Given an array of positive integers of length **n**. Our task is to find minimum number of operations to convert an array so that **arr[i] % 4** is zero for each **i**. In each operation, we can take any two elements from the array, remove both of them and put back their sum in the array.

Examples:

Input : arr = {2 , 2 , 2 , 3 , 3}

Output : 3

Explanation: In 1 operation we pick 2 and 2 and put their sum back to the array , In 2 operation we pick 3 and 3 and do same for that ,now in 3 operation we pick 6 and 2 so overall 3 operation are required.Input: arr = {4, 2, 2, 6, 6}

Output: 2

Explanation: In operation 1, we can take 2 and 2 and put back their sum i.e. 4. In operation 2, we can take 6 and 6 and put back their sum i.e. 12. And array becomes {4, 4, 12}.

**Approach : ** Assume the count of elements leaving remainder **1, 2, 3** when divided by **4** are **brr[1]**, **brr[2]** and **brr[3]**.

If **(brr[1] + 2 * brr[2] + 3 * brr[3])** is not a multiple of **4**, solution does not exist.

Now greedily pair elements of **brr[2]** with **brr[2]** and elements of **brr[1]** with **brr[3]**. This helps us to achieve fixing a maximum of **2** elements at a time. Now, we can either we left with only **1** **brr[2]** element or none. If we are left with **1** **brr[2]** element, then we can pair with **2** remaining **brr[1]** or **brr[3]** elements. This will incur a total of **2** operations.

At last, we would be only left with **brr[1]** or **brr[3]** elements (if possible). This can only we fixed in one way. That is taking **4** of them and fixing them all together in **3** operations. Thus, we are able to fix all the elements of the array.

Below is the implementation:

## CPP

// CPP program to find Minimum number // of operations to convert an array // so that arr[i] % 4 is zero. #include <bits/stdc++.h> using namespace std; // Function to find minimum operations. int minimumOperations(int arr[], int n) { // Counting of all the elements // leaving remainder 1, 2, 3 when // divided by 4 in the array brr. // at positions 1, 2 and 3 respectively. int brr[] = { 0, 0, 0, 0 }; for (int i = 0; i < n; i++) brr[arr[i] % 4]++; // If it is possible to convert the // array so that arr[i] % 4 is zero. if ((brr[1] + 2 * brr[2] + 3 * brr[3]) % 4 == 0) { // Pairing the elements of brr3 and brr1. int min_opr = min(brr[3], brr[1]); brr[3] -= min_opr; brr[1] -= min_opr; // Pairing the brr2 elements. min_opr += brr[2] / 2; // Assigning the remaining brr2 elements. brr[2] %= 2; // If we are left with one brr2 element. if (brr[2]) { // Here we need only two operations // to convert the remaining one // brr2 element to convert it. min_opr += 2; // Now there is no brr2 element. brr[2] = 0; // Remaining brr3 elements. if (brr[3]) brr[3] -= 2; // Remaining brr1 elements. if (brr[1]) brr[1] -= 2; } // If we are left with brr1 and brr2 // elements then, we have to take four // of them and fixing them all together // in 3 operations. if (brr[1]) min_opr += (brr[1] / 4) * 3; if (brr[3]) min_opr += (brr[3] / 4) * 3; // Returns the minimum operations. return min_opr; } // If it is not possible to convert the array. return -1; } // Driver function int main() { int arr[] = { 1, 2, 3, 1, 2, 3, 8 }; int n = sizeof(arr) / sizeof(arr[0]); cout << minimumOperations(arr, n); }

## Java

// Java program to find Minimum number // of operations to convert an array // so that arr[i] % 4 is zero. class GFG { // Function to find minimum operations. static int minimumOperations(int arr[], int n) { // Counting of all the elements // leaving remainder 1, 2, 3 when // divided by 4 in the array brr. // at positions 1, 2 and 3 respectively. int brr[] = { 0, 0, 0, 0 }; for (int i = 0; i < n; i++) brr[arr[i] % 4]++; // If it is possible to convert the // array so that arr[i] % 4 is zero. if ((brr[1] + 2 * brr[2] + 3 * brr[3]) % 4 == 0) { // Pairing the elements of brr3 and brr1. int min_opr = Math.min(brr[3], brr[1]); brr[3] -= min_opr; brr[1] -= min_opr; // Pairing the brr2 elements. min_opr += brr[2] / 2; // Assigning the remaining brr2 elements. brr[2] %= 2; // If we are left with one brr2 element. if (brr[2] == 1) { // Here we need only two operations // to convert the remaining one // brr2 element to convert it. min_opr += 2; // Now there is no brr2 element. brr[2] = 0; // Remaining brr3 elements. if (brr[3] == 1) brr[3] -= 2; // Remaining brr1 elements. if (brr[1]== 1) brr[1] -= 2; } // If we are left with brr1 and brr2 // elements then, we have to take four // of them and fixing them all together // in 3 operations. if (brr[1] == 1) min_opr += (brr[1] / 4) * 3; if (brr[3] == 1) min_opr += (brr[3] / 4) * 3; // Returns the minimum operations. return min_opr; } // If it is not possible to convert the array. return -1; } // Driver function public static void main(String[] args) { int arr[] = { 1, 2, 3, 1, 2, 3, 8 }; int n = arr.length; System.out.println(minimumOperations(arr, n)); } } // This code is contributed by Prerna Saini.

