Bash Script to Check Leap Year with Output and Explanation

Use a Bash script with conditions: if (( year % 400 == 0 )) || (( year % 4 == 0 && year % 100 != 0 )); then echo "Leap year"; else echo "Not leap year"; fi to check leap years.

Examples

Input2000

OutputLeap year

Input1900

OutputNot leap year

Input2024

OutputLeap year

How to Think About It

To check if a year is leap, first see if it divides evenly by 400. If yes, it is leap. If not, check if it divides evenly by 4 but not by 100. If yes, it is leap. Otherwise, it is not leap.

Algorithm

1

Get the year input from the user

2

Check if the year is divisible by 400; if yes, it is a leap year

3

Else check if the year is divisible by 4 but not by 100; if yes, it is a leap year

4

Otherwise, it is not a leap year

5

Print the result

Code

bash

#!/bin/bash
read -p "Enter a year: " year
if (( year % 400 == 0 )) || (( year % 4 == 0 && year % 100 != 0 )); then
  echo "Leap year"
else
  echo "Not leap year"
fi

Output

Enter a year: 2024
Leap year

Dry Run

Let's trace the year 1900 through the code

1

Input year

year = 1900

2

Check divisibility by 400

1900 % 400 = 300 (not zero)

3

Check divisibility by 4 and not by 100

1900 % 4 = 0 and 1900 % 100 = 0 (fails second condition)

4

Result

Print 'Not leap year'

Step	Condition	Result
1	year = 1900	Input received
2	1900 % 400 == 0	False
3	1900 % 4 == 0 && 1900 % 100 != 0	False
4	Print result	Not leap year

Why This Works

Step 1: Divisible by 400

If a year divides evenly by 400, it is always a leap year, so we check this first.

Step 2: Divisible by 4 but not 100

If not divisible by 400, the year must be divisible by 4 but not by 100 to be leap.

Step 3: Otherwise not leap

If neither condition is met, the year is not a leap year.

Alternative Approaches

Using expr command

bash

#!/bin/bash
read -p "Enter a year: " year
if [ $(expr $year % 400) -eq 0 ] || { [ $(expr $year % 4) -eq 0 ] && [ $(expr $year % 100) -ne 0 ]; }; then
  echo "Leap year"
else
  echo "Not leap year"
fi

Uses external expr command for arithmetic, less efficient but compatible with older shells.

Using bc for arithmetic

bash

#!/bin/bash
read -p "Enter a year: " year
is_leap=$(echo "($year % 400 == 0) || (($year % 4 == 0) && ($year % 100 != 0))" | bc)
if [ "$is_leap" -eq 1 ]; then
  echo "Leap year"
else
  echo "Not leap year"
fi

Uses bc calculator for arithmetic, useful if shell arithmetic is limited.

Complexity: O(1) time, O(1) space

Time Complexity

The script performs a fixed number of arithmetic operations and condition checks, so it runs in constant time.

Space Complexity

Only a few variables are used, so space usage is constant.

Which Approach is Fastest?

Using Bash's built-in arithmetic (( )) is fastest and simplest compared to external commands like expr or bc.

Approach	Time	Space	Best For
Bash arithmetic (( ))	O(1)	O(1)	Modern Bash scripts, best performance
expr command	O(1)	O(1)	Older shells compatibility
bc calculator	O(1)	O(1)	Complex arithmetic or limited shell arithmetic