test1
Prompt
Act as a senior research engineer, algorithm designer, and full-stack app developer. In one response, without asking follow-up questions, solve this integrated benchmark as if you were being evaluated for real technical work. Scenario: Build the core logic for a small cross-platform app called “TrajectoryMatch.” The app takes a natural-language request, matches it to the closest preset scenario, then computes a projectile launch angle to hit a target under gravity and linear air drag. Use these fixed inputs: - gravity g = 9.81 m/s^2 - launch speed v0 = 18.0 m/s - launch height y0 = 1.2 m - target position: x = 22.0 m, y = 2.5 m - linear drag coefficient k = 0.08 s^-1 - preset labels: 1) short indoor toss 2) basketball arc 3) long flat throw 4) high lob training 5) windy outdoor drill - user query: “I need a medium-long practice shot with a higher arc and some drag.” Tasks: 1. State assumptions clearly and determine whether the target is reachable. 2. Briefly explain the physics model and choose a numerical method. 3. Design a matching method to map the query to the best preset and justify it. 4. Write clean, runnable Python code using only the standard library that: - matches the query to the best preset, - searches for a launch angle that minimizes miss distance, - reports best preset, best angle, flight time, and final miss distance. 5. Give 3 meaningful test cases with expected behavior. 6. Propose a minimal architecture for turning this into a Windows, Android, and iOS app. 7. Add a short “research discipline” section listing 3 things you would verify from authoritative sources before production. 8. End with the main risks, edge cases, and next improvements. Constraints: - Be concise but complete. - Prefer correctness over style. - Separate facts/calculations from assumptions. - Do not hand-wave code. - Do not use external libraries.
Answer guidance
Answer in the exact structure below, using the same section titles and order. 1. Executive Summary - In 4–8 bullet points, summarize the solution, whether the target is reachable, the chosen preset, the numerical method, and the expected output behavior. 2. Facts vs Assumptions - Split this into two sub-sections: - Facts / Given Inputs - Assumptions / Simplifications - Do not mix them. 3. Physics Reasoning - Briefly explain the governing equations or simulation logic. - State whether a closed-form solution is used or not. - Explain why the chosen numerical method is appropriate. 4. Matching Reasoning - Explain the query-to-preset matching approach clearly. - Show the scoring logic or decision logic explicitly. - State the selected preset and why it won. 5. Python Solution - Provide one complete runnable Python script in a single code block. - Use only the standard library. - Include comments. - Code must actually implement: - preset matching, - trajectory simulation with gravity and linear drag, - launch-angle search, - final reporting of best preset, best angle, flight time, and miss distance. - Do not use placeholder functions. - Do not omit imports. - Do not use pseudocode. 6. Expected Output Behavior - Do not invent exact numeric results unless derived from the code. - Describe what the script should print and what success looks like. - If exact numbers are uncertain without execution, say so. 7. Test Cases - Provide exactly 3 test cases. - For each test case, include: - input/query or parameter change, - what should happen, - why that behavior is expected. 8. App Architecture - Keep this practical and minimal. - Include: - UI layer, - core logic layer, - platform strategy for Windows, Android, and iOS, - data flow. - Prefer realistic implementation choices. 9. Research Discipline - List exactly 3 items that should be verified from authoritative sources before production. - These must be concrete and relevant. 10. Risks, Edge Cases, Improvements - Give concise bullets. - Include numerical stability, parameter sensitivity, and matching limitations. Rules: - Be concise, technical, and explicit. - No marketing language. - No vague claims. - If something is uncertain, label it clearly. - Prioritize correctness and implementation quality over sounding impressive. The answer will be judged on correctness, code completeness, numerical reasoning, transparency about assumptions, and practicality of implementation.
