Count Days Spent Together - Video Solutions

Problem Overview: You receive four dates: Alice's arrival and leave dates, and Bob's arrival and leave dates. Each date is formatted as MM-DD. The goal is to count how many days both people are present at the same time during the same year.

The core observation: the problem reduces to finding the overlap between two date ranges. Once each date is converted to a comparable numeric value, the overlapping segment length becomes easy to compute using max(start) and min(end).

Approach 1: Convert Date to Day of Year (O(1) time, O(1) space)

Convert every MM-DD string into a single integer representing its position in the year (day-of-year). Use a prefix array containing the number of days before each month. Parse the month and day from the string, then compute dayOfYear = prefix[month-1] + day. After converting Alice and Bob's arrival and leave dates, compute the overlap using start = max(aliceArrive, bobArrive) and end = min(aliceLeave, bobLeave). If end < start, there is no overlap; otherwise the answer is end - start + 1. This approach is clean and constant time because the year length is fixed. It primarily uses simple arithmetic from math and straightforward string parsing.

Approach 2: Direct Date Comparison with Month Traversal (O(1) time, O(1) space)

Instead of converting the entire date to a numeric day-of-year value, compare dates using their month and day components. Parse each date into (month, day). To compute the overlap, determine the later arrival date and the earlier leaving date using month-first comparison, then day comparison if months match. Once the range is known, count the days between them by iterating through the months and summing their lengths. A static array storing month lengths simplifies this calculation. This approach works without explicitly flattening the calendar into a single number and demonstrates careful handling of date boundaries using basic math logic and string parsing.

Recommended for interviews: The day-of-year conversion approach is what most interviewers expect. It shows you can normalize a problem into a simpler numeric domain and compute range intersections cleanly. The direct comparison method still works and demonstrates understanding of calendar structure, but the conversion approach is shorter, less error-prone, and easier to reason about under time pressure.