LeetCode 761 | Special Binary String | Java | Hard | Recursion & Greedy Sorting | CodeByTushu
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In today’s video, we solve LeetCode 761 — Special Binary String using Recursion and Greedy Sorting in Java.
A special binary string satisfies two properties: equal numbers of 0s and 1s, and every prefix has at least as many 1s as 0s. This is the classic Dyck language representing balanced parentheses where 1 is an open parenthesis and 0 is a close parenthesis. Because we can repeatedly swap adjacent special substrings, any set of consecutive independent special blocks can be reordered into any arbitrary permutation.
To maximize the string lexicographically, we recursively decompose the string into its top-level primitive special components. Each primitive component starts with 1 and ends with 0, enclosing an inner special substring. We recursively optimize each inner component, wrap it with 1 and 0, and then sort all top-level components in descending order. This divide-and-conquer approach runs in O(n^2 log n) time and O(n) auxiliary space.
🔥 Problem Highlights
✅ Equivalence to Dyck language and balanced parentheses
✅ Partitioning into irreducible primitive special substrings
✅ Recursive divide-and-conquer optimization on nested inner substrings
✅ Greedy descending sorting of top-level components
✅ Clean, idiomatic Java implementation
✅ O(n^2 log n) time complexity and O(n) auxiliary space complexity
⏱️ TIMESTAMPS
00:00 Intro & Problem Overview
01:22 Problem Understanding & Constraints
02:45 Parentheses Isomorphism & Tree Sorting Insight
04:34 Recursive Divide & Conquer Strategy
06:03 Java Solution Walkthrough Line by Line
07:24 Test Cases Walkthrough & Simulation
09:01 Time Complexity Analysis (O(N²) Quadratic)
09:55 Space Complexity Analysis (O(N) Recursion Stack)
10:27 Outro & Wrap-up
📂 Problem Folder & Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/February/20-February/761-Special-Binary-String
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/20-February/761-Special-Binary-String/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/20-February/761-Special-Binary-String/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/20-February/761-Special-Binary-String/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/20-February/761-Special-Binary-String/solution.js
🔗 LeetCode Source Code
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🔥 Perfect For
LeetCode Hard Problems
Java DSA Preparation
Recursion and Divide-and-Conquer
Dyck Language and Parentheses Patterns
Greedy String Sorting
Time Complexity Optimization
Coding Interview Preparation
Problem Solving
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💬 Question of the Day
What classic formal language structure is mathematically equivalent to a special binary string where '1' represents an open parenthesis and '0' represents a close parenthesis?
1️⃣ Regular Grammar
2️⃣ Dyck Language (Balanced Parentheses)
3️⃣ Deterministic Finite Automaton
4️⃣ Context-Sensitive Grammar
#LeetCode761 #LeetCode #SpecialBinaryString #Java #JavaDSA #Recursion #String #Sorting #DSA #CodingInterview #ProblemSolving #LeetCodeHard #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description
In today’s video, we solve LeetCode 761 — Special Binary String using Recursion and Greedy Sorting in Java.
A special binary string satisfies two properties: equal numbers of 0s and 1s, and every prefix has at least as many 1s as 0s. This is the classic Dyck language representing balanced parentheses where 1 is an open parenthesis and 0 is a close parenthesis. Because we can repeatedly swap adjacent special substrings, any set of consecutive independent special blocks can be reordered into any arbitrary permutation.
To maximize the string lexicographically, we recursively decompose the string into its top-level primitive special components. Each primitive component starts with 1 and ends with 0, enclosing an inner special substring. We recursively optimize each inner component, wrap it with 1 and 0, and then sort all top-level components in descending order. This divide-and-conquer approach runs in O(n^2 log n) time and O(n) auxiliary space.
🔥 Problem Highlights
✅ Equivalence to Dyck language and balanced parentheses
✅ Partitioning into irreducible primitive special substrings
✅ Recursive divide-and-conquer optimization on nested inner substrings
✅ Greedy descending sorting of top-level components
✅ Clean, idiomatic Java implementation
✅ O(n^2 log n) time complexity and O(n) auxiliary space complexity
⏱️ TIMESTAMPS
00:00 Intro & Problem Overview
01:22 Problem Understanding & Constraints
02:45 Parentheses Isomorphism & Tree Sorting Insight
04:34 Recursive Divide & Conquer Strategy
06:03 Java Solution Walkthrough Line by Line
07:24 Test Cases Walkthrough & Simulation
09:01 Time Complexity Analysis (O(N²) Quadratic)
09:55 Space Complexity Analysis (O(N) Recursion Stack)
10:27 Outro & Wrap-up
📂 Problem Folder & Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/February/20-February/761-Special-Binary-String
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/20-February/761-Special-Binary-String/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/20-February/761-Special-Binary-String/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/20-February/761-Special-Binary-String/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/20-February/761-Special-Binary-String/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 Hard Problems
Java DSA Preparation
Recursion and Divide-and-Conquer
Dyck Language and Parentheses Patterns
Greedy String Sorting
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
What classic formal language structure is mathematically equivalent to a special binary string where '1' represents an open parenthesis and '0' represents a close parenthesis?
1️⃣ Regular Grammar
2️⃣ Dyck Language (Balanced Parentheses)
3️⃣ Deterministic Finite Automaton
4️⃣ Context-Sensitive Grammar
#LeetCode761 #LeetCode #SpecialBinaryString #Java #JavaDSA #Recursion #String #Sorting #DSA #CodingInterview #ProblemSolving #LeetCodeHard #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description