Solution Explanation for LeetCode 2409: Count Days Spent Together

This problem involves calculating the number of days two individuals, Alice and Bob, are both present in Rome given their arrival and departure dates. The solution focuses on efficient date manipulation to avoid complex calendar calculations.

Approach

The core idea is to:

1. Determine the overlapping period: Find the latest arrival date (max) and the earliest departure date (min) between Alice and Bob. This defines the period when they are both in Rome.

2. Convert dates to day numbers: Represent each date as a day number of the year. This simplifies comparison and avoids dealing with varying month lengths. We accomplish this by summing the days of preceding months plus the day of the current month.

3. Calculate the overlap: Subtract the day number of the latest arrival from the day number of the earliest departure and add 1 to include both endpoints. If the result is negative, it means there's no overlap, and we return 0.

Time and Space Complexity

• Time Complexity: O(1). The algorithm performs a fixed number of operations regardless of the input dates. The conversion to day numbers involves iterating through at most 12 months (a constant).

• Space Complexity: O(1). The algorithm uses a constant amount of extra space to store the days array (month lengths) and intermediate variables.

Code Implementation (Python)

class Solution:
    def countDaysTogether(
        self, arriveAlice: str, leaveAlice: str, arriveBob: str, leaveBob: str
    ) -> int:
        days = [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]  # Days in each month
 
        def date_to_day(date_str: str) -> int:
            month, day = map(int, date_str.split('-'))
            day_num = sum(days[:month]) + day
            return day_num
 
        # Find the overlapping period
        start_day = max(date_to_day(arriveAlice), date_to_day(arriveBob))
        end_day = min(date_to_day(leaveAlice), date_to_day(leaveBob))
 
        # Calculate the number of overlapping days
        overlapping_days = max(0, end_day - start_day + 1)  # Handle cases with no overlap
        return overlapping_days
 

Code Implementation (Java)

class Solution {
    private int[] days = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; // Days in each month
 
    private int dateToDay(String dateStr) {
        String[] parts = dateStr.split("-");
        int month = Integer.parseInt(parts[0]);
        int day = Integer.parseInt(parts[1]);
        int dayNum = 0;
        for (int i = 1; i < month; i++) {
            dayNum += days[i];
        }
        dayNum += day;
        return dayNum;
    }
 
    public int countDaysTogether(String arriveAlice, String leaveAlice, String arriveBob, String leaveBob) {
        int startDay = Math.max(dateToDay(arriveAlice), dateToDay(arriveBob));
        int endDay = Math.min(dateToDay(leaveAlice), dateToDay(leaveBob));
        return Math.max(0, endDay - startDay + 1);
    }
}

The other languages (C++, Go) follow a similar structure, adapting the syntax and data structures accordingly. The key is the efficient conversion from date strings to day numbers and the logic for finding and calculating the overlap.