Python program to find XOR of array elements which are divisible by given number

In this article, we will discuss how to compute the XOR of array elements that are divisible by a given number. The XOR (exclusive OR) is a binary operation that compares the bits of two operands. If the bits are different then it will return 1 whereas it returns 0 if the bits are the same. In this approach, we will use the property of XOR and apply this to this problem. The solution to this problem is shown with a relevant example. Let’s take an example to demonstrate the computation. Consider a simple example for understanding purposes, the array ‘arr’ = [1,2,3,4,5]. We will calculate the XOR of its elements followed by step-by-step process.

• Initialize xor_value to 0.

• Begin iterating over each element:

  • First element num = 1, perform xor_value^num. Since xor_value = 0, result is 1. Update xor_value = 1.

  • 2^nd element num = 2, perform xor_value^num. Current xor_value = 1, result is 3. Update xor_value = 3.

  • 3^rd element num = 3, perform xor_value^num. Current xor_value = 3, result is 0. Update xor_value = 0.

  • 4^th element num = 4, perform xor_value^num. Current xor_value = 0, result is 0. Update xor_value = 4.

  • 5^th element num = 5, perform xor_value^num. Current xor_value = 4, result is 1. Update xor_value = 1.

• Iteration is completed and the final xor_value is 1.

• Return xor_value as the result.

In the given example, The XOR of the array [1,2,3,4,5] is 1.

We can use this computation to any array to obtain the XOR operation of its elements.

Example 1: Python Program to find XOR of array elements that are divisible by given number

Code Explanation and Design Steps

Step 1: Open Jupyter Notebook in the Anaconda prompt and start writing the code in its cell.

Step 2: Use this function ‘xor_divisible_elements’ which takes two parameters ‘arr’ as an input array and ‘divisor’ is a number by which elements must be divisible.

Step 3: Initialize ‘xor_value’ to 0.

Step 4: The XOR value of the divisible number will be stored in ‘xor_value’ for all elements.

Step 5: Use the ‘for’ loop to iterate to each element of ‘num’ in the ‘arr’.

Step 6: In the ‘for’ loop, using modulo operator (%) we check whether ‘num’ is divisible by ‘divisor’ or not. If we get the remainder is 0 then ‘num’ is divisible by ‘divisor’ absolutely. Check the result.

Step 7: Update the ‘xor_value’, performing the XOR operation with ‘num’ using the XOR assignment operator ‘^=’.

Step 8: Bitwise XOR operation performed with ‘xor_value’ and ‘num’ to compute the new XOR value.

Step 9: Create an input array and set the divisor to 10, call the function ‘xor_divisible_elements’ with the input array and store the calculated value in the ‘result’ variable.Check the result.

Code For XOR of array elements that are divisible by a given number

Example

def xor_divisible_elements(arr, divisor):
    xor_value = 0

    for num in arr: # use for Loop 
        if num % divisor == 0: # Check remainder is zero
            xor_value ^= num  # XORing with num to get our result

    return xor_value

# Example 
array = [20,25,30,35,40,50] # input array
divisor = 10     # set divisor value

result = xor_divisible_elements(array, divisor) # Store final value in the result variable
print("XOR of divisible elements:", result) # Printing our result

Output

XOR of divisible elements: 16

Example 2: Python Program to find XOR of array elements that are divisible by given number

Code Explanation and Design Steps

Step 1: Open Jupyter Notebook in the Anaconda prompt and start writing the code in its cell.

Step 2: Use this function ‘xor_divisible_elements’ which takes two parameters ‘arr’ as an input array and ‘divisor’ is a number by which elements must be divisible.

Step 3: Initialize ‘xor_value’ to 0.

Step 4: The XOR value of the divisible number will be stored in ‘xor_value’ for all elements.

Step 5: Use the ‘for’ loop to iterate to each element of ‘num’ in the ‘arr’.

Step 6: In the ‘for’ loop, using the floor division operator (//), calculate the quotient by dividing num by divisor for an individual element. Check if the quotient is odd by checking quotient % 2 == 1.

Step 7: Update the ‘xor_value’, performing the XOR operation with ‘num’ using the XOR assignment operator ‘^=’.

Step 8: Bitwise XOR operation performed with ‘xor_value’ and ‘num’ to compute the new XOR value.

Step 9: Create an input array and set the divisor to 10, call the function ‘xor_divisible_elements’ with the input array and store the calculated value in the ‘result’ variable. Check the result.

Code For XOR of array elements which are divisible by a given number: (Alternate way)

Example

def xor_divisible_elements(arr, divisor):
    xor_value = 0

    for num in arr: # use for Loop 
        quotient = num // divisor  # Calculate quotient by dividing num by  
                                     # divisor using ‘//’ operator

        if quotient % 2 == 1:  # Check for quotient odd
            xor_value ^= num  # XORing with num to get our result

    return xor_value

# Example 
array = [20,25,30,35,40,50] # input array
divisor = 10     # set divisor value

result = xor_divisible_elements(array, divisor) # Store final value in the 
                                                 # result variable
print("XOR of divisible elements:", result) # Print our result

Output

XOR of divisible elements: 15

This code follows method 2 to find the XOR of array elements that are divisible by a given number.

Conclusion

This article takes two methods for calculating the XOR of array elements that are divisible for a given number. Both ways are explained clearly for understanding purposes. Compare the binary value of two operands for the XORing operation, the same bit values will return zero as a result otherwise the result would be 1 for different bit values. We can also modify or change the values of the array and divisor as per our requirements.