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javascriptif-statementleap-year

Can't understand the difference between 2 equations

I am new to Javascript, and have been trying to figure out the best possible equation for a Leap year calculator. I have written the solution like this:

if ((year % 4 ===0 && year % 100 !==0) || (year % 4 ===0 && year % 100 ===0 && year % 400 ===0)) {
  alert("Leap");
} else {
  alert("Not Leap");
}

After having done that, I googled other ways and found out it could be written like this:

if ((year % 4 === 0 && year % 100 !== 0) || (year % 400 ===0)) {
  alert("Leap");
} else {
  alert("Not Leap");
}

But I don't understand how it could be written like that, because knowing the conditions for leap years:

  • If year is divisible by 4 and not divisible by 100 = Leap
  • If year is divisible by 4 and is divisible by 100 and divisible by 400 = Leap
  • Otherwise its not a Leap year.

I don't understand the logic behind the second code sample, to me, it is as if:

  • If year is divisible by 4 and not divisible by 100 = Leap
  • OR
  • Only, if year is divisible by 400 = Leap (not including other conditions)
  • Otherwise its not a Leap year

Could someone please explain why the second code sample is also valid, and how it is interpreted?

Solution

  • The condition for a leap year is if the year is divisible by 4 and not by 100, or year is divisible by 400.

    Mathematically, anything divisible by 400 is divisible by 4 and by 100, this is the reason why the leap year is if (x % 4 AND NOT x % 100) OR (x % 400).

    You can see it like this factor decomposition: 400 = 4 * 100, so any number that may be written as n * 400 may be written as n * 4 * 100, so your condition is just redundant.