数组的所有排列，其中数组中的每个元素必须增加 0 到 n 之间的范围

Question

假设我有一个包含值的元素列表

[1, 2, 3, 5, 6, 7, 9, 12]

基本上，数组中的元素最多可以相差 n，在本例中为三个，递增顺序。

上面的数组会像这样工作：

2-1 = 1 | difference of 1
3-2 = 1 | difference of 1
5-3 = 2 | difference of 2
6-5 = 1 | difference of 1

等等。我将如何找到长度为 x 且最大差为 n 的数组的所有排列？

Answer 1

尝试将其作为递归。应该打印出所有允许的值。
x 被描述为 required_number 而 n 被描述为 diff。

def getPermutations(cur_permutation, arr_to_check, required_number, diff):
    if len(arr_to_check) == 0:
        return

    if required_number == 0:
        print cur_permutation
        return

    cur_last_item = cur_permutation[-1]
    for index, arr_item in enumerate(arr_to_check):
        if arr_item - cur_last_item <= diff:
            new_copy = cur_permutation[:]
            new_copy.append(arr_item)
            return getPermutations(new_copy, arr_to_check[1:], required_number - 1, diff)

（这也可以通过保持要求的长度并检查 cur_permutation 是否为该长度来完成）。

Answer 2

假设您正在寻找绝对值的差异，您可以通过逐步将每个符合条件的元素添加到结果中来递归地执行此操作：

这是一个使用递归生成器函数的示例：

def permuteSort(A,maxDiff,previous=None):
    if not A: yield []; return
    for i,a in enumerate(A):           
        if previous is not None and abs(a-previous) > maxDiff:               
            continue
        yield from ([a]+p for p in permuteSort(A[:i]+A[i+1:],maxDiff,a))

输出

for p in  permuteSort([1, 2, 3, 5, 6, 7, 9, 12],3):
    print(p,"differences:",[b-a for a,b in zip(p,p[1:])])
        
  
[1, 2, 3, 5, 6, 7, 9, 12] differences: [1, 1, 2, 1, 1, 2, 3]
[1, 2, 3, 5, 7, 6, 9, 12] differences: [1, 1, 2, 2, -1, 3, 3]
[1, 2, 3, 6, 5, 7, 9, 12] differences: [1, 1, 3, -1, 2, 2, 3]
[1, 2, 5, 3, 6, 7, 9, 12] differences: [1, 3, -2, 3, 1, 2, 3]
[1, 3, 2, 5, 6, 7, 9, 12] differences: [2, -1, 3, 1, 1, 2, 3]
[1, 3, 2, 5, 7, 6, 9, 12] differences: [2, -1, 3, 2, -1, 3, 3]
[2, 1, 3, 5, 6, 7, 9, 12] differences: [-1, 2, 2, 1, 1, 2, 3]
[2, 1, 3, 5, 7, 6, 9, 12] differences: [-1, 2, 2, 2, -1, 3, 3]
[2, 1, 3, 6, 5, 7, 9, 12] differences: [-1, 2, 3, -1, 2, 2, 3]
[3, 1, 2, 5, 6, 7, 9, 12] differences: [-2, 1, 3, 1, 1, 2, 3]
[3, 1, 2, 5, 7, 6, 9, 12] differences: [-2, 1, 3, 2, -1, 3, 3]
[5, 2, 1, 3, 6, 7, 9, 12] differences: [-3, -1, 2, 3, 1, 2, 3]
[6, 3, 1, 2, 5, 7, 9, 12] differences: [-3, -2, 1, 3, 2, 2, 3]
[7, 5, 2, 1, 3, 6, 9, 12] differences: [-2, -3, -1, 2, 3, 3, 3]
[12, 9, 6, 3, 1, 2, 5, 7] differences: [-3, -3, -3, -2, 1, 3, 2]
[12, 9, 6, 7, 5, 2, 1, 3] differences: [-3, -3, 1, -2, -3, -1, 2]
[12, 9, 6, 7, 5, 2, 3, 1] differences: [-3, -3, 1, -2, -3, 1, -2]
[12, 9, 6, 7, 5, 3, 1, 2] differences: [-3, -3, 1, -2, -2, -2, 1]
[12, 9, 6, 7, 5, 3, 2, 1] differences: [-3, -3, 1, -2, -2, -1, -1]
[12, 9, 7, 5, 2, 1, 3, 6] differences: [-3, -2, -2, -3, -1, 2, 3]
[12, 9, 7, 5, 6, 3, 1, 2] differences: [-3, -2, -2, 1, -3, -2, 1]
[12, 9, 7, 5, 6, 3, 2, 1] differences: [-3, -2, -2, 1, -3, -1, -1]
[12, 9, 7, 6, 3, 1, 2, 5] differences: [-3, -2, -1, -3, -2, 1, 3]
[12, 9, 7, 6, 3, 5, 2, 1] differences: [-3, -2, -1, -3, 2, -3, -1]
[12, 9, 7, 6, 5, 2, 1, 3] differences: [-3, -2, -1, -1, -3, -1, 2]
[12, 9, 7, 6, 5, 2, 3, 1] differences: [-3, -2, -1, -1, -3, 1, -2]
[12, 9, 7, 6, 5, 3, 1, 2] differences: [-3, -2, -1, -1, -2, -2, 1]
[12, 9, 7, 6, 5, 3, 2, 1] differences: [-3, -2, -1, -1, -2, -1, -1]

数组的所有排列，其中数组中的每个元素必须增加 0 到 n 之间的范围

All permutations of array where each element in the array must be increasing by range between 0 and n

python

algorithm

math

rust

array-algorithms