The Number of Beautiful Subsets

arrayhash tablemath

Problem Statement

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.

Examples

Example 1

Input: nums = [2,4,6], k = 2
Output: 4
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
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 <= 18

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

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicHash Table