peuler 0.1.0

A Rust crate with solutions to the Project Euler problems
Documentation 
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use crate::Solution;

problem!(Problem0025, 25, "1000-digit Fibonacci Number");

impl Solution for Problem0025 {
    fn solve(&self) -> String {
        // let a = (1 + sqrt(5)) / 2
        // let b = (1 - sqrt(5)) / 2
        // we can use binet's formula to calculate the nth fibonacci number
        // f(n) = (a^n - b^n) / sqrt(5)

        // we know that the wanted number needs to have at least 1000 digits
        // we first find the smallest number with 1000 digits, that is 10^999
        // now we want to find the first n for which f(n) >= 10^999

        // since b is smaller than 1, b^n will be very small for large n so we can ignore it
        // now binet's formula becomes f(n) = a^n / sqrt(5)

        // plugging that into the inequality, we get a^n / sqrt(5) >= 10^999
        // after some manipulation, we get n >= (999 + log(5) / 2) / log(a)
        // now the only thing left is to find the smallest integer n that satisfies this inequality

        (((999.0_f64 + (5.0_f64.log10() / 2.0_f64))
            / ((1.0_f64 + 5.0_f64.sqrt()) / 2.0_f64).log10())
        .ceil() as u64)
            .to_string()
    }
}

// this is the slow, manual solution that actually calculates the fibonacci numbers
// fn solve() {
//     let mut fibonacci: Vec<Vec<u64>> = vec![vec![1], vec![1]];
//     let mut fibonacci_index: u64 = 2;
//
//     while fibonacci[1].len() < 1000 {
//         let mut result: Vec<u64> = vec![];
//
//         let mut transfer: u64 = 0;
//         for j in (0..fibonacci[1].len()).rev() {
//             let mut working_sum: u64 = transfer;
//             for i in 0..2 {
//                 working_sum += fibonacci[i][j];
//             }
//             result.insert(0, working_sum % 10);
//             transfer = working_sum / 10;
//         }
//         while transfer != 0 {
//             result.insert(0, transfer % 10);
//             transfer /= 10;
//         }
//
//         fibonacci.push(result);
//         fibonacci.remove(0);
//
//         for _ in 0..(fibonacci[1].len() - fibonacci[0].len()) {
//             fibonacci[0].insert(0, 0);
//         }
//
//         fibonacci_index += 1;
//     }
//
//     println!("{}", fibonacci_index);
// }