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g2501_2600.s2597_the_number_of_beautiful_subsets.readme.md Maven / Gradle / Ivy

2597\. The Number of Beautiful Subsets

Medium

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 = 2

**Output:** 4

**Explanation:**

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 = 1

**Output:** 1

**Explanation:**

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`