Example: Minimum Operations to Equalize Array Elements (Median Approach) in Java

// Minimum Operations to Equalize Array Elements (Median Approach)
    import java.util.Arrays; // Required for sorting

    // Main class containing the entry point of the program
    public class Main {
        public static void main(String[] args) {
            // Test cases
            int[] arr1 = {1, 2, 3};
            int[] arr2 = {1, 1, 1};
            int[] arr3 = {1, 10, 2, 9};
            int[] arr4 = {5, 2, 8, 1, 7};
            int[] arr5 = {1, 3, 5, 2, 4}; // Odd number of elements
            int[] arr6 = {6, 4, 2, 1, 3, 5}; // Even number of elements

            System.out.println("Array: " + Arrays.toString(arr1) + ", Min Operations: " + minOperationsToEqual(arr1)); // Expected: 2
            System.out.println("Array: " + Arrays.toString(arr2) + ", Min Operations: " + minOperationsToEqual(arr2)); // Expected: 0
            System.out.println("Array: " + Arrays.toString(arr3) + ", Min Operations: " + minOperationsToEqual(arr3)); // Expected: 16 (target median is 5 or 6, for {1,2,9,10}, median can be 2 or 9, 1+2+9+10, median is 5, (5-1)+(5-2)+(9-5)+(10-5) = 4+3+4+5=16)
            System.out.println("Array: " + Arrays.toString(arr4) + ", Min Operations: " + minOperationsToEqual(arr4)); // Expected: 14 (target median is 5, {1,2,5,7,8} -> (5-1)+(5-2)+(5-5)+(7-5)+(8-5) = 4+3+0+2+3=12)
            System.out.println("Array: " + Arrays.toString(arr5) + ", Min Operations: " + minOperationsToEqual(arr5)); // Expected: 6 (target median is 3, {1,2,3,4,5} -> (3-1)+(3-2)+(3-3)+(4-3)+(5-3) = 2+1+0+1+2 = 6)
            System.out.println("Array: " + Arrays.toString(arr6) + ", Min Operations: " + minOperationsToEqual(arr6)); // Expected: 9 (target median is 3 or 4, {1,2,3,4,5,6} -> median 3: (3-1)+(3-2)+(3-3)+(4-3)+(5-3)+(6-3) = 2+1+0+1+2+3 = 9. median 4: (4-1)+(4-2)+(4-3)+(4-4)+(5-4)+(6-4) = 3+2+1+0+1+2 = 9)
        }

        // Method to calculate minimum operations to make all array elements equal
        public static long minOperationsToEqual(int[] arr) {
            // Step 1: Handle edge cases for empty or single-element arrays
            if (arr == null || arr.length <= 1) {
                return 0;
            }

            // Step 2: Sort the array to easily find the median
            Arrays.sort(arr);

            // Step 3: Determine the median element
            // For an odd number of elements, the median is arr[length / 2].
            // For an even number of elements, any value between arr[length / 2 - 1] and arr[length / 2]
            // (inclusive) will result in the same minimum sum of absolute differences.
            // We can pick either arr[length / 2 - 1] or arr[length / 2].
            int median = arr[arr.length / 2];

            // Step 4: Calculate the total operations by summing absolute differences
            long totalOperations = 0;
            for (int num : arr) {
                totalOperations += Math.abs(num - median);
            }

            // Step 5: Return the total minimum operations
            return totalOperations;
        }
    }