# Leetcode – Decode XORed Array Solution

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.

1. Problem Statement
2. Understanding XOR and the Problem
3. Brute-Force Approach
4. Optimized Algorithm
5. Python Code Walkthrough
6. Time and Space Complexity Analysis
7. Test Cases
8. Common Pitfalls and How to Avoid Them
9. 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.