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(define (leap-year? year)
(and (zero? (modulo year 4))
(or (not (zero? (modulo year 100)))
(zero? (modulo year 400)))))
The Boolean expression (zero? (modulo year 4)) checks the remainder from dividing year by 4.
If a year is evenly divisible by 4, the remainder will be zero.
(zero? n) returns the Boolean value #t when n is zero.
All leap years are divisible by 4, and this pattern is then repeated whether a year is not divisible by 100 and whether it's divisible by 400.
The and and or forms can chain the values from these three Boolean expressions to produce a new value.
The and form produces #f if any expression is #f or it returns the value of the last expression.
Any value besides #f is equivalent to #t.
The or form produces #f if all expressions are #f or it returns the first non-#f value.
| year | divisible by 4 | not divisible by 100 | divisible by 400 | result |
|---|---|---|---|---|
| 2020 | #t | #t | not evaluated | #t |
| 2019 | #f | not evaluated | not evaluated | #f |
| 2000 | #t | #f | #t | #t |
| 1900 | #t | #f | #f | #f |
By situationally skipping some of the tests, we can efficiently calculate the result with fewer operations.
