Leap year calculation

Solution 1:

The length of a year is (more or less) 365.242196 days. So we have to subtract, more or less, a quarter of a day to make it fit :

365.242196 - 0.25 = 364.992196 (by adding 1 day in 4 years) : but oops, now it's too small!! lets add a hundreth of a day (by not adding that day once in a hundred year :-))

364.992196 + 0,01 = 365.002196 (oops, a bit too big, let's add that day anyway one time in about 400 years)

365.002196 - 1/400 = 364.999696

Almost there now, just play with leapseconds now and then, and you're set.

(Note : the reason no more corrections are applied after this step is because a year also CHANGES IN LENGTH!!, that's why leapseconds are the most flexible solution, see for examlple here)

That's why i guess

Solution 2:

There's an algorithm on wikipedia to determine leap years:

function isLeapYear (year):
    if ((year modulo 4 is 0) and (year modulo 100 is not 0))
    or (year modulo 400 is 0)
        then true
    else false

There's a lot of information about this topic on the wikipedia page about leap years, inclusive information about different calendars.

Solution 3:

In general terms the algorithm for calculating a leap year is as follows...

A year will be a leap year if it is divisible by 4 but not by 100. If a year is divisible by 4 and by 100, it is not a leap year unless it is also divisible by 400.

Thus years such as 1996, 1992, 1988 and so on are leap years because they are divisible by 4 but not by 100. For century years, the 400 rule is important. Thus, century years 1900, 1800 and 1700 while all still divisible by 4 are also exactly divisible by 100. As they are not further divisible by 400, they are not leap years

Solution 4:

this is enough to check if a year is a leap year.

if( (year%400==0 || year%100!=0) &&(year%4==0))
    cout<<"It is a leap year";
else
    cout<<"It is not a leap year";

Solution 5:

a) The year is 365.242199 days.

b) If every year was 365 days, in 100 years we would lose 24.2199 days. That's why we add 24 days per century (every 4 years EXCEPT when divisible by 100)

c) But still we lose 0.21299 days/century. So in 4 centuries we lose 0.8796 days. That's why we add 1 day per 4 centuries (every fourth century we DO count a leap year).

d) But that means we lose -0.1204 days (we go forward) per quadricentennial (4 centuries). So in 8 quadricentennial (3200 years) we DO NOT count a leap year.

e) But that means we lose 0.0368 days per 3200 years. So in 24x3200 years (=76800years) we lose 0.8832 days. That's why we DO count a leap year.

and so on... (by then we will have destroyed the planet, so it doesn't matter)

What I cannot understand though, is why we don't count a leap year every 500 years instead of 400. In that way we would converge more rapidly to the correct time (we would lose 2.3 hours/500 years).