From 95c8f4738fdacd7b0f1a465f807519f03c0daa9e Mon Sep 17 00:00:00 2001
From: newt <hi@newty.dev>
Date: Wed, 9 Oct 2024 18:10:13 +0100
Subject: [PATCH] feat(26): complete reciprocal cycles

---
 readme.md           |  4 ++--
 src/bin/26.rs       | 57 +++++++++++++++++++++++++++++++++++++++++++++
 src/commands/run.rs |  3 +++
 3 files changed, 62 insertions(+), 2 deletions(-)
 create mode 100644 src/bin/26.rs

diff --git a/readme.md b/readme.md
index d4be15d..6acad87 100644
--- a/readme.md
+++ b/readme.md
@@ -17,7 +17,7 @@ Here is a [link to my profile](https://projecteuler.net/progress=newtykins).
 
 ## Challenge Completion
 
-### 28 out of 100 public challenges completed.
+### 29 out of 100 public challenges completed.
 
 - [x] 1 - [Multiples of 3 or 5](src/bin/1.rs)
 - [x] 2 - [Even Fibonacci numbers](src/bin/2.rs)
@@ -44,7 +44,7 @@ Here is a [link to my profile](https://projecteuler.net/progress=newtykins).
 - [x] 23 - Non-abundant sums
 - [x] 24 - Lexicographic permutations
 - [x] 25 - 1000-digit Fibonacci number
-- [ ] 26 - Reciprocal cycles
+- [x] 26 - Reciprocal cycles
 - [x] 27 - [Quadratic primes](src/bin/27.rs)
 - [ ] 28 - Number spiral diagonals
 - [ ] 29 - Distinct powers
diff --git a/src/bin/26.rs b/src/bin/26.rs
new file mode 100644
index 0000000..888ae94
--- /dev/null
+++ b/src/bin/26.rs
@@ -0,0 +1,57 @@
+/*
+Problem 26 - Reciprocal Cycles
+
+A unit fraction contains $1$ in the numerator. The decimal representation of the unit fractions with denominators $2$ to $10$ are given:
+\begin{align}
+1/2 &= 0.5\\
+1/3 &=0.(3)\\
+1/4 &=0.25\\
+1/5 &= 0.2\\
+1/6 &= 0.1(6)\\
+1/7 &= 0.(142857)\\
+1/8 &= 0.125\\
+1/9 &= 0.(1)\\
+1/10 &= 0.1
+\end{align}
+Where $0.1(6)$ means $0.166666\cdots$, and has a $1$-digit recurring cycle. It can be seen that $1/7$ has a $6$-digit recurring cycle.
+Find the value of $d \lt 1000$ for which $1/d$ contains the longest recurring cycle in its decimal fraction part.
+*/
+
+fn cycle_length(d: usize) -> usize {
+    let mut remainders = vec![0; d];
+    let mut value = 1;
+    let mut position = 0;
+
+    while remainders[value] == 0 && value != 0 {
+        remainders[value] = position;
+        value *= 10;
+        value %= d;
+        position += 1;
+    }
+
+    if value == 0 {
+        return 0;
+    } else {
+        return position - remainders[value];
+    }
+}
+
+fn longest_cycle(limit: usize) -> usize {
+    let mut max_length = 0;
+    let mut result = 0;
+
+    for d in 2..limit {
+        let length = cycle_length(d);
+        if length > max_length {
+            max_length = length;
+            result = d;
+        }
+    }
+
+    result
+}
+
+pub fn main() {
+    let number = longest_cycle(1000);
+    println!("The value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part is: {}", number);
+}
diff --git a/src/commands/run.rs b/src/commands/run.rs
index a6cea95..fb4cd31 100644
--- a/src/commands/run.rs
+++ b/src/commands/run.rs
@@ -58,6 +58,8 @@ mod two;
 mod twenty_four;
 #[path = "../bin/25.rs"]
 mod twenty_five;
+#[path = "../bin/26.rs"]
+mod twenty_six;
 
 pub async fn execute(
     problem: Option<u8>,
@@ -102,6 +104,7 @@ pub async fn execute(
         23 => twenty_three::main(),
         24 => twenty_four::main(),
         25 => twenty_five::main(),
+        26 => twenty_six::main(),
         _ => {
             exists = false;
             println!(