (11, 15), (14, 20), (23, 39)]   
print(range_overlap_adjust(list_ranges))
# prints [(7, 20), (23, 39)]

Answer 3

Old question. But I wanted to add this answer for future references. sympy can be used to achieve union of intervals:

from sympy import Interval, Union
def union(data):
    """ Union of a list of intervals e.g. [(1,2),(3,4)] """
    intervals = [Interval(begin, end) for (begin, end) in data]
    u = Union(*intervals)
    return [list(u.args[:2])] if isinstance(u, Interval) \
       else list(u.args)

If output of Union is more than two intervals is a Union object while when there is a single interval, the output is an Interval object. That's the reason for the if statement in the return line.

examples:

In [26]: union([(10, 12), (14, 16), (15, 22)])
Out[26]: [[10, 12], [14, 22]]

In [27]: union([(10, 12), (9, 16)])
Out[27]: [[9, 16]]

Answer 4

Let's say, (7, 10) and (11, 13) result into (7, 13):

a = [(7, 10), (11, 13), (11, 15), (14, 20), (23, 39)]
b = []
for begin,end in sorted(a):
    if b and b[-1][1] >= begin - 1:
        b[-1] = (b[-1][0], end)
    else:
        b.append((begin, end))

b is now

[(7, 20), (23, 39)]

EDIT:

As @CentAu correctly notices, [(2,4), (1,6)] would return (1,4) instead of (1,6). Here is the new version with correct handling of this case:

a = [(7, 10), (11, 13), (11, 15), (14, 20), (23, 39)]
b = []
for begin,end in sorted(a):
    if b and b[-1][1] >= begin - 1:
        b[-1][1] = max(b[-1][1], end)
    else:
        b.append([begin, end])

Answer 5

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)]