Count Good Subsets Problem Statement

Given an array ARR of size N consisting of distinct elements, your task is to determine the total number of good subsets. A subset is considered a good subset if the elements can be rearranged such that every element divides the next element in order. Subsets are regarded as different if there is at least one element that exists in one but not the other.

Example:

Input:

ARR = [2, 4, 5, 15]

Output:

6

Explanation:

The good subsets are: (2), (4), (5), (15), (2,4), and (5,15). Thus, the total number of good subsets is 6.

Input:

"The first line contains an integer 'T' representing the number of test cases. Each test case has the following structure: The first line contains an integer 'N' indicating the number of elements in the array. The second line contains 'N' space-separated integers, comprising the array 'ARR'."

Output:

"For each test case, print a single integer that represents the total number of good subsets. Print each test case's result on a new line."

Constraints:

1

Question

Count Good Subsets Problem Statement

Given an array ARR of size N consisting of distinct elements, your task is to determine the total number of good subsets. A subset is considered a good subset if the elements can be rearranged such that every element divides the next element in order. Subsets are regarded as different if there is at least one element that exists in one but not the other.

Example:

Input:

ARR = [2, 4, 5, 15]

Output:

Explanation:

The good subsets are: (2), (4), (5), (15), (2,4), and (5,15). Thus, the total number of good subsets is 6.

Input:

"The first line contains an integer 'T' representing the number of test cases. Each test case has the following structure:
The first line contains an integer 'N' indicating the number of elements in the array.
The second line contains 'N' space-separated integers, comprising the array 'ARR'."

Output:

"For each test case, print a single integer that represents the total number of good subsets.
Print each test case's result on a new line."

Constraints:

1 <= T <= 10
1 <= N <= 10^5
1 <= ARR[i] <= 10^5
All elements in ARR are unique.
Time limit: 1 sec

Accepted Answer

Count the total number of good subsets in an array where elements can be rearranged to divide the next element.

Iterate through all possible subsets of the array.
Check if each subset is a good subset by rearranging elements to divide the next element.
Count the number of good subsets and return the total count.

Accepted Answer

import java.util.Arrays;

public class CountGoodSubsets {

public static void main(String[] args) {

int[] ARR = {2, 3, 4, 6};

int result = countGoodSubsets(ARR);

System.out.println("Total number of good subsets: " + result);

}

public static int countGoodSubsets(int[] ARR) {

int N = ARR.length;

Arrays.sort(ARR); // Sort the array

int[] dp = new int[N];

Arrays.fill(dp, 1); // Initialize each element as a valid subset

int totalGoodSubsets = 0;

for (int i = 0; i < N; i++) {

for (int j = 0; j < i; j++) {

// Check if ARR[i] is divisible by ARR[j]

if (ARR[i] % ARR[j] == 0) {

dp[i] += dp[j];

}

totalGoodSubsets += dp[i];

}

return totalGoodSubsets;

}