From 85b94313f6f643725e5e307d92ab9bac7f7f0772 Mon Sep 17 00:00:00 2001
From: Matej Focko <mfocko@redhat.com>
Date: Fri, 31 Dec 2021 19:10:25 +0100
Subject: [PATCH] 4kyu: add factorial tail

Signed-off-by: Matej Focko <mfocko@redhat.com>
---
 4kyu/factorial_tail/solution.rs | 60 +++++++++++++++++++++++++++++++++
 README.md                       |  1 +
 2 files changed, 61 insertions(+)
 create mode 100644 4kyu/factorial_tail/solution.rs

diff --git a/4kyu/factorial_tail/solution.rs b/4kyu/factorial_tail/solution.rs
new file mode 100644
index 0000000..603d8eb
--- /dev/null
+++ b/4kyu/factorial_tail/solution.rs
@@ -0,0 +1,60 @@
+use std::collections::HashMap;
+use std::collections::HashSet;
+
+type Factors = HashMap<i32, i32>;
+
+fn as_primes(mut n: i32) -> Factors {
+    let mut powers: Factors = HashMap::new();
+
+    (2..((n as f64).sqrt() as i32) + 1).for_each(|x| {
+        let mut q = 0;
+        while n % x == 0 {
+            n /= x;
+            q += 1;
+        }
+
+        if q != 0 {
+            powers.insert(x, q);
+        }
+    });
+
+    if n > 1 {
+        powers.insert(n, 1);
+    }
+
+    powers
+}
+
+fn get_powers(m: i32, primes: HashSet<&i32>) -> Factors {
+    let mut powers: Factors = HashMap::new();
+
+    (2..m + 1).for_each(|mut n| {
+        primes.iter().for_each(|&&x| {
+            let mut q = 0;
+            while n % x == 0 {
+                n /= x;
+                q += 1;
+            }
+
+            powers.insert(x, q + powers.get(&x).unwrap_or(&0));
+        });
+    });
+
+    powers
+}
+
+fn get_zeroes(base: Factors, powers: Factors) -> i32 {
+    let mut adjusted: Factors = HashMap::new();
+
+    for (prime, power) in powers {
+        adjusted.insert(prime, power / base[&prime]);
+    }
+
+    *adjusted.values().min().unwrap()
+}
+
+fn zeroes(base: i32, number: i32) -> i32 {
+    let base_as_primes = as_primes(base);
+    let powers: Factors = get_powers(number, base_as_primes.keys().collect());
+    get_zeroes(base_as_primes, powers)
+}
diff --git a/README.md b/README.md
index 88e53d1..0f52e5e 100644
--- a/README.md
+++ b/README.md
@@ -17,6 +17,7 @@
 ### Rust
 
 - [Sum by Factors](https://www.codewars.com/kata/54d496788776e49e6b00052f) - [solution](4kyu/sum_by_factors)
+- [Factorial tail](https://www.codewars.com/kata/55c4eb777e07c13528000021) - [solution](4kyu/factorial_tail)
 
 ### C#