2024Leap
- Rule
- %4 and not %100
Check Leap Year in Python
What you’ll learn
- Gregorian leap-year rule with 4/100/400 divisibility.
- A clean Python predicate function.
- Printing leap years in a range and live checking.
Overview
Leap years reduce calendar drift by adding February 29 under specific modular rules.
Two programs
Single year check and range listing.
Live preview
Instant result for safe integer years.
Rigor
Century exceptions handled correctly.
Prerequisites
Modulo operator and boolean logic.
- Know
%andand/orconditions in Python. - Use a
forloop for range scan.
What is a leap year?
Leap year has February 29 in Gregorian calendar.
Divisible by 4 is not enough: centuries require divisible by 400.
2024Leap
1900Not
2000Leap
Predicate
(y % 4 == 0 and y % 100 != 0) or (y % 400 == 0)
20242024 % 4 == 0 and 2024 % 100 != 0, so leap year.
Intuition
2021Common
- Rule
2021 % 4 = 1
Takeaway: century years are special cases.
Live preview
Check any integer year in safe range.
Algorithm
Goal: evaluate Gregorian leap predicate.
Divisible by 4
If false, not leap.
Century exception
If divisible by 100, require divisible by 400.
📜 Pseudocode
Pseudocode
function is_leap_year(y):
return (y mod 4 = 0 and y mod 100 != 0) or (y mod 400 = 0)1Single year:
Single year: 2024
Checks one year with the standard Gregorian rule.
python
def is_leap_year(year: int) -> bool:
return (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0)
year = 2024
if is_leap_year(year):
print(f"{year} is a leap year.")
else:
print(f"{year} is not a leap year.")Explanation
Boolean expression directly matches the textbook leap rule.
2Leap years in
Leap years in [2024, 2050]
Prints all leap years in the same range as reference.
python
def is_leap_year(year: int) -> bool:
return (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0)
start_year = 2024
end_year = 2050
print(f"Leap years in the range {start_year} to {end_year}:")
for y in range(start_year, end_year + 1):
if is_leap_year(y):
print(y, end=" ")
print()Explanation
Pattern is mostly every 4 years, with century exceptions outside this interval.
Alternatives
Lookup table: useful for fixed small year ranges in UI code.
Date libraries: prefer standard libs for production-grade date handling.
Interview: state the 4/100/400 rule cleanly first.
❓ FAQ
Leap iff (y%4==0 and y%100!=0) or (y%400==0).
Yes, because it is divisible by 400.
No, divisible by 100 but not by 400.
No. This page uses the usual proleptic Gregorian arithmetic rule.
In code you can still apply the formula to integer years, but historical interpretation differs.
Single-year check is O(1). Range scan is O(b-a+1).
🔄 Input / output examples
Test these years with the predicate.
| Year | Leap? |
|---|---|
2024 | Yes |
2021 | No |
2000 | Yes |
1900 | No |
Edge cases and pitfalls
Leap predicate is only one part of full date validation.
400
Century override
2000 is leap, 1900 is not.
Year systems
Historical vs proleptic
Code usually applies Gregorian formula uniformly.
Range
start > end
Guard or swap bounds in range loops.
Input
Non-integer year
Reject non-integers in UI/preview parsing.
⏱️ Time and space complexity
| Task | Time | Extra space |
|---|---|---|
| One year check | O(1) | O(1) |
| Range [a,b] | O(b-a+1) | O(1) |
No extra structures needed beyond simple counters.
Summary
- Rule:
(y%4==0 and y%100!=0) or (y%400==0). - Code: one predicate function plus optional range loop.
- Watch-outs: century years and historical calendar context.
Did you know?
Gregorian reform refined the simple every-4-years rule: century years are not leap years unless divisible by 400.
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