The challenge
Write a program that will calculate the number of trailing zeros in a factorial of a given number.
N! = 1 * 2 * 3 * ... * N
Be careful 1000! has 2568 digits…
For more info, see: http://mathworld.wolfram.com/Factorial.html
Examples
zeros(6) = 1
# 6! = 1 * 2 * 3 * 4 * 5 * 6 = 720 --> 1 trailing zero
zeros(12) = 2
# 12! = 479001600 --> 2 trailing zeros
The solution in Rust
Option 1:
fn zeros(n: u64) -> u64 {
if n == 0 { 0 }
else { n / 5 + zeros(n / 5) }
}
Option 2:
fn zeros(n: u64) -> u64 {
(1..)
.map(|exp| n / 5_u64.pow(exp))
.take_while(|&x| x != 0)
.sum()
}
Option 3:
fn zeros(n: u64) -> u64 {
let max = (n as f64).log(5.0).floor() as u32;
(1..=max).fold(0, |acc, i| acc + n / 5_u64.pow(i))
}
Test cases to validate our solution
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn fixed_tests() {
assert_eq!(zeros(0), 0);
assert_eq!(zeros(6), 1);
assert_eq!(zeros(14), 2);
assert_eq!(zeros(30), 7);
assert_eq!(zeros(1000), 249);
assert_eq!(zeros(100000), 24999);
assert_eq!(zeros(1000000000), 249999998);
}
fn solution(n: u64) -> u64 {
let mut r = 0;
let mut n = n / 5;
while n > 0 {
r += n;
n /= 5;
}
r
}
use rand::Rng;
#[test]
fn random_tests() {
let mut rng = rand::thread_rng();
for _i in 0..100 {
let n: u64 = rng.gen_range(0..1001);
let expected = solution(n);
let actual = zeros(n);
assert_eq!(actual, expected, "zeros({}): expected {}, got {}", n, expected, actual);
}
for _i in 0..100 {
let n: u64 = rng.gen_range(0..1000001);
let expected = solution(n);
let actual = zeros(n);
assert_eq!(actual, expected, "zeros({}): expected {}, got {}", n, expected, actual);
}
for _i in 0..100 {
let n: u64 = rng.gen_range(0..1000000001);
let expected = solution(n);
let actual = zeros(n);
assert_eq!(actual, expected, "zeros({}): expected {}, got {}", n, expected, actual);
}
}
}
