Refactor intersection tree to eliminate redundant validity checks in recursive methods

[Copilot]

Problem

The current intersection tree implementation performs redundant validity checks when insert and search methods are called recursively. Since these methods validate the same interval multiple times during tree traversal, this creates unnecessary computational overhead.

Solution

This PR refactors the Node class to separate public API validation from internal recursive operations by introducing private methods _insert and _search:

Changes Made

1. Enhanced search method: Added missing interval validation to match the insert method's validation behavior
2. Created _insert private method: Handles recursive insertion without re-validating intervals
3. Created _search private method: Handles recursive searching without re-validating intervals
4. Refactored public methods: Now validate intervals once and delegate to private methods

Code Example

Before - redundant validation on every recursive call:

def insert(self, interval: Interval) -> None:
    if interval[0] >= interval[1]:  # Validated on every recursive call
        raise ValueError(f"Invalid interval...")
    # ... insertion logic with recursive calls to insert()

After - validation only at public API level:

def insert(self, interval: Interval) -> None:
    if interval[0] >= interval[1]:  # Validated once
        raise ValueError(f"Invalid interval...")
    self._insert(interval)  # Delegate to private method

def _insert(self, interval: Interval) -> None:
    # ... insertion logic with recursive calls to _insert()

Benefits

• Performance improvement: Eliminates redundant validation during recursive tree operations
• Maintained functionality: All existing features and error handling preserved
• Backward compatibility: Public API remains unchanged
• Clean separation: Clear distinction between public validation and internal operations

Testing

• ✅ All existing functionality verified
• ✅ Error handling and validation confirmed
• ✅ Integration with utility functions (create_db, execute_queries, etc.) tested
• ✅ Performance improvements validated with comprehensive test suite

The refactoring makes minimal changes while achieving the goal of eliminating redundant validity checks, following the principle of surgical modifications to improve efficiency.

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