Update list of number line intervals with addition of new interval

num_line.py

#!/usr/bin/python
#
# run 'python num_line.py -v' to see doctest results.
# Howard Hamilton
# 17 March 2014

def number_line(L, I):
    '''
    Update number line intervals with addition of new interval.  
    
    If there is an overlap between new and current intervals, 
    create a new interval that covers the overlapped region.

    :params L: Intervals on number line.
    :type L: List of (int, int) tuples
    :params I: Single interval.
    :type I: Tuple of two ints
    :returns: Updated intervals on number line.
    :rtype: List of (int, int) tuples

    >>> L = [(2,3),(6,7),(8,9),(10,15)]
    >>> I = (0,1)
    >>> number_line(L, I)
    [(0, 1), (2, 3), (6, 7), (8, 9), (10, 15)]
    >>> I = (4,5)
    >>> number_line(L, I)
    [(2, 3), (4, 5), (6, 7), (8, 9), (10, 15)]
    >>> I = (3,7)
    >>> number_line(L, I)
    [(2, 7), (8, 9), (10, 15)]
    >>> I = (1,2)
    >>> number_line(L, I)
    [(1, 3), (6, 7), (8, 9), (10, 15)]
    >>> I = (16,20)
    >>> number_line(L, I)
    [(2, 3), (6, 7), (8, 9), (10, 15), (16, 20)]
    '''
    L_prime = []
    (a,b) = I
    for i, (x,y) in enumerate(L):
        # single interval ahead of interval in line
        if b < x:
            # handle edge case at head of list
            if i == 0 or L[i-1][1] < a:
                L_prime.extend([(a,b),(x,y)])
            else:
                L_prime.append((x,y))
        # single interval behind interval in line
        elif a > y:
            # handle edge case at end of list
            if i == len(L)-1:
                L_prime.extend([(x,y),(a,b)])
            else:
                L_prime.append((x,y))
        # handle overlap cases
        elif (x <= a and a <= y) or (x <= b and b <= y) or (a < x and b > y):
            I = (min(a,x),max(b,y))
            # This was the step I was missing -- a recursion call
            # Need to have a break out of loop when done in order
            #   to prevent repeat intervals
            if i < len(L)-1:
                L_prime.extend(number_line(L[i+1:],I))
                break
    return L_prime

if __name__ == "__main__":
    import doctest
    doctest.testmod()