Count Months Whose First Day Is Sunday

Question

The candidate is asked to write a function that counts how many months between January 2000 and December 2024 have their first day on a Sunday, without using any built-in date libraries.

Codemia · Accepted Answer

To solve this problem, we need to determine the day of the week for the first day of each month from January 2000 to December 2024. We know that January 1, 2000, is a Saturday. We will calculate the day of the week for the first of each month by keeping track of the number of days passed and using the modulo operation to find the corresponding day of the week.

1. Initialize a counter for the number of Sundays. 
2. Set the starting day (0 for Saturday). 
3. Loop through each year from 2000 to 2024. 
4. For each month, check if the first day is a Sunday. 
5. Update the starting day based on the number of days in the current month (considering leap years). 
6. Return the counter.

Here is the Python code implementation:
```python
def count_sundays():
    # Days in each month
    month_days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
    # Initialize variables
    sunday_count = 0
    day_of_week = 0  # 0 = Saturday, 1 = Sunday, ..., 6 = Friday

for year in range(2000, 2025):
        for month in range(12):
            if day_of_week == 1:  # Check if it's Sunday
                sunday_count += 1
            # Update day_of_week for the next month
            if month == 1 and ((year % 4 == 0 and year % 100 != 0) or (year % 400 == 0)):
                day_of_week = (day_of_week + 29) % 7  # Leap year
            else:
                day_of_week = (day_of_week + month_days[month]) % 7
    return sunday_count
```

The time complexity of this algorithm is O(n), where n is the number of months we are checking (in this case, 12 months per year for 25 years, totaling 300 iterations). The space complexity is O(1) since we are using a fixed amount of space for variables regardless of the input size.

We need to ensure that leap years are correctly handled. A leap year occurs if the year is divisible by 4, but not divisible by 100, unless it is also divisible by 400. This means that the year 2000 is a leap year, but 2100 will not be.

Count Months Whose First Day Is Sunday

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