## Python3

# Python program to # find Minimum number # of operations to # convert an array # so that arr[i] % 4 is zero. # Function to find # minimum operations. def minimumOperations(arr,n): # Counting of all the elements # leaving remainder 1, 2, 3 when # divided by 4 in the array brr. # at positions 1, 2 and 3 respectively. brr = [ 0, 0, 0, 0 ] for i in range(n): brr[arr[i] % 4]+=1; # If it is possible to convert the # array so that arr[i] % 4 is zero. if ((brr[1] + 2 * brr[2] + 3 * brr[3]) % 4 == 0): # Pairing the elements # of brr3 and brr1. min_opr = min(brr[3], brr[1]) brr[3] -= min_opr brr[1] -= min_opr # Pairing the brr2 elements. min_opr += brr[2] // 2 # Assigning the remaining # brr2 elements. brr[2] %= 2 # If we are left with # one brr2 element. if (brr[2]): # Here we need only two operations # to convert the remaining one # brr2 element to convert it. min_opr += 2 # Now there is no brr2 element. brr[2] = 0 # Remaining brr3 elements. if (brr[3]): brr[3] -= 2 # Remaining brr1 elements. if (brr[1]): brr[1] -= 2 # If we are left with brr1 and brr2 # elements then, we have to take four # of them and fixing them all together # in 3 operations. if (brr[1]): min_opr += (brr[1] // 4) * 3 if (brr[3]): min_opr += (brr[3] // 4) * 3 # Returns the minimum operations. return min_opr # If it is not possible to convert the array. return -1 # Driver function arr = [ 1, 2, 3, 1, 2, 3, 8 ] n =len(arr) print(minimumOperations(arr, n)) # This code is contributed # by Anant Agarwal.

## C#

// C# program to find Minimum number // of operations to convert an array // so that arr[i] % 4 is zero. using System; class GFG { // Function to find minimum operations. static int minimumOperations(int []arr, int n) { // Counting of all the elements // leaving remainder 1, 2, 3 when // divided by 4 in the array brr. // at positions 1, 2 and 3 respectively. int []brr = { 0, 0, 0, 0 }; for (int i = 0; i < n; i++) brr[arr[i] % 4]++; // If it is possible to convert the // array so that arr[i] % 4 is zero. if ((brr[1] + 2 * brr[2] + 3 * brr[3]) % 4 == 0) { // Pairing the elements of brr3 and brr1. int min_opr = Math.Min(brr[3], brr[1]); brr[3] -= min_opr; brr[1] -= min_opr; // Pairing the brr2 elements. min_opr += brr[2] / 2; // Assigning the remaining brr2 elements. brr[2] %= 2; // If we are left with one brr2 element. if (brr[2] == 1) { // Here we need only two operations // to convert the remaining one // brr2 element to convert it. min_opr += 2; // Now there is no brr2 element. brr[2] = 0; // Remaining brr3 elements. if (brr[3] == 1) brr[3] -= 2; // Remaining brr1 elements. if (brr[1]== 1) brr[1] -= 2; } // If we are left with brr1 and brr2 // elements then, we have to take four // of them and fixing them all together // in 3 operations. if (brr[1] == 1) min_opr += (brr[1] / 4) * 3; if (brr[3] == 1) min_opr += (brr[3] / 4) * 3; // Returns the minimum operations. return min_opr; } // If it is not possible to convert the array. return -1; } // Driver function public static void Main() { int []arr = { 1, 2, 3, 1, 2, 3, 8 }; int n = arr.Length; Console.WriteLine(minimumOperations(arr, n)); } } // This code is contributed by vt_m

Output:

3

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