feat(algorithms, intervals): count days without meetings

[BrianLusina]

Describe your change:

Count days without meetings interval algorithm problem

• 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

• New Features

  • Added an algorithm to compute available days excluding meeting intervals.

• Documentation

  • Added detailed documentation for the "count days without meetings" problem.
  • Updated directory index to include the new entry.

• Tests

  • Added a comprehensive parameterized test suite covering varied scenarios.

• Refactor

  • Clarified interval merging logic for improved readability.

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

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📥 Commits

Reviewing files that changed from the base of the PR and between 7f523ef and 33819d4.

📒 Files selected for processing (2)

• algorithms/intervals/count_days/README.md
• algorithms/intervals/count_days/__init__.py

📝 Walkthrough

Walkthrough

Adds a new "Count Days Without Meetings" algorithm (two implementations), documentation, and tests under algorithms/intervals/count_days; also minor refactor in merge intervals to use explicit interval variables for clarity.

Changes

Cohort / File(s)	Summary
Index / Directory DIRECTORY.md	Added "Count Days" entry under Intervals linking to the new test/readme.
New algorithm docs algorithms/intervals/count_days/README.md	Added README describing problem, examples, merge-based solution, step-by-step algorithm, and complexity notes.
Algorithm implementations algorithms/intervals/count_days/__init__.py	Added count_days(days, meetings) and count_days_2(days, meetings) implementations (sorting + gap accumulation and sorting + merging respectively).
Tests algorithms/intervals/count_days/test_count_days_without_meetings.py	New parameterized tests covering multiple cases; tests both implementations.
Refactor (clarity) algorithms/intervals/merge_intervals/__init__.py	Reworked merge logic to use intermediate variables for current interval start/end and last merged end time; behavior unchanged.

Estimated code review effort

🎯 3 (Moderate) | ⏱️ ~25 minutes

Possibly related PRs

• feat(algorithms, intervals): count days without meetings #128 — Adds the same count_days/count_days_2 functions, README, tests, and DIRECTORY entry for "Count Days Without Meetings" (strong overlap).

Poem

🐰 I hopped through ranges, sorted every line,
Merged overlapping hops to mark busy time.
I counted the gaps where no meeting lay,
Free days for carrots and sunshine play! 🥕✨

Pre-merge checks and finishing touches

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 40.00% which is insufficient. The required threshold is 80.00%.	You can run @coderabbitai generate docstrings to improve docstring coverage.

✅ Passed checks (2 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title 'feat(algorithms, intervals): count days without meetings' clearly and concisely describes the main change: adding an algorithm for counting days without meetings in the intervals category.
Description check	✅ Passed	The description is mostly complete with all required checklist items addressed. However, the description lacks detailed explanation of the actual changes made in the PR (beyond the generic title).

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[github-actions]

	Warnings
⚠️	❗ Big PR

: Pull Request size seems relatively large. If Pull Request contains multiple changes, split each into separate PR will helps faster, easier review.

Generated by 🚫 dangerJS against 33819d4

[coderabbitai]

Actionable comments posted: 5

🧹 Nitpick comments (1)

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

24-37: Consider minor optimization to reduce redundant checks.

The refactoring improves code clarity by introducing intermediate variables. However, there's a minor optimization opportunity:

1. Line 27 computes last_merged_interval_end_time on every iteration, even when it was just used in line 36.
2. The not merged check on line 30 is redundant since last_merged_interval_end_time is -inf when merged is empty, which naturally satisfies the condition.

🔎 Optional refactor for efficiency

     for interval in closed_intervals:
         current_interval_start_time = interval[0]
         current_interval_end_time = interval[1]
-        last_merged_interval_end_time = merged[-1][1] if merged else float("-inf")
 
         # if the merged array is empty or the last interval in the merged array does not overlap with the current interval
-        if not merged or last_merged_interval_end_time < current_interval_start_time:
+        if not merged or merged[-1][1] < current_interval_start_time:
             # add it to the merged list
             merged.append(interval)
         else:
             # else we merge the intervals, by updating the max end time of the last interval in the merged list
             merged[-1][1] = max(
-                last_merged_interval_end_time, current_interval_end_time
+                merged[-1][1], current_interval_end_time
             )

This eliminates the intermediate variable that's only used once per branch and removes the redundant not merged check.

📜 Review details

Configuration used: defaults

Review profile: CHILL

Plan: Pro

📥 Commits

Reviewing files that changed from the base of the PR and between 3f1b0db and 7f523ef.

⛔ Files ignored due to path filters (15)

• algorithms/intervals/count_days/images/examples/count_days_without_meetings_example_1.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/examples/count_days_without_meetings_example_2.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/examples/count_days_without_meetings_example_3.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_1.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_10.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_11.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_12.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_2.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_3.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_4.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_5.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_6.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_7.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_8.png is excluded by !**/*.png
• algorithms/intervals/count_days/images/solutions/count_days_without_meetings_solution_9.png is excluded by !**/*.png

📒 Files selected for processing (5)

• DIRECTORY.md
• algorithms/intervals/count_days/README.md
• algorithms/intervals/count_days/__init__.py
• algorithms/intervals/count_days/test_count_days_without_meetings.py
• algorithms/intervals/merge_intervals/__init__.py

🧰 Additional context used

🧬 Code graph analysis (1)

algorithms/intervals/count_days/test_count_days_without_meetings.py (1)

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

• count_days (4-54)
• count_days_2 (57-84)

🪛 LanguageTool

algorithms/intervals/count_days/README.md

[style] ~45-~45: Using many exclamation marks might seem excessive (in this case: 11 exclamation marks for a text that’s 3203 characters long)
Context: ...t_days_without_meetings_solution_1.png) ![Solution 11](./images/solutions/count_d...

(EN_EXCESSIVE_EXCLAMATION)

🪛 markdownlint-cli2 (0.18.1)

DIRECTORY.md

104-104: Unordered list indentation
Expected: 2; Actual: 4

(MD007, ul-indent)

---

105-105: Unordered list indentation
Expected: 4; Actual: 6

(MD007, ul-indent)

🔇 Additional comments (2)

algorithms/intervals/count_days/test_count_days_without_meetings.py (1)

1-525: LGTM! Comprehensive test coverage.

The test file is well-structured with:

• Excellent edge case coverage including boundary conditions (0 free days, maximum constraints)
• Both count_days and count_days_2 tested with identical test cases for consistency
• Proper use of parameterized testing to reduce duplication
• Clean organization with 9 test cases ranging from simple to complex scenarios

DIRECTORY.md (1)

104-105: LGTM! Documentation properly updated.

The new "Count Days" entry is correctly added to the Intervals section with proper indentation and linking. The indentation is consistent with the rest of the file structure.

Note: The static analysis hints about indentation are false positives - the indentation follows the established pattern used throughout the file.