"Day 414 of #500DaysOfCode: 2D Prefix Sum Optimization for Matrix Manipulation"

🚀 Day 414 of #500DaysOfCode 🔢 LeetCode 2536: Increment Submatrices by One (Medium) Today I worked on an interesting matrix manipulation problem that teaches an important optimization idea — 2D Difference Arrays. 🧠 Problem Summary We are given an n x n matrix initialized with zeros and a list of queries. Each query represents a submatrix, and we need to increment every element inside that submatrix by 1. A brute-force solution would update each cell for every query, which becomes inefficient when the matrix and number of queries grow. ⚡ Key Insight Instead of updating all cells directly, we use a 2D prefix / difference matrix technique: Update only the corners of each submatrix Convert the difference matrix into the final matrix using prefix sums Achieve O(n² + q) performance instead of O(q · n²) A neat trick that’s extremely useful for range update problems! ✅ Takeaways Difference arrays are not just for 1D — they scale beautifully to 2D Matrix prefix sums simplify many complex update operations Thinking in terms of range operations often leads to faster algorithms 💻 Tech Used Java 2D prefix sum optimization Matrix manipulation Another day, another concept mastered. On to the next challenge! 💪🔥 #coding #leetcode #java #programming #dsa #matrix #problemsolving #500DaysOfCode #Day414

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