Optimizing Sum of Distances with Prefix Sums

 Moving Beyond Brute Force: Optimizing Sum of Distances 🚀 In software engineering, writing code that works is only the first step. Writing code that scales is where the real challenge lies. I recently tackled LeetCode 2615 (Sum of Distances), and it’s a perfect example of why understanding time complexity is crucial for a developer. The Problem: Given an array, for each element, calculate the sum of absolute differences  ∣i−j∣ ∣i−j∣  for all other indices j j  where the values are identical.The Developer’s Approach: 1️⃣ Identify the Bottleneck: A naive nested loop ( O(n2) O(n2 ) ) would attempt billions of operations for an input size of 105 105 , leading to a Time Limit Exceeded (TLE) error. We need an O(n) O(n)  solution.2️⃣ Data Grouping: Use a HashMap to group indices of the same value. This narrows our focus only to relevant elements. 3️⃣ The Math Pivot (Prefix Sums): Instead of re-calculating distances for every index, we use mathematics. The total distance for any index can be split into: Left Side: (count_of_elements_on_left * current_index) - (sum_of_left_indices) Right Side: (sum_of_right_indices) - (count_of_elements_on_right * current_index) The Result: By maintaining a running prefix sum while iterating through the grouped indices, we transform a complex quadratic problem into a linear one. Key Takeaway: When you see "sum of absolute differences" in an array, think Prefix Sums. It’s one of the most powerful tools in a developer’s arsenal to turn inefficient logic into high-performance code. How do you approach optimization when you hit a performance wall? Let’s discuss in the comments! 💻✨ #SoftwareEngineering #Coding #Algorithms #Optimization #LeetCode #ProblemSolving #DeveloperMindset #CleanCode

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