D
DevExCode

LeetCode 2597: The Number of Beautiful Subsets Solution

Master LeetCode problem 2597 (The Number of Beautiful Subsets), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming to count the number of beautiful subsets. We can define a state dp[mask][last] which represents the number of beautiful subsets of the array nums where the subset has elements represented by the bits set in mask, and the last element selected is nums[last]. We can then iterate over all possible subsets and calculate the count while taking care not to violate the condition of absolute difference equal to k.

Algorithmic Idea:

  1. Initialize a 2D array dp[mask][last] where mask represents the subset and last represents the last element chosen.
  2. Iterate over all possible subsets and for each subset, iterate over all elements in the subset to calculate the count of beautiful subsets.
  3. Use dynamic programming to update the count based on the condition of absolute difference k.
  4. Finally, return the total count of beautiful subsets.

Time Complexity:

The time complexity of this solution is O(2^n * n) where n is the length of the input array nums.

Space Complexity:

The space complexity of this solution is O(2^n).

:

Solution Code

class Solution {
    public int countBeautifulSubsets(int[] nums, int k) {
        int n = nums.length;
        int[][] dp = new int[1 << n][n];
        
        for (int i = 0; i < n; i++) {
            dp[1 << i][i] = 1;
        }
        
        for (int mask = 0; mask < (1 << n); mask++) {
            for (int last = 0; last < n; last++) {
                if (dp[mask][last] == 0) continue;
                for (int i = 0; i < n; i++) {
                    if ((mask & (1 << i)) == 0 && Math.abs(nums[i] - nums[last]) != k) {
                        dp[mask | (1 << i)][i] += dp[mask][last];
                    }
                }
            }
        }
        
        int res = 0;
        for (int mask = 1; mask < (1 << n); mask++) {
            for (int i = 0; i < n; i++) {
                res += dp[mask][i];
            }
        }
        
        return res;
    }
}

Try It Yourself

Loading code editor...

Related LeetCode Problems

Frequently Asked Questions

How to solve LeetCode 2597 (The Number of Beautiful Subsets)?

This page provides optimized solutions for LeetCode problem 2597 (The Number of Beautiful Subsets) in Java, C++, and Python, along with a detailed explanation and an interactive code editor to test your code.

What is the time complexity of LeetCode 2597 (The Number of Beautiful Subsets)?

The time complexity for LeetCode 2597 (The Number of Beautiful Subsets) varies by solution. Check the detailed explanation section for specific complexities in Java, C++, and Python implementations.

Can I run code for LeetCode 2597 on DevExCode?

Yes, DevExCode provides an interactive code editor where you can write, test, and run your code for LeetCode 2597 in Java, C++, or Python.

Back to LeetCode Solutions