LeetCode 1720 | Decode XORed Array | Bit Manipulation & Array Reconstruction Explained | Pen & Paper

LeetCode 1720 | Decode XORed Array | Bit Manipulation & Array Reconstruction Explained | Pen & Paper In this video we solve LeetCode 1720 — Decode XORed Array. You are given an encoded integer array (of length n−1) and an integer first which is the first element of the hidden original array arr. The encoding rule is: encoded[i] = arr[i] XOR arr[i + 1] Your task: reconstruct the full original array arr of length n. What you’ll learn in this video: • The key XOR property: if a XOR b = c then a XOR c = b and b XOR c = a. This is what allows decoding. AlgoMonster +2 goodtecher.com +2 • How to initialize: set arr[0] = first. • For each i from 0 to encoded.length−1, compute arr[i+1] = arr[i] XOR encoded[i] This yields each next element in O(1) time. WalkCCC • Explanation with a worked example: Example: encoded = [1,2,3], first = 1 → arr = [1, 0, 2, 1] because: 1 XOR 0 = 1; 0 XOR 2 = 2; 2 XOR 1 = 3. • Time complexity: O(n) (single pass), space complexity: O(n) (output array). Leetcode +1 • Why this pattern is important for tech interviews: it demonstrates array manipulation and fundamental bit-wise reasoning. • Bonus: How to explain this solution clearly during coding rounds (how you derive arr[i+1] = arr[i] XOR encoded[i], why XOR is its own inverse). If you want to strengthen your bit-manipulation toolkit, this is a must-know pattern. 📘 Visit penpaperpreparation.com for full handwritten notes, downloadable examples, and problem sets.