The project follows a modular, decoupled architecture in .NET 10 designed for testability, performance analysis, and clean code practices:

• Abstraction (ISortAlgorithm<T>): All sorting implementations implement a generic interface with the constraint where T : IComparable<T>, ensuring strict typing and support for any comparable data type (integers, strings, custom objects).
• In-Place vs. Auxiliary Memory: Algorithms are implemented adhering to their theoretical spatial boundaries (e.g., $O(1)$ space for QuickSort/HeapSort, $O(N)$ auxiliary allocation for MergeSort).
• Unit Testing (xUnit): Full coverage including edge cases (already sorted arrays, empty arrays, duplicate values, negative numbers, and string sorting).
• Automated Benchmarking: Integrated with BenchmarkDotNet for precision CPU cycle profiling and Garbage Collector (MemoryDiagnoser) memory tracking.

The benchmarks were executed under the following environment:

• Tool: BenchmarkDotNet v0.15.8
• Runtime: .NET 10.0 (X64 RyuJIT x86-64-v3)
• Dataset: 1,000 randomly generated integers (N = 1000)

Note: The baseline 3.93 KB allocation across all methods corresponds to the initial dataset clone required for isolated execution per iteration.

1. QuickSort (Top Performance - 16.43 µs): Outperformed all algorithms (~102x faster than BubbleSort). Its contiguous array partitioning maximizes CPU L1/L2 cache locality, minimizing cache misses.
2. HeapSort (Guaranteed $O(1)$ Auxiliary Space - 26.82 µs): Achieved steady $O(N \log N)$ execution without incurring Garbage Collector overhead (0 GC collections), making it optimal for memory-constrained or real-time environments.
3. MergeSort (Memory Trade-off - 36.85 µs & 94.07 KB Allocated): Demonstrated guaranteed $O(N \log N)$ stability, but required auxiliary array allocations during the merge phases, triggering Garbage Collector passes (Gen0/Gen1).
4. BubbleSort (Baseline Comparison - 1.67 ms): Confirmed theoretical $O(N^2)$ quadratic degradation, serving as a baseline for algorithmic optimization.## 📐 Architecture & Design Principles

The project follows a modular, decoupled architecture in .NET 10 designed for testability, performance analysis, and clean code practices:

• Abstraction (ISortAlgorithm<T>): All sorting implementations implement a generic interface with the constraint where T : IComparable<T>, ensuring strict typing and support for any comparable data type (integers, strings, custom objects).
• In-Place vs. Auxiliary Memory: Algorithms are implemented adhering to their theoretical spatial boundaries (e.g., $O(1)$ space for QuickSort/HeapSort, $O(N)$ auxiliary allocation for MergeSort).
• Unit Testing (xUnit): Full coverage including edge cases (already sorted arrays, empty arrays, duplicate values, negative numbers, and string sorting).
• Automated Benchmarking: Integrated with BenchmarkDotNet for precision CPU cycle profiling and Garbage Collector (MemoryDiagnoser) memory tracking.

The benchmarks were executed under the following environment:

• Tool: BenchmarkDotNet v0.15.8
• Runtime: .NET 10.0 (X64 RyuJIT x86-64-v3)
• Dataset: 1,000 randomly generated integers (N = 1000)

Note: The baseline 3.93 KB allocation across all methods corresponds to the initial dataset clone required for isolated execution per iteration.

1. QuickSort (Top Performance - 16.43 µs): Outperformed all algorithms (~102x faster than BubbleSort). Its contiguous array partitioning maximizes CPU L1/L2 cache locality, minimizing cache misses.
2. HeapSort (Guaranteed $O(1)$ Auxiliary Space - 26.82 µs): Achieved steady $O(N \log N)$ execution without incurring Garbage Collector overhead (0 GC collections), making it optimal for memory-constrained or real-time environments.
3. MergeSort (Memory Trade-off - 36.85 µs & 94.07 KB Allocated): Demonstrated guaranteed $O(N \log N)$ stability, but required auxiliary array allocations during the merge phases, triggering Garbage Collector passes (Gen0/Gen1).
4. BubbleSort (Baseline Comparison - 1.67 ms): Confirmed theoretical $O(N^2)$ quadratic degradation, serving as a baseline for algorithmic optimization.