feat(algorithms, intervals): interval list intersections

[BrianLusina]

Describe your change:

Interval list intersection algorithm problem of finding all the intersections of intervals from two interval lists.

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
• If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.

Summary by CodeRabbit

Release Notes

• New Features

  • Added interval intersection algorithm for computing intersections between two sorted interval lists.

• Documentation

  • Added comprehensive documentation for the interval intersection problem with examples and complexity analysis.

• Tests

  • Added parameterized test suite covering interval intersection scenarios, including edge cases.

• Style

  • Updated string quote formatting in trie implementation.

_{✏️ Tip: You can customize this high-level summary in your review settings.}

[coderabbitai]

Walkthrough

This pull request introduces a new interval intersection algorithm with complete documentation, implementation, and test coverage. Changes include a new README, a two-pointer-based implementation function, parameterized unit tests, and a directory entry. Additionally, a minor style change updates quote formatting in an unrelated file.

Changes

Cohort / File(s)	Summary
Interval Intersection Feature DIRECTORY.md, algorithms/intervals/interval_intersection/README.md, algorithms/intervals/interval_intersection/__init__.py, algorithms/intervals/interval_intersection/test_intervals_intersection.py	Introduces new interval intersection algorithm with comprehensive documentation covering problem statement, constraints, and two approaches (naive and optimized); implements intervals_intersection() using two-pointer traversal to compute pairwise intersections between sorted interval lists; adds parameterized test suite with edge cases and multiple overlap scenarios.
Code Style Update datastructures/trees/trie/alphabet_trie/alphabet_trie.py	Converts string literals in range comparison from single quotes to double quotes; no behavioral change.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~15 minutes

• The interval intersection algorithm is a straightforward two-pointer approach with clear logic flow
• Test coverage appears comprehensive but follows standard parameterized patterns
• Verify the overlap detection logic and pointer advancement conditions in intervals_intersection()
• Confirm test cases cover edge cases (empty lists, non-overlapping intervals, partial overlaps)

Suggested labels

Documentation

Poem

🐰 Two pointers dance through intervals neat,
Finding where the overlapping beats meet,
Left and right, they gracefully glide,
Intersections bloom with algorithmic pride!
✨

Pre-merge checks and finishing touches

❌ Failed checks (1 warning, 1 inconclusive)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 25.00% which is insufficient. The required threshold is 80.00%.	You can run @coderabbitai generate docstrings to improve docstring coverage.
Description check	❓ Inconclusive	The description follows the template structure and addresses the main change, but marks three mutually exclusive options (Add, Fix, Documentation) as all checked, which is logically inconsistent with a single focused PR.	Clarify the primary purpose by checking only the most relevant option (likely 'Add an algorithm?') and uncheck contradictory selections.

✅ Passed checks (1 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title clearly and specifically describes the main change: adding an interval list intersections algorithm to the intervals module.

✨ Finishing touches

• 📝 Generate docstrings

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch feat/interval-list-intersections

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[coderabbitai]

Actionable comments posted: 0

🧹 Nitpick comments (1)

algorithms/intervals/interval_intersection/__init__.py (1)

22-23: Consider clarifying the early return condition.

The condition if not interval_list_a and not interval_list_b: only returns early when both lists are empty. This either:

1. Is redundant since the while loop naturally handles empty lists, or
2. Should use or instead to short-circuit when either list is empty.

For better clarity, consider:

-    if not interval_list_a and not interval_list_b:
+    if not interval_list_a or not interval_list_b:
         return []

This makes the intent clearer and avoids unnecessary length calculations when either list is empty.

📜 Review details

Configuration used: defaults

Review profile: CHILL

Plan: Pro

📥 Commits

Reviewing files that changed from the base of the PR and between ce15ab0 and 0f39f65.

⛔ Files ignored due to path filters (13)

• algorithms/intervals/interval_intersection/images/examples/interval_intersection_example_1.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/examples/interval_intersection_example_2.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/examples/interval_intersection_example_3.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/examples/interval_intersection_example_4.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/examples/interval_intersection_example_5.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/solutions/interval_intersection_solution_1.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/solutions/interval_intersection_solution_2.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/solutions/interval_intersection_solution_3.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/solutions/interval_intersection_solution_4.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/solutions/interval_intersection_solution_5.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/solutions/interval_intersection_solution_6.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/solutions/interval_intersection_solution_7.png is excluded by !**/*.png
• algorithms/intervals/interval_intersection/images/solutions/interval_intersection_solution_8.png is excluded by !**/*.png

📒 Files selected for processing (5)

• DIRECTORY.md (1 hunks)
• algorithms/intervals/interval_intersection/README.md (1 hunks)
• algorithms/intervals/interval_intersection/__init__.py (1 hunks)
• algorithms/intervals/interval_intersection/test_intervals_intersection.py (1 hunks)
• datastructures/trees/trie/alphabet_trie/alphabet_trie.py (1 hunks)

🧰 Additional context used

🧬 Code graph analysis (1)

algorithms/intervals/interval_intersection/test_intervals_intersection.py (1)

algorithms/intervals/interval_intersection/__init__.py (1)

• intervals_intersection (4-60)

🪛 LanguageTool

algorithms/intervals/interval_intersection/README.md

[grammar] ~100-~100: Use a hyphen to join words.
Context: ...ach that we have used to solve the above mentioned problem: - Set two pointers, ...

(QB_NEW_EN_HYPHEN)

🪛 markdownlint-cli2 (0.18.1)

DIRECTORY.md

98-98: Unordered list indentation
Expected: 2; Actual: 4

(MD007, ul-indent)

---

99-99: Unordered list indentation
Expected: 4; Actual: 6

(MD007, ul-indent)

🔇 Additional comments (7)

datastructures/trees/trie/alphabet_trie/alphabet_trie.py (1)

9-9: Cosmetic quote style change—no functional impact.

The switch from single to double quotes in the range comparison is purely stylistic. The validation logic and behavior remain unchanged.

DIRECTORY.md (1)

98-99: LGTM! Directory entry added correctly.

The new Interval Intersection subsection is properly placed within the Intervals grouping and follows the repository's organizational pattern.

algorithms/intervals/interval_intersection/README.md (1)

1-118: Excellent documentation!

The README provides comprehensive coverage of the interval intersection problem, including clear problem statement, constraints, multiple examples, and detailed solution approaches with complexity analysis. The explanation of the two-pointer optimized approach is particularly well-structured.

algorithms/intervals/interval_intersection/__init__.py (2)

4-21: Well-documented function with accurate complexity analysis.

The function signature includes proper type hints, and the docstring clearly explains the algorithm's time and space complexity, including the distinction between auxiliary space and the result list size.

---

26-58: Two-pointer implementation is correct and efficient.

The algorithm correctly:

• Computes intersection boundaries using max and min
• Checks for valid overlaps with closed_interval_start <= closed_interval_end
• Advances the pointer for the interval that ends earlier

The implementation matches the documented O(n+m) time complexity.

algorithms/intervals/interval_intersection/test_intervals_intersection.py (2)

6-45: Comprehensive test coverage with good edge cases.

The test cases cover:

• Multiple overlapping intervals (various patterns)
• Boundary touches and exact point intersections
• Empty results when intervals don't overlap
• Single interval scenarios
• One list completely containing another

Particularly good coverage of edge cases like [[13, 13], [25, 25]] which test boundary touches.

---

48-61: Clean test structure using parameterized testing.

Good use of the @parameterized.expand decorator to avoid test duplication. The test method includes proper type hints for clarity.