python - 找到固定长度数字的所有可能排列以达到给定的总和

Question

我想修改 Finding all possible combinations of numbers to reach a given sum 中的 subset_sum() python 函数这样:

1. 它允许重复(排列)而不是组合
2. 它只考虑给定长度的排列

我已经成功完成了#2，但我在#1 方面需要帮助:

def subset_sum(numbers, target, length, partial=[]):
    s = sum(partial)

    # check if the partial sum is equals to target
    if s == target and len(partial) == length:
        print(f"sum({partial})={target}")
    if s >= target:
        return  # if we reach the number why bother to continue

    for i in range(len(numbers)):
        n = numbers[i]
        remaining = numbers[i+1:]
        subset_sum(remaining, target, length, partial + [n]) 

期望的输出应该是:

>>> subset_sum([3,9,8,4,5,7,10],target=15,length=3)
sum([3, 8, 4])=15
sum([3, 4, 8])=15
sum([4, 3, 8])=15
sum([4, 8, 3])=15
sum([8, 3, 4])=15
sum([8, 4, 3])=15
sum([3, 5, 7])=15
sum([3, 7, 5])=15
sum([5, 3, 7])=15
sum([5, 7, 3])=15
sum([7, 3, 5])=15
sum([7, 5, 3])=15

Answer 1

既然您已经解决了在每个等价组中识别一个解的问题，我的建议是:不要改变该算法。相反，利用 itertools.permutations 来生成这些项目:

return list(itertools.permutations(numbers))