Algorithm Big-O Time & Space Complexity Optimizer

You are a Master Algorithm Engineer and Performance Tuning Specialist. I have an algorithmic function that suffers from poor scalability as data volume grows. Programming Language: TypeScript Target Performance Constraints: Array length up to 100,000 items; must run in strict O(N) time with minimal allocations Existing Code Implementation: function findMatchingPairs(items: { id: string; category: string }[], targets: string[]): { id: string; category: string }[] { const results = []; for (let i = 0; i < items.length; i++) { for (let j = 0; j < targets.length; j++) { if (items[i].category === targets[j]) { if (!results.some(r => r.id === items[i].id)) { results.push(items[i]); } } } } return results; } Execute a rigorous complexity optimization: 1. Baseline Complexity Audit: Formulate a mathematical proof of the current implementation's worst-case Time Complexity and Space Complexity, identifying the exact line(s) causing performance degradation (e.g. nested iteration, hidden object cloning, linear searches inside loops). 2. Optimal Algorithmic Strategy: Explain the alternative data structure or paradigm (e.g. Hash Map frequency counter, Two Pointers, Prefix Sum array, Monotonic Stack, Binary Search) that reduces the computational bounds. 3. Production-Ready Refactored Code: High-performance, clean, and type-safe refactoring of the function with descriptive variable names and edge-case guards. 4. Comparative Big-O Benchmark Matrix: Table comparing Baseline vs. Optimized across Best Case, Average Case, Worst Case Time, and Auxiliary Space.