DEV Community

Cover image for 2597. The Number of Beautiful Subsets
MD ARIFUL HAQUE
MD ARIFUL HAQUE

Posted on • Edited on

1

2597. The Number of Beautiful Subsets

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].

Example 3:

  • Input: nums = [4,2,5,9,10,3], k = 1
  • Output: 23

Constraints:

  • 1 <= nums.length <= 20
  • 1 <= nums[i], k <= 1000

Solution:

class Solution {

    /**
     * @param Integer[] $nums
     * @param Integer $k
     * @return Integer
     */
    function beautifulSubsets($nums, $k) {
        $countBeautifulSubsets = -1;
        $countNums = array_fill(0, 1010, 0);
        $size = count($nums);
        $dfs = function($index) use (&$dfs, &$countBeautifulSubsets, &$nums, &$countNums, $size, $k) {
            if ($index >= $size) {
                ++$countBeautifulSubsets;
                return;
            }
            $dfs($index + 1);
            $isBeautifulIncrement = $nums[$index] + $k >= 1010 || $countNums[$nums[$index] + $k] == 0;
            $isBeautifulDecrement = $nums[$index] - $k < 0 || $countNums[$nums[$index] - $k] == 0;
            if ($isBeautifulIncrement && $isBeautifulDecrement) {
                ++$countNums[$nums[$index]];
                $dfs($index + 1);
                --$countNums[$nums[$index]];
            }
        };

        $dfs(0);
        return $countBeautifulSubsets;
    }
}
Enter fullscreen mode Exit fullscreen mode

Contact Links

If you found this series helpful, please consider giving the repository a star on GitHub or sharing the post on your favorite social networks 😍. Your support would mean a lot to me!

Image of Docusign

Bring your solution into Docusign. Reach over 1.6M customers.

Docusign is now extensible. Overcome challenges with disconnected products and inaccessible data by bringing your solutions into Docusign and publishing to 1.6M customers in the App Center.

Learn more

Top comments (0)

Sentry image

See why 4M developers consider Sentry, “not bad.”

Fixing code doesn’t have to be the worst part of your day. Learn how Sentry can help.

Learn more