# Java: Divide a given array of integers into given k non-empty subsets whose sums are all equal

## Java Basic: Exercise-201 with Solution

Write a Java program to divide a given array of integers into given k non-empty subsets whose sums are all equal. Return true if all sums are equal otherwise return false.

Example:
nums = {1,3,3,5,6,6}, k = 4;
4 subsets (5,1), (3, 3), (6), (6) with equal sums.

Visual Presentation: Sample Solution:

Java Code:

``````// Import Arrays and other utility classes from java.util package
import java.util.Arrays;

// Main class for the solution
public class Solution {
// Main method to execute the solution
public static void main(String[] args) {
// Sample input array and target value for testing subset partitioning
int[] nums = {1, 3, 3, 5, 6, 6};
int target = 4;

// Display the original array
System.out.print("Original Array: " + Arrays.toString(nums));

// Display the target value for subsets
System.out.print("\nTarget of subsets: " + target);

// Display the result after removing duplicate characters using partition_k_subsets function
System.out.print("\nAfter removing duplicate characters: " + partition_k_subsets(nums, target));
}

// Function to recursively search for valid subsets with a specific sum
static boolean search_subset(int used, int n, boolean[] flag, int[] nums, int target) {
// Base case: all elements used, subset found
if (n == 0) {
return true;
}

// Check if the current subset has not been considered before
if (!flag[used]) {
// Mark the current subset as visited
flag[used] = true;

// Calculate the remaining sum needed for the subset
int remain_num = (n - 1) % target + 1;

// Iterate through the elements in the array
for (int i = 0; i < nums.length; i++) {
// Check if the current element is not used in the subset and its value is less than or equal to the remaining sum
if ((((used >> i) & 1) == 0) && nums[i] <= remain_num) {
// Recursively search for the subset with the updated parameters
if (search_subset(used | (1 << i), n - nums[i], flag, nums, target)) {
return true;
}
}
}
}
return false;
}

// Function to partition an array into k subsets with equal sum
public static boolean partition_k_subsets(int[] nums, int k) {
// Calculate the total sum of the elements in the array
int sum = Arrays.stream(nums).sum();

// Check if the sum is not divisible by k, return false
if (sum % k > 0) {
return false;
}

// Create a boolean array to track visited subsets
boolean[] flag = new boolean[1 << nums.length];

// Call the recursive search_subset function to check for valid subsets
return search_subset(0, sum, flag, nums, sum / k);
}
}
```
```

Sample Output:

```Original Array: [1, 3, 3, 5, 6, 6]
Target of subsets: 4
After removing duplicate characters: true
```

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