LeetCode 3314 | Construct the Minimum Bitwise Array I | Java | Easy | Bit Manipulation | CodeByTushu
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In today’s video, we solve LeetCode 3314 - Construct the Minimum Bitwise Array I using Bit Manipulation in Java.
We are tasked with constructing an array ans such that for every element in nums, the bitwise OR of ans[i] and ans[i] + 1 equals nums[i], while simultaneously minimizing ans[i]. Crucially, the bitwise OR of any integer x with x + 1 always produces an odd number because either x or x + 1 is odd. Since nums contains only prime integers, the only even prime is 2, for which no valid integer x exists, resulting in -1.
For every odd prime, the binary representation consists of higher bits followed by a contiguous block of trailing 1s. The operation of taking the bitwise OR of x and x + 1 turns the lowest 0-bit of x into a 1. To reconstruct the minimum possible value of x that yields nums[i], we must subtract the largest possible bit from its contiguous trailing 1s block. By isolating the lowest set bit of nums[i] + 1 and shifting it right by one, we obtain this exact bit in O(1) time, yielding an optimal O(n) runtime and O(1) auxiliary space.
🔥 Problem Highlights
✅ Parity invariant observation: the bitwise OR of x and x + 1 is always odd
✅ Special base case: even prime 2 immediately returns -1
✅ Analysis of bitwise transitions when adding 1 to binary representations
✅ Contiguous trailing 1s block identification
✅ O(1) bit trick using the lowest set bit of p + 1 shifted right by one
✅ Optimal O(n) time and O(1) auxiliary space complexity
⏱️ TIMESTAMPS
00:00 Intro
01:07 Problem Understanding and Constraints
02:31 Core Observations and Mathematical Insight
03:30 Algorithmic Approach and Bit Manipulation Strategy
04:29 Line-by-Line Java Code Walkthrough
05:39 Step-by-Step Test Run and Dry Run
07:05 Time Complexity Analysis
07:44 Space Complexity Analysis
08:19 Outro and Key Takeaways
📂 Problem Folder and Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I/solution.js
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💬 Question of the Day
Why does the bitwise OR of x and x + 1 always produce an odd number for any non-negative integer x?
1️⃣ Adding 1 always sets the most significant bit
2️⃣ One of the two numbers x or x + 1 is guaranteed to have bit 0 set to 1
3️⃣ Only prime numbers have this property
4️⃣ The bitwise OR operation clears bit 0
#LeetCode3314 #LeetCode #ConstructTheMinimumBitwiseArrayI #Java #JavaDSA #BitManipulation #Array #DSA #CodingInterview #ProblemSolving #LeetCodeEasy #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description
In today’s video, we solve LeetCode 3314 - Construct the Minimum Bitwise Array I using Bit Manipulation in Java.
We are tasked with constructing an array ans such that for every element in nums, the bitwise OR of ans[i] and ans[i] + 1 equals nums[i], while simultaneously minimizing ans[i]. Crucially, the bitwise OR of any integer x with x + 1 always produces an odd number because either x or x + 1 is odd. Since nums contains only prime integers, the only even prime is 2, for which no valid integer x exists, resulting in -1.
For every odd prime, the binary representation consists of higher bits followed by a contiguous block of trailing 1s. The operation of taking the bitwise OR of x and x + 1 turns the lowest 0-bit of x into a 1. To reconstruct the minimum possible value of x that yields nums[i], we must subtract the largest possible bit from its contiguous trailing 1s block. By isolating the lowest set bit of nums[i] + 1 and shifting it right by one, we obtain this exact bit in O(1) time, yielding an optimal O(n) runtime and O(1) auxiliary space.
🔥 Problem Highlights
✅ Parity invariant observation: the bitwise OR of x and x + 1 is always odd
✅ Special base case: even prime 2 immediately returns -1
✅ Analysis of bitwise transitions when adding 1 to binary representations
✅ Contiguous trailing 1s block identification
✅ O(1) bit trick using the lowest set bit of p + 1 shifted right by one
✅ Optimal O(n) time and O(1) auxiliary space complexity
⏱️ TIMESTAMPS
00:00 Intro
01:07 Problem Understanding and Constraints
02:31 Core Observations and Mathematical Insight
03:30 Algorithmic Approach and Bit Manipulation Strategy
04:29 Line-by-Line Java Code Walkthrough
05:39 Step-by-Step Test Run and Dry Run
07:05 Time Complexity Analysis
07:44 Space Complexity Analysis
08:19 Outro and Key Takeaways
📂 Problem Folder and Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/20-January/3314-Construct-the-Minimum-Bitwise-Array-I/solution.js
🔗 LeetCode Source Code
📌 Admin type the link
🌐 All LeetCode Solutions
📌 https://codebytushu.com/Leetcode/
📱 Join CodeByTushu on WhatsApp
Get coding updates, LeetCode solutions, daily questions and more.
https://whatsapp.com/channel/0029Vb8k5mCDeON2Xwlkxe40
❤️ Donate
📌 https://codebytushu.com/Leetcode/donate.php
🔥 Perfect For
LeetCode Easy Problems
Java DSA Preparation
Bit Manipulation
Binary Representation Analysis
Lowbit Isolation Tricks
Time Complexity Optimization
Coding Interview Preparation
Problem Solving
🌐 Follow CodeByTushu
▶️ YouTube: https://www.youtube.com/@codebytushu
📸 Instagram: https://instagram.com/codebytushu/
💼 LinkedIn: https://www.linkedin.com/company/codebytushu/
🌍 Website: https://codebytushu.com
🐙 GitHub: https://github.com/CodeByTushu
❤️ Don’t Forget To
👍 Like | 💬 Comment | 🔔 Subscribe
💬 Question of the Day
Why does the bitwise OR of x and x + 1 always produce an odd number for any non-negative integer x?
1️⃣ Adding 1 always sets the most significant bit
2️⃣ One of the two numbers x or x + 1 is guaranteed to have bit 0 set to 1
3️⃣ Only prime numbers have this property
4️⃣ The bitwise OR operation clears bit 0
#LeetCode3314 #LeetCode #ConstructTheMinimumBitwiseArrayI #Java #JavaDSA #BitManipulation #Array #DSA #CodingInterview #ProblemSolving #LeetCodeEasy #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description