solution 5

rust/src/euler/math.rs

@@ -0,0 +1,8 @@
+pub fn gcd(mut a: u64, mut b: u64) -> u64 {
+    while b != 0 {
+        let t = a;
+        a = b;
+        b = t % b;
+    }
+    a
+}

rust/src/euler/mod.rs

@@ -1,6 +1,8 @@
 pub mod prime;
+pub mod math;
 
 pub mod problem_001;
 pub mod problem_002;
 pub mod problem_003;
 pub mod problem_004;
+pub mod problem_005;

rust/src/euler/prime.rs

@@ -14,7 +14,8 @@ fn subfactors(mut n: u64, p: u64) -> (u64, Vec<u64>) {
     (n, subfactors)
 }
 
-pub fn trial_factorization(mut n: u64) -> Vec<u64> {
+pub fn trial_factorization(n: u64) -> Vec<u64> {
+    let mut n = n;
     let mut factors = Vec::new();
 
     let (num, division_by_two) = subfactors(n, 2);
@@ -42,6 +43,24 @@ pub fn trial_factorization(mut n: u64) -> Vec<u64> {
     factors
 }
 
+fn root(n: u64, f: u64) -> u64 {
+    let mut n = n;
+    let mut result = 0;
+
+    while n % f == 0 {
+        result += 1;
+        n /= f;
+    }
+
+    result
+}
+
+pub fn prime_factorization(n: u64) -> Vec<(u64, u64)> {
+    let factors = trial_factorization(n);
+    let exponents = factors.iter().map( |&f| root(n, f) );
+    factors.iter().zip(exponents).map( |(&i, j)| (i, j) ).collect()
+}
+
 #[cfg(test)]
 mod tests {
     use euler::prime::trial_factorization;

rust/src/euler/problem_005.rs

@@ -0,0 +1,21 @@
+use euler::math;
+
+fn smallest_divisible_by_all_up_to(n: u64) -> u64 {
+    (2..n).fold(1, |acc, i| {
+        acc * i / math::gcd(i, acc)
+    })
+}
+
+pub fn solution() -> u64 {
+    smallest_divisible_by_all_up_to(20)
+}
+
+#[cfg(test)]
+mod tests {
+    use euler::problem_005::solution;
+
+    #[test]
+    fn problem_005() {
+        assert_eq!(solution(), 232_792_560);
+    }
+}