Algorithm & Data Structure Visualization
BST operations, graph traversal, sorting animation traces, heap construction.
Subject Overview
25%
of Total Question Bank
Tied for 2nd largest
6
Sub-Domains
CS · EE · ME · Materials · Civil · ChemE
7
Diagram Types
Circuit · CAD · Flow · Phase · Structure · Code · Schematic
Engineering disciplines present unique multimodal challenges: circuit schematics, engineering CAD drawings, thermodynamic cycle diagrams, material phase diagrams, structural analysis diagrams, and code listings interleaved with visual outputs. These require models to reason across radically different visual languages — from geometric constraints in CAD to symbolic notation in circuit diagrams. Langhui Engineering benchmark systematically covers these high-value difficulty zones.
Sub-Domains & High-Value Difficulty Zones
Computer Science (40%)
Code Debugging & Reasoning
Python/C++ bug localization, output prediction, complexity analysis with code+output screenshots.
Evidence: SOTA models fail to debug multi-file dependency bugs.
Computer Architecture
Pipeline diagrams, cache mapping, branch prediction schematics.
Electronic Engineering (20%)
Analog Circuit Analysis
Op-amp circuits, active/passive filters, Bode plot interpretation.
Digital Logic & VLSI
Karnaugh maps, state machine diagrams, timing diagrams, transistor-level schematics.
Signal Processing
Fourier transform visualizations, spectrograms, filter design.
Mechanical Engineering (15%)
Engineering Drawing & CAD
Orthographic projection, section views, dimensional tolerance interpretation.
Thermodynamics & Fluid Mechanics
P-V/T-S diagrams, Bernoulli principle diagrams, pipe flow analysis.
Mechanics of Materials
Stress-strain curves, beam deflection diagrams, Mohr's circle analysis.
Materials Science (10%)
Phase Diagrams
Fe-C, binary eutectic, ternary phase diagram interpretation and lever rule calculations.
Evidence: Fe-C phase diagram reasoning is a known blind spot for VLMs.
Crystal Structures
BCC/FCC/HCP identification, Miller indices, XRD pattern interpretation.
Civil Engineering (8%)
Structural Analysis
Shear/moment diagrams, truss analysis, influence lines.
Geotechnical Engineering
Soil classification charts, consolidation curves, slope stability diagrams.
Chemical Engineering (7%)
Process Flow Diagrams (PFD)
PFD/P&ID interpretation, unit operation identification, mass/energy balance.
Reaction Engineering
Reactor design diagrams, residence time distribution, kinetic curve analysis.
Difficulty Distribution
| Level | Stage | Share | Typical Question Types |
|---|---|---|---|
| L1 Lower Undergrad | Introductory courses | 10% | Basic circuit analysis, simple code output prediction |
| L2 Upper Undergrad | Core engineering courses | 50% | Multi-stage circuit analysis, CAD dimension reasoning |
| L3 Graduate Entry | FE/PE exam level | 30% | Cross-domain synthesis, design optimization problems |
| L4 Research | Advanced / research | 10% | Novel circuit design, paper-level algorithm analysis |
Sample Questions
STEM-2026-ENG-0000456L2 Upper Undergrad
Python · Recursion Bug Localization
Prompt: A Python recursive function to compute the nth Fibonacci number is provided as a screenshot. The code has a subtle bug: it uses n-1 and n-1 (instead of n-1 and n-2) for the two recursive calls. Identify the bug, explain why it causes infinite recursion for n>1, and provide the corrected code.
Answer: The recursive call fib(n-1) is duplicated instead of fib(n-1) + fib(n-2). For n>1:
each call spawns two identical calls to fib(n-1), never reducing the subproblem to the base case, resulting in infinite recursion until stack overflow. Correct: return fib(n-1) + fib(n-2).
