Ternary operator

year=$1
if (( year % 100 == 0 ? year % 400 == 0 : year % 4 == 0 )); then
    echo true
else
    echo false
fi 

A conditional operator, also known as a "ternary conditional operator", or just "ternary operator". This structure uses a maximum of two checks to determine if a year is a leap year.

It starts by testing the outlier condition of the year being evenly divisible by 100. It does this by using the remainder operator: year % 100 == 0. If the year is evenly divisible by 100, then the expression is true, and the ternary operator returns the result of testing if the year is evenly divisible by 400. If the year is not evenly divisible by 100, then the expression is false, and the ternary operator returns the result of testing if the year is evenly divisible by 4.

Although it uses a maximum of two checks, the ternary operator tests an outlier condition first, making it less efficient than another approach that would first test if the year is evenly divisible by 4, which is more likely than the year being evenly divisible by 100.

Refactoring for readability

This is a place where a helper function can result in more elegant code.

is_leap() {
    local year=$1
    if (( year % 100 == 0 )); then
        return $(( !(year % 400 == 0) ))
    else
        return $(( !(year % 4 == 0) ))
    fi
}

is_leap "$1" && echo true || echo false

The result of the arithmetic expression year % 400 == 0 will be 1 if true and 0 if false. The value is negated to correspond to the shell's return statuses: 0 is "success" and 1 is "failure. Then the function can be used to branch between the "true" and "false" output.

The function's return statements can be written as

(( year % 400 != 0 ))
# or even
(( year % 400 ))

Without an explicit return, the function returns with the status of the last command executed. The (( construct will be the last command.