🎯 Prefix Sum Technique: Efficient Range Query Pattern for Frontend Interviews
Category: dsa
Difficulty: hard
Interview Importance: 🔴 Critical — This technique appears in 30% of frontend coding interviews for array manipulation and range query problems. Essential for optimizing O(n) repeated queries to O(1) constant time lookups. 1️⃣ What is the Prefix Sum Technique? The Prefix Sum Technique (also called cumulative sum) is an algorithmic pattern that preprocesses an array to answer range sum queries in constant time. Instead of repeatedly summing elements in a range, we build a prefix sum array once and use simple arithmetic to get any range sum instantly. Visual Representation: [code example] Real-World Analogy: Think of it like a running total on your bank statement. Instead of adding up all transactions every time you want to know your balance between two dates, you just subtract the balance at the start date from the balance at the end date. The bank keeps cumulative totals, not individual transactions, for quick lookups. 2️⃣ Why Use Prefix Sum? / Why Does This Matter? Without Prefix Sum Benefit O(n) - iterate and sum 1000x faster for repeated queries Multiple range queries O(n + q) - O(n) build + O(1) per query O(n²) - check all subarrays Linear time solution Find equilibrium index O(n) - single pass O(nq) - update each element Batch updates efficiently Aspect Sliding Window Segment Tree Build Time N/A O(n) Query Time O(1) O(log n) Update Time O(1) O(log n) Space O(1) O(n) Best For Contiguous windows Many queries + updates Frontend Use Real-time streams Live data feeds Operation Space Complexity Build prefix sum O(n) O(1) Subtraction of two values Update single element O(1) O(n) Single pass with hash map Find equilibrium index O(n) O(nm) Iterate all cells in matrix 2D range sum query O(1) O(n + q) O(n) build + O(1) per query Category Definition O(n) - single pass to create prefix array Query Time O(n) - requires rebuild (use segment tree if frequent) Space Many queries, few updates; range sum problems Formula 🎯 5 Key Takeaways Prefix sum trades space for time by prep...