Ehab the Xorcist (CF D 1700 Rated) | Bit Manipulation Series #23

Welcome back to the Bit Manipulation series! Today, we are tackling a brilliant Codeforces Div. 2 D problem: "Ehab the Xorcist".

The problem gives us two integers, u (the bitwise XOR of an array) and v (the standard sum of that array), and asks us to construct the shortest possible array that satisfies both conditions.

If you try to brute-force or simulate this, you will be stuck forever. Instead, we are going to unlock the fundamental algebraic relationship between Addition and XOR! In this video, I will prove to you mathematically why v - u must always be an even number, and how we can use that difference to instantly construct an array of length 0, 1, 2, or 3 in O(1) time complexity.

📌 What you will learn in this video:

- The Golden Formula: Understanding why A + B = (A ^ B) + 2 * (A & B).

- Identifying Impossible Cases: Why u greater than v or an odd v - u difference makes the array mathematically impossible (outputting -1).

- The Length 3 Strategy: How to distribute the difference x = (v - u) / 2 to guarantee an array of [u, x, x].

- The Length 2 Optimization: Using the Bit Independence Principle to check if (u & x) == 0, allowing us to compress the array into just [u + x, x].

- C++ Implementation: Writing a clean, O(1) logic tree that instantly solves the problem without any loops.

𝐏𝐫𝐨𝐛𝐥𝐞𝐦 𝐋𝐢𝐧𝐤: https://codeforces.com/problemset/problem/1325/D

𝐂𝐨𝐝𝐞: https://github.com/yash7xm/cp-topics/tree/master/bit_manipulation

🔗 𝐏𝐥𝐚𝐲𝐥𝐢𝐬𝐭: https://youtube.com/playlist?list=PLtfqa971vD5FCglZmCX6tbAf1BayFzrpv&si=otFZEOGugiMGgCxX
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👤 WHO IS THIS FOR?
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✅ CP programmers who want to go beyond "it works" and understand "why it works"
✅ Anyone targeting Codeforces Div 2 C/D or HackerRank hard problems
✅ People who want to build the mathematical intuition behind bit tricks
✅ Students preparing for ICPC, CodeChef, or product company placements

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Видео Ehab the Xorcist (CF D 1700 Rated) | Bit Manipulation Series #23 канала Yash Poonia