Android Repo for the FibMatrix App
FibMatrix is a contemporary Android application, developed exclusively with Jetpack Compose, which functions as an interactive, visual compendium for mastering the O(log n) matrix exponentiation algorithm used for calculating Fibonacci numbers.
This application is engineered not merely as a utility, but as an educational resource to facilitate a deeper comprehension among students and engineers regarding the rationale and implementation of this powerful and prevalent technical interview algorithm.
💡 It is highly recommended to insert an animated GIF (10–15 seconds) here, demonstrating the application's core functionalities, such as theoretical exploration, sandbox computation, and dynamic chart updates.
A comprehensive, step-by-step guide articulating the mathematical principles behind the pivotal matrix:
| 1 1 | | 1 0 |
The application's central utility. Users may input any integer n to instantly compute:
- The Fibonacci number
F(n) - The final matrix
Mⁿ - A comparative visualization of O(n) vs O(log n) computational complexity
A visual tracer for the power(M, n) function, designed to elucidate the exponentiation by squaring methodology.
An interactive bar chart, rendered via the Vico library, quantitatively illustrating the performance disparity between the two algorithmic approaches.
A syntax-highlighted presentation of the complete Java algorithm, formatted for readability.
Implemented with Material 3 components, featuring a polished, responsive interface that adapts to light and dark themes.
This project demonstrates modern Android development best practices, featuring a clean and scalable software architecture.
ViewModel (FibonacciViewModel.kt)
Encapsulates all business logic, computation, and state management. Validates user input (e.g., ensuring numerical range safety) for application stability.
View (screens/*.kt)
Stateless @Composable functions organized as screens. They observe state from the ViewModel and communicate user actions via a UiEvent system (e.g., SandboxCalculate).
Model (UiState.kt)
A single immutable UiState data class represents the complete application state, managed via a StateFlow.
- Fully Declarative: The UI is built entirely with Jetpack Compose, including navigation and matrix visualizations.
- Material 3: Adheres to the latest Material Design 3 guidelines for components, color systems, and typography (
theme/Theme.kt). - Custom Layouts:
MatrixDisplayandVectorDisplaycomposables manage complex, dynamic data layouts with proper alignment and scrollable overflow using a customEquationBox. - State-Driven Recomposition: Efficient recomposition occurs only when
UiStatechanges.
- Unidirectional Data Flow (UDF):
State flows downward (ViewModel → UI) and events propagate upward (UI → ViewModel). - StateFlow:
A privateMutableStateFlowmanages the internal state, exposed as immutableStateFlow<UiState>for UI consumption. - UiEvent Sealed Class:
Defines all user interactions as discrete events, ensuring traceability and a clean ViewModel API.
The app uses androidx.navigation:navigation-compose within a Single-Activity architecture.
AppNavigation.kt:
A centralized NavHost component manages all screen transitions and navigational logic.
- Vico (Charting): Demonstrates integration and customization of the Vico charting library.
Includes a customChartDisplaycomposable with:- Custom axis labels (O(n) vs O(log n))
- Integer-only Y-axis formatting
- Persistent data labels for each bar
The application's core logic is based on the following matrix identity:
| F(n+1) | = | 1 1 | × | F(n) | | F(n) | | 1 0 | | F(n−1) |
This relationship can be extended through induction to yield:
| F(n) | = | 1 1 |^(n−1) × | F(1) | | F(n−1) | | 1 0 | | F(0) |
Consequently, F(n) can be determined by computing the (n−1)th power of the matrix:
M = | 1 1 |
| 1 0 |
A naive approach would require n−1 multiplications (O(n) time).
This app implements exponentiation by squaring, reducing it to O(log n) time.
The algorithm uses BigInteger to handle large Fibonacci values.
- Jetpack Compose (BOM, UI, Material 3, Foundation)
- Compose Navigation
- Lifecycle ViewModel (Compose)
- Vico (Charting)
- Kotlin Coroutines (for
StateFlow)
- Clone the repository.
- Open the project directory in Android Studio (latest stable version).
- Allow Gradle synchronization to complete.
- Build and deploy to an emulator or physical device.
MIT License
Copyright (c) 2025 [Your Name]
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.