2000Leap
- Reason
- Divisible by
400
Check Leap Year in Java
What you’ll learn
- Gregorian leap-year rule with 4/100/400 logic.
- Single year check and range listing in Java.
- Handling classic edge years like 1900 and 2000.
Prerequisites
Modulo operator, boolean expressions, and loops in Java.
- Understand
%checks divisibility. - Know how to combine conditions with
&&and||.
Math definition
A Gregorian year y is leap if (y % 4 == 0 && y % 100 != 0) || (y % 400 == 0).
Intuition
1900Not leap
- Reason
- Century not divisible by
400
Live preview
Algorithm
Goal: evaluate the Gregorian leap predicate for a year.
Check divisibility by 4
If the year is not divisible by 4, it is a common year.
Apply century exception
Years divisible by 100 are leap only when also divisible by 400.
📜 Pseudocode
Pseudocode
function isLeapYear(y):
return (y mod 4 == 0 and y mod 100 != 0) or (y mod 400 == 0)1Single year:
Single year: 2024
java
public class Main {
static boolean isLeapYear(int year) {
return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);
}
public static void main(String[] args) {
int year = 2024;
if (isLeapYear(year)) {
System.out.println(year + " is a leap year.");
} else {
System.out.println(year + " is not a leap year.");
}
}
}📤 Output
2024 is a leap year.
Explanation
The predicate checks the full Gregorian rule in one boolean expression: divisible by 4 and not by 100, or divisible by 400. For 2024, the first part is true, so the year is leap.
2Leap years in
Leap years in [2024, 2050]
java
public class Main {
static boolean isLeapYear(int year) {
return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);
}
public static void main(String[] args) {
int startYear = 2024;
int endYear = 2050;
System.out.println("Leap years in the range " + startYear + " to " + endYear + ":");
for (int y = startYear; y <= endYear; y++) {
if (isLeapYear(y)) System.out.print(y + " ");
}
System.out.println();
}
}📤 Output
Leap years in the range 2024 to 2050: 2024 2028 2032 2036 2040 2044 2048
Explanation
The loop evaluates each year with the same isLeapYear helper and prints only matching years. In this interval, leap years appear every 4 years and there is no century exception boundary.
Optimization
Single check: direct condition is already O(1); no extra optimization needed.
Range listing: for long ranges, avoid string concatenation in loops; use buffered output.
❓ FAQ
Leap iff (y%4==0 && y%100!=0) || (y%400==0).
Yes, because it is divisible by 400.
No, because it is divisible by 100 but not by 400.
No. This page uses standard proleptic Gregorian arithmetic.
Java arithmetic still works, but civil-calendar interpretation depends on convention.
Single check is O(1); scanning a range is O(n) in range length.
🔄 Input / output examples
| Year | Leap? |
|---|---|
2024 | Yes |
2021 | No |
2000 | Yes |
1900 | No |
Edge cases and pitfalls
Century
1900
Divisible by 100 but not 400, so not leap.
400 Rule
2000
Divisible by 400, so leap.
Bounds
Invalid range
Handle startYear > endYear in range-based programs.
⏱️ Time and space complexity
| Task | Time | Extra space |
|---|---|---|
| One year check | O(1) | O(1) |
| Range scan | O(end - start + 1) | O(1) |
Summary
- Leap rule is based on
4 / 100 / 400divisibility. - One predicate function works for both single year and range checks.
- Remember classic exceptions:
1900no,2000yes.
Did you know?
Gregorian leap rule: divisible by 4, except centuries unless divisible by 400. That is why 1900 is not leap but 2000 is leap.
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