Create a list that contains all subsets from an upperbound (but where lst[i] ≤ upper bound[i])

问题

I'm trying to build a function that:

• accepts as an argument a list of positive integers of length n and
• returns a list of all lists of length n consisting of non-negative integers with the following property:
  • for a list lst it holds that for all indices i, lst[i] ≤ upper bound[i]

For example, if the input list was [1, 1, 2], then the output would be

[ [ 0 , 0 , 0 ] ,
[ 0 , 0 , 1 ] ,
[ 0 , 0 , 2 ] ,
[ 0 , 1 , 0 ] ,
[ 0 , 1 , 1 ] ,
[ 0 , 1 , 2 ] ,
[ 1 , 0 , 0 ] ,
[ 1 , 0 , 1 ] ,
[ 1 , 0 , 2 ] ,
[ 1 , 1 , 0 ] ,
[ 1 , 1 , 1 ] ,
[ 1 , 1 , 2 ] , ]

This is how far I've gotten:

def bounded_list(ub):
    f = len(ub) * [0]
    l = ub
    res = [f]

    while res[-1] != l:
        res += [lex_suc1(res[-1], ub)]

    return res


def lex_suc1(lst, ub):
    res = lst[:]

    i = len(res) - 1
    while res[i] == ub[i]:
        res[i] = 0
        i -= 1

    res[i] = ub[i]
    return res

which gives the output:

[[0, 0, 0], 
[0, 0, 2], 
[0, 1, 0], 
[0, 1, 2], 
[1, 0, 0], 
[1, 0, 2], 
[1, 1, 0], 
[1, 1, 2]]

I'm not able to understand how to include the missing lists, any help woul be great.

回答1:

this is an option:

from itertools import product

for lst in product(range(2), range(2), range(3)):
    print(lst)

note that your list [1, 1, 2] translates to range(2), range(2), range(3) here.

or more directly:

res = list(product(range(2), range(2), range(3)))
# [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (0, 1, 1), (0, 1, 2), 
#  (1, 0, 0), (1, 0, 1), (1, 0, 2), (1, 1, 0), (1, 1, 1), (1, 1, 2)]

or even:

lst = [1, 1, 2]
res = list(product(*(range(i+1) for i in lst)))

回答2:

You should take a look at itertools package and list comprehensions.

Then a solution is:

def f(upper_bounds):
    return list(itertools.product(*(range(ub+1) for ub in upper_bounds)))

回答3:

You can use itertools.product for this.

from  itertools import product
li = [1, 1, 2]

#Generate a list of possible numbers to generate the output from the given list
iters = [list(range(item+1)) for item in li]
#[[0, 1], [0, 1], [0, 1, 2]]

#Generate all possible combinations of these lists
print(list(product(*iters)))

The output will then be.

[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), 
(0, 1, 1), (0, 1, 2), (1, 0, 0), (1, 0, 1), 
(1, 0, 2), (1, 1, 0), (1, 1, 1), (1, 1, 2)]

来源：https://stackoverflow.com/questions/55920343/create-a-list-that-contains-all-subsets-from-an-upperbound-but-where-lsti-%e2%89%a4-u