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fn usqrt(n: u64) -> u64 {
let (mut low, mut high) = (1, n);
let mut mid = (low + high) / 2;
while low < high {
mid = (low + high) / 2;
let square = mid * mid;
if square == n {
return mid;
} else if square > n {
high = mid - 1
} else {
low = mid + 1
}
}
if mid * mid == n {
mid
} else {
high
}
}
#[cfg(test)]
mod usqrt_tests {
use super::usqrt;
#[test]
fn small_perfect_squares() {
let inputs = (1..11).collect::<Vec<u64>>();
let squares = inputs.iter().map(|x| x * x).collect::<Vec<u64>>();
let outputs = squares.into_iter().map(usqrt).collect::<Vec<u64>>();
assert_eq!(inputs, outputs);
}
#[test]
fn large_perfect_squares() {
let inputs = (1000..10000).step_by(37).collect::<Vec<u64>>();
let squares = inputs.iter().map(|x| x * x).collect::<Vec<u64>>();
let outputs = squares.into_iter().map(usqrt).collect::<Vec<u64>>();
assert_eq!(inputs, outputs);
}
#[test]
fn edge_case_zero() {
assert_eq!(usqrt(0), 0);
}
#[test]
fn edge_case_one() {
assert_eq!(usqrt(1), 1);
}
#[test]
fn rounds_up_when_not_a_perfect_square() {
assert_eq!(usqrt(2), 2);
}
#[test]
fn large_not_perfect_square() {
let x = 12345;
assert_eq!(usqrt(x * x + 1), x + 1)
}
}
fn is_prime(n: u64) -> bool {
if n == 2 || n == 3 {
return true;
}
if n % 2 == 0 || n <= 1 {
return false;
}
let lower = 3;
let upper = usqrt(n);
(lower..(upper + 1))
.step_by(2)
.all(|maybe_divisor| n % maybe_divisor != 0)
}
#[cfg(test)]
mod is_prime_tests {
use super::is_prime;
#[test]
fn small_primes() {
let primes = vec![2, 3, 5, 7, 11, 13, 17, 19, 23];
assert_eq!(
primes
.clone()
.into_iter()
.map(is_prime)
.collect::<Vec<bool>>(),
vec![true; primes.len()]
);
}
}
pub fn next_prime(mut n: u64) -> u64 {
if n <= 2 {
return 2;
}
if n % 2 == 0 {
n += 1;
}
while !is_prime(n) {
n += 2;
}
n
}
#[cfg(test)]
mod next_prime_tests {
use super::next_prime;
#[test]
fn edge_case_two() {
assert_eq!(next_prime(2), 2);
}
#[test]
fn finds_small_primes() {
let primes = vec![5, 7, 11, 13, 17, 19, 23, 29];
assert_eq!(
primes,
primes
.iter()
.map(|x| next_prime(x - 1))
.collect::<Vec<u64>>()
);
}
#[test]
fn returns_argument_when_it_is_already_prime() {
assert_eq!(next_prime(101), 101);
}
#[test]
fn finds_a_very_large_prime() {
assert_eq!(next_prime(472_888_178), 472_888_217)
}
}