File: count-days-spent-together/solution.py

Date: 2026-06-06

Time: 15:56

Purpose

This file solves LeetCode 2409: Count Days Spent Together. It determines how many days two people (Alice and Bob) are simultaneously in Rome, given their arrival and departure dates as "MM-DD" strings within a single non-leap year. The file is self-contained: solution function, helper, and unit tests all in one module.

Key Components

DAYSINMONTH (constant)

A 12-element list of days per month for a non-leap year. Used as a lookup table to convert month-day strings into absolute day-of-year values. The problem guarantees a non-leap year, so February is always 28.

dateto_day(date: str) -> int

Converts a "MM-DD" string to a 1-indexed day-of-year. It slices the string directly (date[:2], date[3:5]) rather than splitting on "-", then sums the days of all preceding months via DAYSINMONTH[:month - 1] and adds the day. For example, "02-05" becomes 31 + 5 = 36.

days_together(...) -> int

The main solver. Converts all four date strings to day-of-year integers, then computes the overlap of two closed intervals [a0, a1] and [b0, b1] using the standard formula:

max(0, min(a1, b1) - max(a0, b0) + 1)

The + 1 accounts for inclusive endpoints (both arrival and departure days count).

TestDaysTogether (unittest.TestCase)

Eight test cases covering: partial overlap, no overlap, identical ranges, single-day overlap, containment, same single day, adjacent-but-disjoint months, and cross-month overlap.

Patterns

• Day-of-year normalization: Reduces a 2D problem (month, day) to a 1D problem (day-of-year), making interval arithmetic straightforward.
• Interval overlap formula: The max(0, min(end1, end2) - max(start1, start2) + 1) idiom is the canonical way to compute overlap length of two closed intervals. The max(0, ...) handles the non-overlapping case, returning 0 instead of a negative number.
• Self-contained module: Solution, helper, and tests colocated in one file — consistent with the rest of this repo's convention.

Dependencies

Imports: Only unittest from the standard library. No external dependencies.

Imported by: The test_solution.py in the same directory imports from this file. The massive "Imported By" list in the prompt is an artifact of the repo-wide cross-reference — those are other problems' test files, not actual importers of this module.

Flow

1. Caller passes four "MM-DD" strings to days_together.

2. Each string is converted to an integer day-of-year via dateto_day.

3. The overlap of the two date ranges is computed as a single arithmetic expression.

4. Returns 0 if no overlap, otherwise the count of shared days (inclusive).

Invariants

• Non-leap year assumed: DAYSINMONTH has February as 28. The problem guarantees this; the code does not validate it.
• Input format: Expects exactly "MM-DD" with zero-padded two-digit month and day. No validation — malformed input would produce wrong results or raise ValueError from int().
• Arrival <= Departure: The problem guarantees arriveAlice <= leaveAlice and arriveBob <= leaveBob. The formula produces correct results under this assumption; swapped inputs would yield negative values clamped to 0.
• Same calendar year: All dates are within a single year. No year component exists.

Error Handling

None. The code trusts its inputs per the LeetCode contract. Invalid date strings would propagate a ValueError from int(). There are no try/except blocks or defensive checks.

Topics to Explore

• [file] count-days-spent-together/plan.md — The planning doc that preceded this solution, showing the approach selection rationale
• [file] count-days-spent-together/review.md — Post-implementation review with quality assessment and alternative approaches
• [function] number-of-days-between-two-dates/solution.py:dateto_day — A related date-conversion helper that likely handles leap years, contrasting with the simpler version here
• [general] interval-overlap-pattern — The max(0, min(e1,e2) - max(s1,s2) + 1) idiom appears across multiple solutions (e.g., determine-if-two-events-have-conflict); worth tracing as a cross-cutting pattern
• [file] day-of-the-year/solution.py — Another day-of-year conversion that may handle leap years, showing the fuller version of the same transformation

Beliefs

• days-together-non-leap-year — DAYSINMONTH sums to 365 and assumes February has 28 days; leap years are out of scope per the problem contract
• days-together-inclusive-endpoints — The + 1 in the overlap formula means both arrival and departure days are counted as days spent together
• date-to-day-string-slicing — dateto_day relies on fixed-position slicing ([:2], [3:5]), not delimiter splitting, so it requires zero-padded "MM-DD" format
• days-together-zero-on-no-overlap — When intervals don't overlap, max(0, ...) ensures the return value is 0 rather than a negative number