Leetcode #1720: Decode XORed Array
In this guide, we solve Leetcode #1720 Decode XORed Array in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
There is a hidden integer array arr that consists of n non-negative integers. It was encoded into another integer array encoded of length n - 1, such that encoded[i] = arr[i] XOR arr[i + 1].
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Bit Manipulation, Array
Intuition
The problem structure lets us track state with bitwise operations.
Bit operations are constant time and avoid extra memory.
Approach
Apply XOR/AND/OR and shifts to maintain the required invariant.
Aggregate the result in a single pass.
Steps:
- Identify a bitwise invariant.
- Combine values with bit operations.
- Return the aggregated result.
Example
Input: encoded = [1,2,3], first = 1
Output: [1,0,2,1]
Explanation: If arr = [1,0,2,1], then first = 1 and encoded = [1 XOR 0, 0 XOR 2, 2 XOR 1] = [1,2,3]
Python Solution
class Solution:
def decode(self, encoded: List[int], first: int) -> List[int]:
ans = [first]
for x in encoded:
ans.append(ans[-1] ^ x)
return ans
Complexity
The time complexity is , and the space complexity is , where is the length of the array. The space complexity is , where is the length of the array.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.