From 727c36e795adc6f2dbbad75febc26b765be444bd Mon Sep 17 00:00:00 2001
From: Evan Hemsley <evan@moonside.games>
Date: Sun, 6 Oct 2019 22:43:22 -0700
Subject: [PATCH] solution 5

---
 rust/src/euler/math.rs        |  8 ++++++++
 rust/src/euler/mod.rs         |  4 +++-
 rust/src/euler/prime.rs       | 21 ++++++++++++++++++++-
 rust/src/euler/problem_005.rs | 21 +++++++++++++++++++++
 4 files changed, 52 insertions(+), 2 deletions(-)
 create mode 100644 rust/src/euler/math.rs
 create mode 100644 rust/src/euler/problem_005.rs

diff --git a/rust/src/euler/math.rs b/rust/src/euler/math.rs
new file mode 100644
index 0000000..c012e7d
--- /dev/null
+++ b/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
+}
\ No newline at end of file
diff --git a/rust/src/euler/mod.rs b/rust/src/euler/mod.rs
index 1dd8e64..7282160 100644
--- a/rust/src/euler/mod.rs
+++ b/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;
\ No newline at end of file
+pub mod problem_004;
+pub mod problem_005;
\ No newline at end of file
diff --git a/rust/src/euler/prime.rs b/rust/src/euler/prime.rs
index c5f41a2..fd867de 100644
--- a/rust/src/euler/prime.rs
+++ b/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;
diff --git a/rust/src/euler/problem_005.rs b/rust/src/euler/problem_005.rs
new file mode 100644
index 0000000..fece3a3
--- /dev/null
+++ b/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);
+    }
+}
\ No newline at end of file