Minimum Moves to Make Array Complementary | LeetCode 1674 | Brute Force | Prefix Sum

In this video, we solve LeetCode 1674: Minimum Moves to Make Array Complementary, a very interesting problem that builds strong intuition around pair analysis, range contribution, prefix sums, and optimization techniques. At first, the problem looks difficult because changing every pair individually seems expensive. But once you understand how each pair contributes to different target sums, the solution becomes extremely elegant. 💡 Core Idea: For every pair: nums[i] + nums[n - 1 - i] we want all pairs to achieve the SAME target sum using minimum operations. Instead of brute forcing every possibility: ✔ Analyze pair contribution ranges ✔ Use difference array optimization ✔ Calculate minimum moves efficiently for every target sum 🚀 What’s covered in this video: ✅ Problem statement with examples ✅ Understanding complementary arrays ✅ Pair-wise analysis intuition ✅ Brute force thinking ✅ Difference array optimization ✅ Prefix sum technique ✅ Step-by-step dry run ✅ Clean and optimized code walkthrough 🧠 Key Insight: Every pair contributes differently depending on the target sum. For a target: 👉 Some sums require 0 moves 👉 Some sums require 1 move 👉 Some sums require 2 moves Using range updates + prefix sums helps compute all answers efficiently in linear time. 🎯 Why this problem is important: Builds strong range update intuition Excellent problem for prefix sum optimization Helps in pair contribution analysis Common interview-style optimization pattern 🔥 What you’ll learn: Difference array technique Prefix sum optimization Pair-based greedy thinking Efficient range contribution handling Writing optimized interview-level solutions If you found this helpful: 👍 Like 💬 Comment 🔔 Subscribe #Leetcode #DSA #CodingInterview #Algorithms #PrefixSum #Greedy #Optimization #ProblemSolving