Advanced Exercism • r

Leap

Challenge Overview

Determine whether a given year is a leap year.

Visit the leap exercise on Exercism to read the full instructions and download the exercise files.

Dig Deeper

Boolean chain

Chain of boolean expressions

leap <- function(year) {
  year %% 4 == 0 && (year %% 100 != 0 || year %% 400 == 0)
}

The first boolean expression uses the modulo operator (%%) to check if the year is evenly divided by 4.

If the year is not evenly divisible by 4, then the chain will “short circuit” due to the next operator being a logical AND &), and will return FALSE.
If the year is evenly divisible by 4, then the year is checked to not be evenly divisible by 100.
If the year is not evenly divisible by 100, then the expression is TRUE and the chain will “short-circuit” to return TRUE, since the next operator is a logical OR (|).
If the year is evenly divisible by 100, then the expression is FALSE, and the returned value from the chain will be if the year is evenly divisible by 400.

year	year %% 4 == 0	year %% 100 != 0	year %% 400 == 0	is leap year
2020	TRUE	TRUE	not evaluated	TRUE
2019	FALSE	not evaluated	not evaluated	FALSE
2000	TRUE	FALSE	TRUE	TRUE
1900	TRUE	FALSE	FALSE	FALSE

The chain of boolean expressions is efficient, as it proceeds from testing the most likely to least likely conditions. It is the fastest approach when testing a year that is not evenly divisible by 100 and is not a leap year.

Refactoring

By using the falsiness of 0, the not operator (!) can be used instead of comparing equality to 0. For example:

leap <- function(year) {
    !year %% 4 && (year %% 100 != 0 || !year %% 400)
}

It can be thought of as the expression not having a remainder. While it may harm readability (this is of course subjective), based on benchmarking this is slightly faster than checking whether the remainder equals zero.

Vectorised implementation

In R many operations are vectorised (by default), or can be vectorised. | and & (by contrast to || and &&) are vectorised versions of logical operators which could also be used if one wanted to allow for a vector of years as input.

leap <- function(year) {
    year %% 4 == 0 & (year %% 100 != 0 | year %% 400 == 0)
}

In general with vectorised operations the trade-off is that it tends to be slower for operations on vectors of length 1 (R doesn’t have an atomic scalar data type so scalars are still just vectors of length 1), but in many cases vectorised implementations can be more efficient than naive looping when dealing with multiple input values, and the difference can be quite dramatic for more complex computations.

Conditional expression

leap <- function(year) {
    if (year %% 100 == 0)
      year %% 400 == 0
    else
      year %% 4 == 0
}

A conditional expression 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 modulo operator (%%) and checking whether the remainder is 0.

If the year is evenly divisible by 100, then the expression is TRUE, and the conditional expression returns if the year is evenly divisible by 400.
If the year is not evenly divisible by 100, then the expression is FALSE, and the conditional expression returns if the year is evenly divisible by 4.

year	year %% 100 == 0	year %% 400 == 0	year %% 4 == 0	is leap year
2020	FALSE	not evaluated	TRUE	TRUE
2019	FALSE	not evaluated	FALSE	FALSE
2000	TRUE	TRUE	not evaluated	TRUE
1900	TRUE	FALSE	not evaluated	FALSE

Although it uses a maximum of only two checks, the conditional expression 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. The conditional expression was fastest in benchmarking when the year was a leap year or was evenly divisible by 100, but those are the least likely conditions.

In R many operations are vectorised (by default), or can be vectorised. ifelse is a vectorised version of if ... else ..., which could also be used if one wanted to allow for a vector of years as input.

leap <- function(year) {
    ifelse(year %% 100 == 0, year %% 400 == 0, year %% 4 == 0)
}

Source: Exercism r/leap