feat(problem): 14 - longest collatz sequence

readme.md

@@ -9,7 +9,7 @@ All of the solutions here are written in rust. [main.rs](src/main.rs) is the hom
 
 ## Challenge Completion
 
-### <!-- completed -->13<!-- completed --> out of 100 public challenges completed.
+### <!-- completed -->14<!-- completed --> 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)
@@ -24,7 +24,7 @@ All of the solutions here are written in rust. [main.rs](src/main.rs) is the hom
 - [x] 11 - [Largest product in a grid](src/bin/11.rs)
 - [x] 12 - [Highly divisible triangular number](src/bin/12.rs)
 - [x] 13 - [Large sum](src/bin/13.rs)
-- [ ] 14 - Longest Collatz sequence
+- [x] 14 - [Longest Collatz sequence](src/bin/14.rs)
 - [ ] 15 - Lattice paths
 - [ ] 16 - Power digit sum
 - [ ] 17 - Number letter counts

src/bin/11.rs

@@ -80,26 +80,66 @@ fn largest_grid_product(grid: Vec<Vec<usize>>, adjacent_digits: usize) -> usize
 
 fn main() {
     let grid: Vec<Vec<usize>> = vec![
-        vec![8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8],
+        vec![
-        vec![49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0],
+            8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8,
-        vec![81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65],
+        ],
-        vec![52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91],
+        vec![
-        vec![22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80],
+            49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0,
-        vec![24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50],
+        ],
-        vec![32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70],
+        vec![
-        vec![67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21],
+            81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65,
-        vec![24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
+        ],
-        vec![21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95],
+        vec![
-        vec![78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
+            52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91,
-        vec![16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57],
+        ],
-        vec![86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
+        vec![
-        vec![19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40],
+            22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80,
-        vec![4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
+        ],
-        vec![88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
+        vec![
-        vec![4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36],
+            24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50,
-        vec![20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16],
+        ],
-        vec![20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54],
+        vec![
-        vec![1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]
+            32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70,
+        ],
+        vec![
+            67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21,
+        ],
+        vec![
+            24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72,
+        ],
+        vec![
+            21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95,
+        ],
+        vec![
+            78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92,
+        ],
+        vec![
+            16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57,
+        ],
+        vec![
+            86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58,
+        ],
+        vec![
+            19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40,
+        ],
+        vec![
+            4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66,
+        ],
+        vec![
+            88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69,
+        ],
+        vec![
+            4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36,
+        ],
+        vec![
+            20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16,
+        ],
+        vec![
+            20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54,
+        ],
+        vec![
+            1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48,
+        ],
     ];
 
     let value = largest_grid_product(grid, 4);

src/bin/13.rs

@@ -204,7 +204,7 @@ const NUMBERS: [f64; 100] = [
     77158542502016545090413245809786882778948721859617.0,
     72107838435069186155435662884062257473692284509516.0,
     20849603980134001723930671666823555245252804609722.0,
-    53503534226472524250874054075591789781264330331690.0
+    53503534226472524250874054075591789781264330331690.0,
 ];
 
 fn first_n_digits(number: f64, n: usize) -> Option<usize> {
@@ -214,7 +214,9 @@ fn first_n_digits(number: f64, n: usize) -> Option<usize> {
         return None;
     }
 
-    let new_number = String::from_iter(string_number.chars().collect::<Vec<char>>()[0..n].iter()).parse::<usize>().unwrap();
+    let new_number = String::from_iter(string_number.chars().collect::<Vec<char>>()[0..n].iter())
+        .parse::<usize>()
+        .unwrap();
 
     return Some(new_number);
 }

src/bin/14.rs

@@ -0,0 +1,54 @@
+/*
+Problem 14 - Longest Collatz sequence
+
+The following iterative sequence is defined for the set of positive integers:
+n  →  n /2 ( n  is even)  n  → 3 n  + 1 ( n  is odd)
+Using the rule above and starting with 13, we generate the following sequence:
+13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
+It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
+Which starting number, under one million, produces the longest chain?
+NOTE:  Once the chain starts the terms are allowed to go above one million.
+*/
+
+use std::collections::HashMap;
+
+fn f(n: usize) -> usize {
+    if n % 2 == 0 {
+        return n / 2;
+    } else {
+        return ((3 * n) + 1) / 2;
+    }
+}
+
+fn longest_collatz_sequence(greatest_start: usize) -> usize {
+    let mut sequence_lengths: HashMap<usize, usize> = HashMap::new();
+
+    for i in 1..(greatest_start + 1) {
+        let mut sequence_length: usize = 0;
+        let mut current_number = i;
+
+        while current_number > 1 {
+            current_number = f(current_number);
+
+            // Eventually the sequence will break down into one we have already computed the length for!
+            if sequence_lengths.contains_key(&current_number) {
+                sequence_length += *sequence_lengths.get(&current_number).unwrap();
+                break;
+            }
+
+            sequence_length += 1;
+        }
+
+        sequence_lengths.insert(i, sequence_length);
+    }
+
+    return *sequence_lengths.iter().max_by_key(|x| x.1).unwrap().0;
+}
+
+fn main() {
+    let starting_number = longest_collatz_sequence(1_000_000);
+
+    println!(
+        "The starting number which produces the longest collatz sequence is {starting_number}"
+    );
+}

src/bin/2.rs

@@ -24,5 +24,8 @@ fn main() {
     let even = sequence.iter().filter(|n| *n % 2 == 0);
     let sum: usize = even.sum();
 
