创建一个包含所有上限子集的列表(但lst [i]≤上限[i]) [英] Create a list that contains all subsets from an upperbound (but where lst[i] ≤ upper bound[i])

问题描述

我正在尝试构建一个功能:

I'm trying to build a function that:

• 接受长度为n和的正整数列表作为参数.
• 返回长度为n的所有列表的列表，该列表由具有以下属性的非负整数组成:
  • 对于列表lst，它适用于所有索引i，lst[i] ≤ upper bound[i]
  • 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]

    例如，如果输入列表为[1, 1, 2]，则输出为

    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 ] , ]
    

    这是我所走的路:

    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
    

    给出输出:

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

    我无法理解如何添加缺少的列表，任何帮助都会很棒.

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

    推荐答案

    这是一个选择:

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

    请注意，您的列表[1, 1, 2]在此处翻译为range(2), range(2), range(3).

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

    或更直接地:

    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)]
    

    甚至:

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

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