Appendix C

if (year % 400 == 0) then
    return LEAP_YEAR
else if (year % 100 == 0) then
    return NOT_LEAP_YEAR
else if (year % 4 == 0) then
    return LEAP_YEAR
else
    return NOT_LEAP_YEAR

Implementation Examples

C Language

int is_leap_year(int year) {
    return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);
}

// Or a clearer version
int is_leap_year_verbose(int year) {
    if (year % 400 == 0) {
        return 1;  // Divisible by 400: leap year
    }
    if (year % 100 == 0) {
        return 0;  // Divisible by 100 but not 400: common year
    }
    if (year % 4 == 0) {
        return 1;  // Divisible by 4 but not 100: leap year
    }
    return 0;  // Otherwise: common year
}

Python

def is_leap_year(year):
    """Determine if year is a leap year"""
    return (year % 400 == 0) or (year % 4 == 0 and year % 100 != 0)

# Or use Python calendar module
import calendar
print(calendar.isleap(2000))  # True

JavaScript

function isLeapYear(year) {
    return (year % 400 === 0) || (year % 4 === 0 && year % 100 !== 0);
}

Java

public static boolean isLeapYear(int year) {
    return (year % 400 == 0) || (year % 4 == 0 && year % 100 != 0);
}

// Or use Java 8+ GregorianCalendar
import java.util.GregorianCalendar;
boolean isLeap = GregorianCalendar.isLeapYear(2000);

Historical Leap Year Examples

Recent Leap Years (21st Century)

2000: Leap year ✅ (divisible by 400)
2001: Common year ❌
2002: Common year ❌
2003: Common year ❌
2004: Leap year ✅ (divisible by 4, not by 100)
2008: Leap year ✅
2012: Leap year ✅
2016: Leap year ✅
2020: Leap year ✅
2024: Leap year ✅
2028: Leap year ✅

Century Years (Special Cases)

1600: Leap year ✅ (divisible by 400)
1700: Common year ❌ (divisible by 100 but not 400)
1800: Common year ❌ (divisible by 100 but not 400)
1900: Common year ❌ (divisible by 100 but not 400)
2000: Leap year ✅ (divisible by 400)
2100: Common year ❌ (divisible by 100 but not 400)
2200: Common year ❌
2300: Common year ❌
2400: Leap year ✅ (divisible by 400)

Days in Each Month

Understanding leap years is crucial for determining days in each month:

def days_in_month(year, month):
    """Return number of days in specified year and month"""
    days_per_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
    
    if month == 2 and is_leap_year(year):
        return 29
    return days_per_month[month - 1]

# Examples
print(days_in_month(2000, 2))  # 29 (leap year February)
print(days_in_month(1900, 2))  # 28 (common year February)
print(days_in_month(2024, 4))  # 30 (April always 30 days)

Date Validation

def is_valid_date(year, month, day):
    """Validate if date is valid"""
    if month < 1 or month > 12:
        return False
    
    if day < 1:
        return False
    
    max_day = days_in_month(year, month)
    if day > max_day:
        return False
    
    return True

# Tests
print(is_valid_date(2000, 2, 29))  # True (leap year)
print(is_valid_date(1900, 2, 29))  # False (common year)
print(is_valid_date(2002, 4, 31))  # False (April has only 30 days)

History of Leap Years

Julian vs Gregorian Calendar

Julian Calendar:

• Introduced by Julius Caesar in 46 BC
• Simple rule: leap year every 4 years
• Average year length: 365.25 days
• Problem: about 11 minutes longer than actual solar year

Gregorian Calendar:

• Introduced by Pope Gregory XIII in 1582
• Modified rule: century years must be divisible by 400
• Average year length: 365.2425 days
• Closer to actual solar year (365.2422 days)

Adoption of Gregorian Calendar

Different countries adopted the Gregorian calendar at different times:

1582: Italy, Spain, Portugal
1752: Great Britain and colonies (including US)
1917: Russia
1923: Greece

 = 100 - 4 + 1 = 97)

def validate_rfc3339_date(year, month, day):
    if year < 0 or year > 9999:
        return False, "Year must be 0000-9999"
    
    if month < 1 or month > 12:
        return False, "Month must be 01-12"
    
    if not is_valid_date(year, month, day):
        max_day = days_in_month(year, month)
        return False, f"Day must be 01-{max_day:02d} for {year}-{month:02d}"
    
    return True, "Valid date"

print(validate_rfc3339_date(2000, 2, 29))  # (True, 'Valid date')
print(validate_rfc3339_date(1900, 2, 29))  # (False, '...')

---