-	print!("The sum of the first 4000000 even fibonacci numbers is {}", sum);
+    print!(
+        "The sum of the first 4000000 even fibonacci numbers is {}",
+        sum
+    );
 }

src/main.rs

@@ -1,15 +1,19 @@
 use clap::{Parser, Subcommand};
 use owo_colors::OwoColorize;
-use std::{fs::{self, File, OpenOptions}, path::Path, io::{Write, BufRead}};
-use scraper::{Html, Selector};
 use regex::Regex;
-use std::io::{BufReader};
+use scraper::{Html, Selector};
+use std::io::BufReader;
+use std::{
+    fs::{self, File, OpenOptions},
+    io::{BufRead, Write},
+    path::Path,
+};
 
 #[derive(Parser)]
 #[clap(about, author, version)]
 struct Value {
     #[clap(subcommand)]
-    command: Commands
+    command: Commands,
 }
 
 #[derive(Subcommand)]
@@ -55,13 +59,19 @@ async fn new() -> Result<(), Box<dyn std::error::Error>> {
                     Err("Please ensure that your input is valid!".to_owned())
                 }
             })
-            .build()
+            .build(),
-    ).unwrap().as_int().unwrap();
+    )
+    .unwrap()
+    .as_int()
+    .unwrap();
 
     // todo: thoughts documents (?)
 
     // Fetch the problem information
-    let body = reqwest::get(format!("https://projecteuler.net/problem={problem_number}")).await?.text().await?;
+    let body = reqwest::get(format!("https://projecteuler.net/problem={problem_number}"))
+        .await?
+        .text()
+        .await?;
 
     let document = Html::parse_document(body.as_str());
     let title_selector = Selector::parse("h2")?;
@@ -84,7 +94,7 @@ async fn new() -> Result<(), Box<dyn std::error::Error>> {
                 .unwrap()
                 .inner_html()
                 .as_str(),
-            " "
+            " ",
         )
         .to_string()
         .replace("$$", " ");
@@ -117,17 +127,13 @@ fn main() {{
     // Read the contents of the readme for editing
     let readme_path = base_dir.join("readme.md");
 
-    let mut readme_file = OpenOptions::new()
+    let mut readme_file = OpenOptions::new().read(true).open(&readme_path).unwrap();
-        .read(true)
-        .open(&readme_path)
-        .unwrap();
 
     let mut readme_content = BufReader::new(&readme_file)
         .lines()
         .map(|s| s.unwrap())
         .collect::<Vec<String>>();
 
-
     drop(readme_file);
 
     // Mark the problem as done on the readme
@@ -138,7 +144,10 @@ fn main() {{
 
         if readme_regex.is_match(line) {
             let matched = readme_regex.captures(line).unwrap();
-            readme_content[i] = format!("- [x] {problem_number} - [{}](src/bin/{problem_number}.rs)", &matched[1].trim());
+            readme_content[i] = format!(
+                "- [x] {problem_number} - [{}](src/bin/{problem_number}.rs)",
+                &matched[1].trim()
+            );
         }
     }
 
@@ -147,26 +156,30 @@ fn main() {{
 
     let completed_regex = Regex::new("<!-- completed -->([0-9]+)<!-- completed -->").unwrap();
 
-    let new_completed = completed_regex
+    let new_completed = completed_regex.captures(readme_string.as_str()).unwrap()[1]
-        .captures(readme_string.as_str())
-        .unwrap()[1]
         .parse::<u8>()
-        .unwrap() + 1;
+        .unwrap()
+        + 1;
 
-    readme_string = completed_regex.replace(readme_string.as_str(), format!("<!-- completed -->{new_completed}<!-- completed -->")).to_string();
+    readme_string = completed_regex
+        .replace(
+            readme_string.as_str(),
+            format!("<!-- completed -->{new_completed}<!-- completed -->"),
+        )
+        .to_string();
 
     // Write the new content to the readme
-    readme_file = OpenOptions::new()
+    readme_file = OpenOptions::new().write(true).open(&readme_path).unwrap();
-        .write(true)
-        .open(&readme_path)
-        .unwrap();
 
     readme_file.write(readme_string.as_bytes()).unwrap();
 
     drop(readme_file);
 
     // Announce completion!
-    println!("{}", "File successfully created! Good luck (:".green().bold());
+    println!(
+        "{}",
+        "File successfully created! Good luck (:".green().bold()
+    );
 
     Ok(())
 }
@@ -175,6 +188,6 @@ fn main() {
     let value = Value::parse();
 
     match value.command {
-        Commands::New => new().unwrap()
+        Commands::New => new().unwrap(),
     }
 }