5-Model Evaluation
GPT-5.1
3/5
Claude Opus 4.6
2/5
Gemini-3.1-Pro
2/5
Qwen3.6-Plus
1/5
DeepSeek-V4
1/5
STEM-2026-ENG-0000457L3 Graduate Entry
Circuits · 2nd-Order Active Low-Pass Filter
Prompt: A Sallen-Key 2nd-order active low-pass filter schematic is shown. Given R1 = R2 = 10kΩ, C1 = 100nF, C2 = 47nF, calculate the cutoff frequency fc and the quality factor Q. Determine whether the response is Butterworth, Bessel, or Chebyshev.
Answer: fc = 1/(2π√(R1R2C1C2)) = 1/(2π√(10k·10k·100n·47n)) ≈ 1/(2π√(4.7e-10)) ≈ 1/(2π·2.168e-5) ≈ 7,340 Hz. Q = √(R1R2C1C2)/(C2(R1+R2)) = √(4.7e-10)/(47n·20k) = 2.168e-5/9.4e-4 ≈ 0.023. This is heavily overdamped — closer to a Bessel characteristic.
5-Model Evaluation
GPT-5.1
1/5
Claude Opus 4.6
0/5
Gemini-3.1-Pro
1/5
Qwen3.6-Plus
0/5
DeepSeek-V4
0/5
STEM-2026-ENG-0000458L3 Graduate Entry
Materials · Fe-C Phase Diagram — Eutectoid Steel
Prompt: The Fe-Fe3C phase diagram (partial, 0-6.67 wt% C) is shown. An alloy with 0.77 wt% C (eutectoid composition) is slowly cooled from 850°C to room temperature. Identify all phase transformations, the resulting microstructure, and calculate the relative amounts of each phase at room temperature.
Answer: At 850°C: 100% austenite (γ). At 727°C (eutectoid): γ(0.77%C)→α(0.022%C)+Fe3C(6.67%C) via pearlite formation. At room temperature: ~100% pearlite (α+Fe3C lamellae). Lever rule: Wα = (6.67-0.77)/(6.67-0.022) = 88.7%, WFe3C = 11.3%.
Step-by-Step Reasoning
- At 850°C, 0.77wt%C → single-phase γ (austenite) region.
- Cool to 727°C: eutectoid isotherm. γ(0.77%) decomposes via eutectoid reaction.
- Eutectoid: γ→α+Fe3C forms pearlite (alternating lamellae).
- Lever rule at room temperature: Wα = (6.67-0.77)/(6.67-0.022) ≈ 88.7%.
- WFe3C = (0.77-0.022)/(6.67-0.022) ≈ 11.3%.
5-Model Evaluation
GPT-5.1
2/5
Claude Opus 4.6
1/5
Gemini-3.1-Pro
1/5
Qwen3.6-Plus
0/5
DeepSeek-V4
0/5
Delivery & API
JSONL Bulk Download: Full fields + image URLs + 5-model evaluation + reasoning chains.
REST API: GET /DataAssetsAPI/stem-questions/engineering. For enterprise API keys, contact lk@langhuiai.com.
FAQ
How is the difficulty threshold enforced?
Every question must achieve ≤40% pass rate across 5 models × 5 passes (GPT-5.1 / Claude Opus 4.6 / Gemini-3.1-Pro / Qwen3.6-Plus / DeepSeek-V4). Human expert accuracy ≥95%, dual-review.
What sub-domains does the Engineering benchmark cover?
6 sub-domains: Computer Science (40%), Electronic Engineering (20%), Mechanical Engineering (15%), Materials Science (10%), Civil Engineering (8%), Chemical Engineering (7%).
What diagram types does the Engineering benchmark emphasize?
Circuit schematics, CAD engineering drawings, flowcharts, phase diagrams, crystal structures, code+output screenshots, and process flow diagrams (PFD/P&ID).
Does the CS portion include programming questions?
Yes — code debugging, output prediction, complexity analysis, and algorithm visualization. All code questions include screenshot-based code listings to test visual code understanding, not just text-based reasoning.
Is there overlap with public engineering benchmarks?
Zero overlap. <0.5% pHash+n-gram fingerprint overlap with MMMU-Engineering, EngineeringQA, and 6 other public benchmarks.