Find all possible combinations that overlap by end and start

问题

In the post find all combinations with non-overlapped regions (code pasted below), the function is given a set of tuples and it recursively finds every possible collection of tuples with non-overlapping values. On the list of tuples T = [(0.0, 2.0), (0.0, 4.0), (2.5, 4.5), (2.0, 5.75), (2.0, 4.0), (6.0, 7.25)], for example, we get

def nonovl(l, idx, right, ll):
    if idx == len(l):
        if ll:
            print(ll)
        return

    next = idx + 1  
    while next < len(l) and right >= l[next][0]:
        next += 1
    nonovl(l, next, right, ll)

    next = idx + 1
    right = l[idx][1]
    while next < len(l) and right >= l[next][0]:
        next += 1
    nonovl(l, next, right, ll + str(l[idx]))

>>> T = [(0.0, 2.0), (0.0, 4.0), (2.5, 4.5), (2.0, 5.75), (2.0, 4.0), (6.0, 7.25)]
>>> l.sort()
>>> nonovl(l, 0, -1, "")
(6.0, 7.25)
(2.5, 4.5)
(2.5, 4.5)(6.0, 7.25)
(2.0, 5.75)
(2.0, 5.75)(6.0, 7.25)
(2.0, 4.0)
(2.0, 4.0)(6.0, 7.25)
(0.0, 4.0)
(0.0, 4.0)(6.0, 7.25)
(0.0, 2.0)
(0.0, 2.0)(6.0, 7.25)
(0.0, 2.0)(2.5, 4.5)
(0.0, 2.0)(2.5, 4.5)(6.0, 7.25)

How might we modify the nonovl() function so that it also allows for combinations that overlap by the start and end values of two tuples? Running it on the same list, for example, we would also get:

(0.0, 2.0)(2.0, 4.0)(6.0, 7.25)

回答1:

Change >= to >. Right now, the code skips over the "next" tuple if the left index value of the "next" tuple is less than or equal to the right index value of the "current" tuple. It finds the first tuple that has a left index value that is strictly greater than the current tuple's right index value.

def nonovl(l, idx, right, ll):
    if idx == len(l):
        if ll:
            print(ll)
        return

    next = idx + 1  
    while next < len(l) and right > l[next][0]:
        next += 1
    nonovl(l, next, right, ll)

    next = idx + 1
    right = l[idx][1]
    while next < len(l) and right > l[next][0]:
        next += 1
    nonovl(l, next, right, ll + str(l[idx]))

Output:

(6.0, 7.25)
(2.5, 4.5)
(2.5, 4.5)(6.0, 7.25)
(2.0, 5.75)
(2.0, 5.75)(6.0, 7.25)
(2.0, 4.0)
(2.0, 4.0)(6.0, 7.25)
(0.0, 4.0)
(0.0, 4.0)(6.0, 7.25)
(0.0, 2.0)
(0.0, 2.0)(6.0, 7.25)
(0.0, 2.0)(2.5, 4.5)
(0.0, 2.0)(2.5, 4.5)(6.0, 7.25)
(0.0, 2.0)(2.0, 5.75)
(0.0, 2.0)(2.0, 5.75)(6.0, 7.25)
(0.0, 2.0)(2.0, 4.0)
(0.0, 2.0)(2.0, 4.0)(6.0, 7.25)

来源：https://stackoverflow.com/questions/59887631/find-all-possible-combinations-that-overlap-by-end-and-start

标签

python

list

sorting

recursion

dynamic-programming