LeetCode 3548 | Equal Sum Grid Partition II | Java | Hard | Matrix Partitioning | CodeByTushu
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In today’s video, we solve LeetCode 3548 — Equal Sum Grid Partition II using Prefix Sum, Hash Set, and Matrix Transformations in Java.
We are given an m x n matrix of positive integers. Our task is to determine whether a single horizontal or vertical cut can divide the matrix into two non-empty sections with equal sums. If their sums are not equal, we can make them equal by discounting at most one cell from one section, while ensuring that the remaining cells in that section stay connected.
To solve this efficiently, we use important connectivity properties of rectangular grid graphs. A subgrid with at least 2 rows and 2 columns remains connected even after removing any single cell. However, in a single row or column, removing an interior cell can disconnect the remaining cells, so only the two extreme endpoints can be removed safely.
We simplify the solution by checking horizontal cuts across four different matrix orientations: the original matrix, reversed rows, transposed matrix, and reversed transposed matrix. This symmetry-based approach allows us to handle both horizontal and vertical cuts efficiently, achieving O(m * n) time complexity and O(m * n) auxiliary space.
🔥 Problem Highlights
✅ Horizontal and Vertical Cuts: Evaluates both possible directions for dividing the grid into two non-empty sections
✅ Fast Value Lookup: Uses Hash Sets and Prefix Sums to efficiently find a cell with the required value
✅ Graph Connectivity Insight: Uses the property that rectangular grid subgraphs with at least 2 rows and 2 columns remain connected after removing any single vertex
✅ 1D Boundary Handling: Restricts valid cell removal in single-row or single-column sections to their extreme endpoints
✅ Four-Way Symmetry Reduction: Uses matrix reversal and transposition to simplify the implementation and avoid redundant branching
✅ Optimal Complexity: Achieves O(m * n) time and O(m * n) auxiliary space
⏱️ TIMESTAMPS
00:00 Intro & Daily Challenge Overview
01:27 Problem Understanding & Cut Constraints
03:33 Key Observations: 2-Connectivity & 1D Path Endpoints
05:39 Algorithmic Strategy: 4-Way Symmetry Reduction
07:39 Clean Java Solution Walkthrough Line by Line
09:12 Dry Run & Step-by-Step Example Walkthrough
11:09 Time Complexity Analysis (O(M × N) - 85 ms, Optimal)
12:23 Space Complexity Analysis (O(M × N) Auxiliary Space)
13:12 Outro & Resources
📂 Problem Folder & Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II/solution.js
🔗 LeetCode Source Code
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💬 Question of the Day
Why does removing an interior cell from a rectangular subgrid with at least 2 rows and 2 columns never disconnect the remaining cells?
1️⃣ Because such grid graphs are 2-vertex-connected and provide alternative paths around any removed cell
2️⃣ Because cells with positive values always provide diagonal connectivity
3️⃣ Because any cut can only be made along straight horizontal lines
4️⃣ Because all elements in the grid are positive integers
#LeetCode3548 #LeetCode #EqualSumGridPartitionII #Java #JavaDSA #PrefixSum #Matrix #DSA #CodingInterview #ProblemSolving #LeetCodeHard #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description
In today’s video, we solve LeetCode 3548 — Equal Sum Grid Partition II using Prefix Sum, Hash Set, and Matrix Transformations in Java.
We are given an m x n matrix of positive integers. Our task is to determine whether a single horizontal or vertical cut can divide the matrix into two non-empty sections with equal sums. If their sums are not equal, we can make them equal by discounting at most one cell from one section, while ensuring that the remaining cells in that section stay connected.
To solve this efficiently, we use important connectivity properties of rectangular grid graphs. A subgrid with at least 2 rows and 2 columns remains connected even after removing any single cell. However, in a single row or column, removing an interior cell can disconnect the remaining cells, so only the two extreme endpoints can be removed safely.
We simplify the solution by checking horizontal cuts across four different matrix orientations: the original matrix, reversed rows, transposed matrix, and reversed transposed matrix. This symmetry-based approach allows us to handle both horizontal and vertical cuts efficiently, achieving O(m * n) time complexity and O(m * n) auxiliary space.
🔥 Problem Highlights
✅ Horizontal and Vertical Cuts: Evaluates both possible directions for dividing the grid into two non-empty sections
✅ Fast Value Lookup: Uses Hash Sets and Prefix Sums to efficiently find a cell with the required value
✅ Graph Connectivity Insight: Uses the property that rectangular grid subgraphs with at least 2 rows and 2 columns remain connected after removing any single vertex
✅ 1D Boundary Handling: Restricts valid cell removal in single-row or single-column sections to their extreme endpoints
✅ Four-Way Symmetry Reduction: Uses matrix reversal and transposition to simplify the implementation and avoid redundant branching
✅ Optimal Complexity: Achieves O(m * n) time and O(m * n) auxiliary space
⏱️ TIMESTAMPS
00:00 Intro & Daily Challenge Overview
01:27 Problem Understanding & Cut Constraints
03:33 Key Observations: 2-Connectivity & 1D Path Endpoints
05:39 Algorithmic Strategy: 4-Way Symmetry Reduction
07:39 Clean Java Solution Walkthrough Line by Line
09:12 Dry Run & Step-by-Step Example Walkthrough
11:09 Time Complexity Analysis (O(M × N) - 85 ms, Optimal)
12:23 Space Complexity Analysis (O(M × N) Auxiliary Space)
13:12 Outro & Resources
📂 Problem Folder & Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/March/26-March/3548-Equal-Sum-Grid-Partition-II/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
Prefix Sum Patterns
Matrix Manipulations and Transformations
Graph Connectivity and Articulation Points
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 removing an interior cell from a rectangular subgrid with at least 2 rows and 2 columns never disconnect the remaining cells?
1️⃣ Because such grid graphs are 2-vertex-connected and provide alternative paths around any removed cell
2️⃣ Because cells with positive values always provide diagonal connectivity
3️⃣ Because any cut can only be made along straight horizontal lines
4️⃣ Because all elements in the grid are positive integers
#LeetCode3548 #LeetCode #EqualSumGridPartitionII #Java #JavaDSA #PrefixSum #Matrix #DSA #CodingInterview #ProblemSolving #LeetCodeHard #DailyLeetCode #JavaProgramming #CodeByTushu
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