feat(25): complete 1000-digit fibonacci number

readme.md

@@ -17,7 +17,7 @@ Here is a [link to my profile](https://projecteuler.net/progress=newtykins).
 
 ## Challenge Completion
 
-### 27 out of 100 public challenges completed.
+### 28 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)
@@ -43,7 +43,7 @@ Here is a [link to my profile](https://projecteuler.net/progress=newtykins).
 - [x] 22 - [Names scores](src/bin/22.rs)
 - [x] 23 - Non-abundant sums
 - [x] 24 - Lexicographic permutations
-- [ ] 25 - 1000-digit Fibonacci number
+- [x] 25 - 1000-digit Fibonacci number
 - [ ] 26 - Reciprocal cycles
 - [x] 27 - [Quadratic primes](src/bin/27.rs)
 - [ ] 28 - Number spiral diagonals

src/bin/25.rs

@@ -0,0 +1,64 @@
+/*
+Problem 25 - $1000$-digit Fibonacci Number
+
+The Fibonacci sequence is defined by the recurrence relation:
+$F_n = F_{n - 1} + F_{n - 2}$, where $F_1 = 1$ and $F_2 = 1$.
+Hence the first $12$ terms will be:
+\begin{align}
+F_1 &= 1\\
+F_2 &= 1\\
+F_3 &= 2\\
+F_4 &= 3\\
+F_5 &= 5\\
+F_6 &= 8\\
+F_7 &= 13\\
+F_8 &= 21\\
+F_9 &= 34\\
+F_{10} &= 55\\
+F_{11} &= 89\\
+F_{12} &= 144
+\end{align}
+The $12$th term, $F_{12}$, is the first term to contain three digits.
+What is the index of the first term in the Fibonacci sequence to contain $1000$ digits?
+*/
+
+fn fibonacci_with_digits(digits: usize) -> usize {
+    let mut antepenultimate = vec![1];
+    let mut previous = vec![1];
+    let mut index = 2;
+
+    while previous.len() < digits {
+        let mut current = vec![0; previous.len().max(antepenultimate.len())];
+        let mut carry = 0;
+
+        for i in 0..current.len() {
+            let sum = if i < antepenultimate.len() {
+                antepenultimate[i]
+            } else {
+                0
+            } + if i < previous.len() { previous[i] } else { 0 }
+                + carry;
+            current[i] = sum % 10;
+            carry = sum / 10;
+        }
+
+        while carry > 0 {
+            current.push(carry % 10);
+            carry /= 10;
+        }
+
+        antepenultimate = previous;
+        previous = current;
+        index += 1;
+    }
+
+    index
+}
+
+pub fn main() {
+    let index: usize = fibonacci_with_digits(1000);
+    println!(
+        "The index of the first term in the Fibonacci sequence to contain 1000 digits is {}!",
+        index
+    );
+}

src/commands/run.rs

@@ -56,6 +56,8 @@ mod twenty_two;
 mod two;
 #[path = "../bin/24.rs"]
 mod twenty_four;
+#[path = "../bin/25.rs"]
+mod twenty_five;
 
 pub async fn execute(
     problem: Option<u8>,
@@ -99,6 +101,7 @@ pub async fn execute(
         21 => twenty_one::main(),
         23 => twenty_three::main(),
         24 => twenty_four::main(),
+        25 => twenty_five::main(),
         _ => {
             exists = false;
             println!(