TikTok Server Network Optimization

Problem Overview

• Compute the minimum total cost to connect all servers so each can communicate, where connecting i and j costs min(|x[i]-x[j]|, |y[i]-y[j]|).
• Input: integer arrays x and y of length n; Output: an int for the minimum network cost.
• Constraints: 2 ≤ n ≤ 1e5, 0 ≤ x[i], y[i] ≤ 1e9, duplicates allowed.
• Real-world context: optimize TikTok’s grid-based server network expansion.
• From TikTok interviews; a coding interview problem and common interview question.