XOR (Exclusive OR) is a bitwise operation that is often found in computer science problems, including coding interviews. One such problem is “Decode XORed Array” on Leetcode, which is an excellent exercise for understanding bitwise operations and array manipulations in Python. In this comprehensive guide, we’ll explore various strategies to tackle this problem, starting from understanding the problem statement to walking through the Python code.

## Table of Contents

- Problem Statement
- Understanding XOR and the Problem
- Brute-Force Approach
- Optimized Algorithm
- Python Code Walkthrough
- Time and Space Complexity Analysis
- Test Cases
- Common Pitfalls and How to Avoid Them
- Conclusion

### 1. Problem Statement

You are given a **non-empty** encoded array `encoded`

, which contains `n`

integers. You are also given an integer `first`

that represents the first integer of the original array `arr`

.The original array `arr`

is obtained by XORing each pair of adjacent elements in `encoded`

. Your task is to decode the `encoded`

array and return the original array `arr`

.

#### Constraints

- The length of the
`encoded`

array will be`n`

(1 ≤ n ≤ 100), which means the length of the`arr`

will be`n+1`

. - The integers in
`arr`

are in the range of [1, 10^5].

### 2. Understanding XOR and the Problem

The XOR operation is denoted by the ^ symbol. In Python, XOR can be performed using this symbol. The operation follows these rules:

- 0 ^ 0 = 0
- 1 ^ 0 = 1
- 0 ^ 1 = 1
- 1 ^ 1 = 0

The challenge in this problem is to find the original array `arr`

using the XOR operation and the `encoded`

array.

### 3. Brute-Force Approach

A brute-force approach might involve generating all possible arrays and encoding them to see if they match with the given `encoded`

array. However, this would be highly inefficient.

### 4. Optimized Algorithm

Given that XOR is a reversible operation, we can directly compute the original array from the encoded array and the first element.

### 5. Python Code Walkthrough

Let’s walk through the Python code for the optimized approach.

```
def decode(encoded, first):
arr = [first]
for num in encoded:
arr.append(arr[-1] ^ num)
return arr
```

Here, we initialize `arr`

with the known `first`

value. We then iterate through the `encoded`

array, calculating the next element by XORing the last element of `arr`

with the current element from `encoded`

.

### 6. Time and Space Complexity Analysis

The optimized algorithm operates in linear time O(n) and uses linear space O(n).

### 7. Test Cases

You should test your function with various test cases to make sure it works as expected.

```
print(decode([1,2,3], 1)) # Should return [1, 0, 2, 1]
print(decode([6,2,7,3], 4)) # Should return [4, 2, 0, 7, 4]
```

### 8. Common Pitfalls and How to Avoid Them

**Not Initializing the Output Array Correctly**: Make sure to initialize your`arr`

list with the given`first`

element.**Ignoring the Constraints**: Always be cautious about the problem constraints, such as array lengths and integer limits, to make sure your solution can handle edge cases.

### 9. Conclusion

The “Decode XORed Array” problem is an excellent way to familiarize yourself with bitwise operations and array manipulations in Python. It tests your ability to think critically about how to reverse-engineer a process, in this case, decoding an XORed array. The problem is also straightforward enough to allow for an optimized solution that operates in linear time and space.