<p>You are given an array <code>nums</code> of positive integers and a <strong>positive</strong> integer <code>k</code>.</p>

<p>A subset of <code>nums</code> is <strong>beautiful</strong> if it does not contain two integers with an absolute difference equal to <code>k</code>.</p>

<p>Return <em>the number of <strong>non-empty beautiful </strong>subsets of the array</em> <code>nums</code>.</p>

<p>A <strong>subset</strong> of <code>nums</code> is an array that can be obtained by deleting some (possibly none) elements from <code>nums</code>. Two subsets are different if and only if the chosen indices to delete are different.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,4,6], k = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> The beautiful subsets of the array nums are: [2], [4], [6], [2, 6].
It can be proved that there are only 4 beautiful subsets in the array [2,4,6].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1], k = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong> The beautiful subset of the array nums is [1].
It can be proved that there is only 1 beautiful subset in the array [1].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 20</code></li>
	<li><code>1 &lt;= nums[i], k &lt;= 1000</code></li>
</ul>

from itertools import chain, combinations

class Solution:
    def generateSubsets(self, nums):
        return chain.from_iterable([combinations(nums, r) for r in range(1, len(nums)+1)])

    def isBeautiful(self, nums, k):
        disallowed = set()
        for n in nums:
            if n in disallowed:
                return False
            disallowed.add(n-k)
            disallowed.add(n+k)
        return True

    def beautifulSubsets(self, nums: List[int], k: int) -> int:
        # the overall number of subsets is 2^len(nums)
        # for each num, there may be multiple other nums that stand in the way of beauty
        # let's do a brute force search first

        num_beautiful = 0
        for subset in self.generateSubsets(nums):
            if self.isBeautiful(subset, k):
                num_beautiful += 1

        return num_beautiful
16200