Add array-based intersection tree section to intersection_trees.ipynb

[Copilot]

This PR adds a comprehensive section showcasing the array-based intersection tree implementation to the intersection_trees.ipynb notebook, following the established pattern of existing implementation sections.

Changes Made

New Array-based Implementation Section

Added a complete "Array-based intersection trees" section that includes:

• Code Display: Uses %pycat to show the array_intersection_tree.py implementation
• Demonstration: Creates and visualizes sample databases with tree structure output
• Search Functionality: Shows how to perform intersection queries with result examples
• Performance Benchmarking: Comprehensive timing analysis using timeit across multiple database sizes
• Comparative Visualization: Enhanced plotting that compares all four implementations:
  • Naive Pythonic approach
  • Naive non-Pythonic approach
  • Node-based intersection tree
  • Array-based intersection tree (new)
• Performance Analysis: Calculates and displays performance ratios between implementations
• Technical Documentation: Explains algorithmic complexity and trade-offs of the array-based approach

Updated Testing Section

Enhanced the existing testing section to include validation of the array-based implementation:

# Now tests all implementations for consistency
assert set(db_results) == set(naive_db_result) == set(array_db_results)

Implementation Details

The array-based implementation offers an alternative to traditional node-based trees by storing tree data in arrays rather than individual objects. This approach can provide:

• Better cache locality for large datasets
• Reduced per-node memory overhead
• Dynamic array resizing instead of individual node allocation

The new section maintains the same educational structure as existing sections, making it easy for users to understand and compare the different approaches to interval intersection problems.

Validation

• ✅ All implementations produce identical results
• ✅ Performance benchmarks execute successfully
• ✅ Notebook structure validated (45 → 56 cells)
• ✅ JSON format verified and compatible
• ✅ Follows established section patterns

The array-based intersection tree implementation is now fully integrated into the educational notebook alongside the existing approaches.

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