# Find array using different XORs of elements in groups of size 4 in Java

JavaServer Side ProgrammingProgramming

We are given with an integer array of size N(size of multiple 4) and we have to perform Xclusive OR operation on the array such that input[1- 4] resembles utility_arr[1- 4] and the conditions of computing is If arr[1 – 4] = {a1, a2, a3, a4} then q[1 – 4] = {a1 ⊕ a2 ⊕ a3, a1 ⊕ a2 ⊕ a4, a1 ⊕ a3 ⊕ a4, a2 ⊕ a3 ⊕ a4}

Let us see various input output scenarios for this -

In − int[] input = { 5, 2, 3, 4 };

Out − Result after XOR operation 4 3 2 5

Explanation −An Exclusive-OR gate's output only goes "HIGH" when both of its input terminals are at "DIFFERENT" logic levels from one another. The output is a "0" if these two inputs, A and B, are both at logic level "1" or "0," making the gate a "odd but not the even gate." In other words, when the inputs have an odd number of 1s, the output is "1."

a1 ⊕ a2 ⊕ a3 = 5 ⊕ 2 ⊕ 3 = 4

a1 ⊕ a2 ⊕ a4 = 5 ⊕ 2 ⊕ 4 = 3

a1 ⊕ a3 ⊕ a4 = 5⊕ 3 ⊕ 4 = 2

a2 ⊕ a3 ⊕ a4 = 2 ⊕ 3 ⊕ 4 = 5

In − int[] input = { 7, 6, 4, 4, 3, 8, 9, 5 };

Out − Result after XOR operations 5 5 7 6 2 14 15 4

Explanation − An Exclusive-OR gate's output only goes "HIGH" when both of its input terminals are at "DIFFERENT" logic levels from one another. The output is a "0" if these two inputs, A and B, are both at logic level "1" or "0," making the gate a "odd but not the even gate." In other words, when the inputs have an odd number of 1s, the output is "1." Will only work for input[] of size multiples of 4, other sized input arrays will show 0s in place of odd placed numbers.

## Approach used in the below program is as follows −

• According to the properties of XOR a ⊕ a = 0 and a ⊕ 0 = a. (a ⊕ b ⊕ c) ⊕ (b ⊕ c ⊕ d) = a ⊕ d (As (b ⊕ c) ⊕ (b ⊕ c) = 0)

• For computation the array is divided into groups of 4 and we will follow the properties of XOR to calculate the results of each group.

• Taking reference from the above property using (a ⊕ d) we can calculate b and c (a ⊕ b ⊕ d) ⊕ (a ⊕ d) = b (a ⊕ c ⊕ d) ⊕ (a ⊕ d) = c

• And by using b and c we can get a and d by using the following approach (a ⊕ b ⊕ c) ⊕ (b) ⊕ (c) = a (b ⊕ c ⊕ d) ⊕ (b) ⊕ (c) = d

• The process is repeated for all four groups

• A loop is iterated with 2 pointers i and j till length of the array divided by four and a temp value(ans) and an utility array(which stores answers) is introduced.

• Inside the for loop following xor operations are implemented

ans= input array[i] ⊕ input array[i+3]

Utility array[i+1](calculating b)= input array[i+1] ⊕ ans

Utility array[i+2](calculating c)= input array[i+2] ⊕ ans

Utility array[i](calculating a)= input array[i] ⊕ ((Utility array[i + 1]) ^ (Utility array[i + 2]))

Utility array[i](calculating d)= input array[i+3] ⊕ ((Utility array[i + 1]) ^ (Utility array[i + 2]))

• And the pointer is updated for next set of four characters

• Finally, the array is printed and the result is returned to the user.

## Example

import java.util.Arrays;
import java.util.List;
public class Tutorials{
static int ans = 0;
public static void main(String args[]){
int[] input = {7, 1, 2, 3};
int[] arr = new int[input.length];
for (int i = 0, j = 0; j < input.length / 4; j++){
ans = input[i] ^ input[i + 3];
arr[i + 1] = input[i + 1] ^ ans;
arr[i + 2] = input[i + 2] ^ ans;
arr[i] = input[i] ^ ((arr[i + 1]) ^ (arr[i + 2]));
arr[i + 3] = input[i + 3] ^ (arr[i + 1] ^ arr[i + 2]);
i += 4;
}
System.out.println("Different XORs of elements in groups of size 4 is: ");
for (int i = 0; i < arr.length; i++){
System.out.println(arr[i]);
}
}
}

## Output

If we run the above code it will generate the following Output

Different XORs of elements in groups of size 4 is :
4
5
6
0