Python职位组合列表

Question

I'm trying to generate a list of all possible 1-dimensional positions for an arbitrary number of identical objects. I want it formatted so each coordinate is the distance from the previous object, so for 3 objects (0,5,2) would mean one object is at position 0, another is at position 5 and another is at position 7.

So the main restraint is that the sum of the coordinates is <=D. Nested for loops works well for this. For example, with 3 objects with maximum coordinate D:

def positions(D):
    output=[]
    for i in range(D+1):
        for j in range(D+1-i):
            for k in range(D+1-i-j):
                 output.append((i,j,k))
     return(output)

What's the best way to extend this to an arbitrary number of objects? I can't find a good way without explicitly writing a specific number of for loops.

Answer 1

I think you can combine itertools.combinations , which will give you the locations, with taking the difference, which should give you your "distance from the previous object" behaviour. For example, using

def diff(loc):
    return [y-x for x,y in zip((0,) + loc, loc)]

we have

In [114]: list(itertools.combinations(range(4), 3))
Out[114]: [(0, 1, 2), (0, 1, 3), (0, 2, 3), (1, 2, 3)]

for the possible positions , and then

In [115]: [diff(x) for x in itertools.combinations(range(4), 3)]
Out[115]: [[0, 1, 1], [0, 1, 2], [0, 2, 1], [1, 1, 1]]

for your relative-distance version.