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Problem: XOR All Elements Between Two Arrays

This README explains the solution to the problem step by step for multiple programming languages: C++, Java, JavaScript, Python, and Go. Each explanation is provided in an incremental and intuitive manner, helping you understand the approach and logic.

Steps to Solve the Problem

C++ Code

  1. Initialize XOR values: Start by defining two variables, xor1 and xor2, to store the XOR of all elements in nums1 and nums2 respectively. Both are initialized to 0.

  2. Compute XOR for nums1: Iterate through each element in nums1, XORing the current value with xor1. This will give the cumulative XOR of all elements in nums1.

  3. Compute XOR for nums2: Similarly, iterate through each element in nums2, XORing the current value with xor2. This will give the cumulative XOR of all elements in nums2.

  4. Check the length of arrays:

    • If the length of nums1 is odd, every element in nums2 will contribute to the final XOR result. Add xor2 to the result.
    • If the length of nums2 is odd, every element in nums1 will contribute to the final XOR result. Add xor1 to the result.

  5. Return the result: Combine the XOR values based on the above conditions and return the final result.

Java Code

  1. Declare variables for XOR values: Create two variables, xor1 and xor2, initialized to 0, to hold the cumulative XOR values of elements in nums1 and nums2.

  2. Iterate over nums1: Use a for loop to traverse each element of nums1. At each step, XOR the current value with xor1 to compute the cumulative XOR.

  3. Iterate over nums2: Similarly, use a for loop to traverse each element of nums2. XOR each value with xor2 to compute the cumulative XOR.

  4. Check the array lengths:

    • If the length of nums1 is odd, include xor2 in the result.
    • If the length of nums2 is odd, include xor1 in the result.

  5. Return the final XOR result: Combine the XOR values conditionally and return the result.

JavaScript Code

  1. Define variables: Start with two variables, xor1 and xor2, both set to 0, to store the XOR results for nums1 and nums2.

  2. Compute XOR for nums1: Use a for...of loop to iterate through each element in nums1. At every iteration, XOR the current value with xor1 to accumulate the XOR.

  3. Compute XOR for nums2: Similarly, iterate through nums2 with a for...of loop and XOR the values with xor2.

  4. Determine contributions:

    • Check if the length of nums1 is odd. If so, include xor2 in the final XOR result.
    • Check if the length of nums2 is odd. If so, include xor1 in the final XOR result.

  5. Return the result: Return the combined XOR result based on the length checks.

Python Code

  1. Initialize XOR variables: Define xor1 and xor2 and set them to 0 to hold the XOR of all elements in nums1 and nums2.

  2. Iterate through nums1: Use a for loop to go through each element of nums1. At each iteration, XOR the current value with xor1.

  3. Iterate through nums2: Similarly, iterate through nums2 using a for loop and XOR each value with xor2.

  4. Check array lengths:

    • If the length of nums1 is odd, include xor2 in the result.
    • If the length of nums2 is odd, include xor1 in the result.

  5. Return the combined XOR result: Return the result based on the conditions evaluated.

Go Code

  1. Initialize XOR variables: Create two variables, xor1 and xor2, initialized to 0. These will store the XOR of all elements in nums1 and nums2.

  2. Compute XOR for nums1: Use a for loop to traverse nums1. For each value, XOR it with xor1 to calculate the cumulative XOR.

  3. Compute XOR for nums2: Similarly, iterate through nums2 with a for loop and XOR each value with xor2.

  4. Evaluate lengths of arrays:

    • Check if the length of nums1 is odd. If true, include xor2 in the result.
    • Check if the length of nums2 is odd. If true, include xor1 in the result.

  5. Return the final XOR: Combine xor1 and xor2 based on the array length checks and return the result.

Key Takeaways

  • The XOR operation has unique properties:

    • (a \oplus a = 0) (cancels itself).
    • (a \oplus 0 = a).
    • Order doesn’t matter (commutative and associative).

  • By precomputing the XOR of both arrays and analyzing the lengths, we can solve the problem in (O(m + n)) time and (O(1)) space.

  • The approach is consistent across all languages, making it efficient and easy to implement.

Feel free to explore the solution in your preferred language! Let me know if you have any questions. 😊