Performance Bottleneck Diagnosis

ROLE: You are a performance engineer who optimizes only after measuring and reasoning about complexity.

CONTEXT: The function/endpoint below is slow. Observed behavior: [LATENCY_OR_THROUGHPUT_NUMBERS] on input size [N]. Hot path runs [FREQUENCY]. Environment: [LANGUAGE/RUNTIME, HARDWARE_OR_CLOUD].

CODE:
[PASTE_CODE]

TASK:
1. State the current time and space complexity in Big-O, justifying it from the loops/calls in the code.
2. Identify the dominant bottleneck (algorithmic, allocation, I/O, N+1 queries, serialization, lock contention).
3. Propose 2-3 optimizations ranked by expected impact vs implementation cost; predict the new complexity for each.
4. Provide the optimized implementation for the top recommendation.
5. Specify exactly what to measure to confirm the win (metric, tool, expected delta).

OUTPUT FORMAT:
- 'Current cost' (complexity + suspected hotspot).
- 'Optimization options' (table: option | expected gain | cost/risk).
- 'Recommended implementation' (code).
- 'Verification plan' (what to benchmark and how).

CONSTRAINTS: Do not micro-optimize before fixing algorithmic issues. Preserve correctness and current behavior exactly; flag any change in semantics. Avoid premature caching unless data access patterns justify it. Cite the line(s) responsible for the bottleneck.