How do you solve Decode XORed Array on LeetCode?

Decode XORed Array (LeetCode #1720) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: XOR operation is reversible and can be used to derive original values from encoded values.

What is the brute force solution for Decode XORed Array?

The brute force approach for Decode XORed Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves trying to derive the original array by guessing the values based on the encoded array. However, this method is inefficient as it requires checking multiple combinations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Decode XORed Array?

Decode XORed Array uses the following concepts: Array, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Array.

What are the interview tips for Decode XORed Array?

Clearly explain your thought process as you derive the solution. Be prepared to discuss the properties of XOR and how they apply to this problem. Practice similar problems to become comfortable with bit manipulation.

What are common mistakes when solving Decode XORed Array?

Confusing the properties of XOR, especially that a XOR a = 0. Not initializing the array correctly or misunderstanding the indices.

#1720

Decode XORed Array

Easy

ArrayBit ManipulationBit ManipulationArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal solution leverages the properties of XOR to directly compute each element of the original array using the encoded values. This method is efficient and straightforward.

⚙️

Algorithm

3 steps

1Step 1: Initialize an array 'arr' of size n.
2Step 2: Set arr[0] to 'first'.
3Step 3: Iterate through the encoded array and compute arr[i+1] as arr[i] XOR encoded[i].

solution.py9 lines

1# Full working Python code
2
3def decode(encoded, first):
4    n = len(encoded) + 1
5    arr = [0] * n
6    arr[0] = first
7    for i in range(n - 1):
8        arr[i + 1] = arr[i] ^ encoded[i]
9    return arr

ℹ

Complexity note: The time complexity is O(n) because we iterate through the encoded array once, and the space complexity is O(n) due to the storage of the original array.

1XOR operation is reversible and can be used to derive original values from encoded values.
2The first element is crucial as it sets the base for deriving the rest of the array.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.