🧩 Color Puzzle — Algorithmic Logic Engine

A mobile cognitive puzzle game driven by Recursive Spatial Subdivision. The system scales difficulty dynamically by mathematically refining the grid resolution (O(N²) complexity) while maintaining stable performance on legacy hardware.

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🧠 Core Engineering Concepts

Recursive Spatial Subdivision

The game does not simply spawn random squares. It uses a recursive algorithm that mathematically bisects the grid coordinates:

• Level 1: 3x3 Grid (Low Complexity)

• Level 10: 6x6 Grid (Medium Complexity)

• Level 20: 12x12 Grid (High Complexity)

Polymorphic Logic Engine

The validation system switches runtime rules dynamically based on the current mode:

• Frequency Analysis: "Count X items" ($O(N)$)

• Inverse Key-Lookup: "Find the color with count Y" (Reverse Dictionary Search)

• Boolean Logic: "Is Blue Count == Red Count?" (True/False Evaluation)

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🎮 Logic & Algorithm Visualization

1. The Profiler: Memory Optimization

46.8% Reduction in GC Allocation Snapshot of the Unity Profiler validating my custom memory management strategy. By implementing component caching and optimizing string concatenation in the render loop, I reduced Garbage Collection (GC) spikes to near zero, ensuring a stable 16ms (60 FPS) frame time.

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2. Recursive Base State (3x3)

Frequency Analysis Algorithm The initialization of the recursive algorithm. The system generates a base 3x3 matrix and executes a frequency count to validate user input. This sets the baseline for the scaling logic.

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3. Spatial Subdivision (6x6)

Inverse Key-Value Lookup The algorithm has recursively subdivided the grid into a 6x6 matrix. The logic engine switches to Inverse Lookup mode: instead of counting colors, it performs a reverse dictionary search (finding the Key associated with Value 4).

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4. High-Density Recursion (12x12)

Boolean Logic Evaluation The peak of the recursive algorithm. The grid has subdivided into a high-density matrix. The logic engine shifts to Boolean Evaluation, comparing two distinct frequency distributions in real-time to return a True/False validity state.

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5. State Management & Complexity

Constraints & Complexity The application manages strict state transitions (Play → Fail) based on time complexity constraints. As the grid subdivides, the search space grows quadratically (O(N^2)), requiring optimized input validation loops to prevent frame drops during rapid state changes.

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6. Full SDLC & Production Deployment

Evidence of the complete Software Development Life Cycle (SDLC). I independently managed the build pipeline, compliance, and App Store Optimization (ASO) for both iOS and Android, successfully shipping the application to a global audience with 2,172+ organic users.

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📊 Technical Stats

• Memory Optimization: Reduced GC Allocation by 46.8%.

• User Base: 2,172+ Organic Installs.

• Frame Rate: Stable 60 FPS on low-end Android devices.