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Count Days Spent Together

Difficulty: Easy

Problem Description

Alice and Bob are traveling to Rome for separate business meetings. You are given 4 strings arriveAlice, leaveAlice, arriveBob, and leaveBob. Alice will be in the city from the dates arriveAlice to leaveAlice (inclusive), while Bob will be in the city from the dates arriveBob to leaveBob (inclusive). Each will be a 5-character string in the format "MM-DD". Return the total number of days that Alice and Bob are in Rome together.

Key Insights

  • Both Alice and Bob have defined arrival and leave dates.
  • The overlap in their stay can be determined by comparing their arrival and leave dates.
  • We can represent dates as integers for easier comparison.
  • The number of days in each month must be accounted for since the dates are in a non-leap year.

Space and Time Complexity

Time Complexity: O(1)
Space Complexity: O(1)

Solution

To solve the problem, we can follow these steps:

  1. Convert the arrival and leave dates of Alice and Bob from the "MM-DD" format into a single integer representing the day of the year. This allows for easier comparison.
  2. Determine the latest arrival date and the earliest leave date to find the overlap period.
  3. Calculate the number of overlapping days by subtracting the latest arrival date from the earliest leave date and adding one (to include both endpoints).
  4. Ensure that the computed overlap is not negative; if it is, return 0.

This approach uses basic arithmetic and comparisons to determine the overlapping days.

Code Solutions

def countDaysSpentTogether(arriveAlice: str, leaveAlice: str, arriveBob: str, leaveBob: str) -> int:
    # Function to convert date from "MM-DD" to day of the year
    def date_to_day(date: str) -> int:
        month, day = map(int, date.split('-'))
        days_in_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
        return sum(days_in_month[:month - 1]) + day

    # Convert dates to day of the year
    arriveAliceDay = date_to_day(arriveAlice)
    leaveAliceDay = date_to_day(leaveAlice)
    arriveBobDay = date_to_day(arriveBob)
    leaveBobDay = date_to_day(leaveBob)

    # Calculate the overlap
    start = max(arriveAliceDay, arriveBobDay)
    end = min(leaveAliceDay, leaveBobDay)

    return max(0, end - start + 1)  # Return the number of overlapping days
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