2597. The Number of Beautiful Subsets

Medium

280

77

You are given an array `nums`

of positive integers and a **positive** integer `k`

.

A subset of `nums`

is **beautiful** if it does not contain two integers with an absolute difference equal to `k`

.

Return *the number of non-empty beautiful subsets of the array*

`nums`

.A **subset** of `nums`

is an array that can be obtained by deleting some (possibly none) elements from `nums`

. Two subsets are different if and only if the chosen indices to delete are different.

**Example 1:**

Input:nums = [2,4,6], k = 2Output:4Explanation: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].

**Example 2:**

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

**Constraints:**

`1 <= nums.length <= 20`

`1 <= nums[i], k <= 1000`

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