computorv1/src/lib.rs

use std::error::Error;
use crate::parser::tokenizer::tokenize;
use crate::parser::sanitizer::sanitize_tokens;
use crate::parser::ast_builder::{build_ast, Node};
use crate::maths::GaussianRational;

pub mod parser;
pub mod maths;


pub fn format(v: &Vec<GaussianRational>) -> String {
    let mut format;
    format = v[0].format();
    if v.len() > 1 {
        if format == "" {
            format = format!("{}x", v[1].format());
        } else {
            format = format!("{format} + {}x", v[1].format());
        }
    }
    for i in 2..v.len() {
        let tmp = v[i].format();
        if tmp != "" {
            if format == ""{
                format = format!("{tmp}x^{i}");
            } else {
                format = format!("{format} + {}x^{i}", tmp);
            }
        }
    }
    format = format.split("+ -").collect::<Vec<_>>().join("- ");
    format = format.split("1x").collect::<Vec<_>>().join("x");
    format.split("1i").collect::<Vec<_>>().join("i")
}

pub fn parse(query: &str) -> Result<Node, Box<dyn Error>> {
    let tokens = tokenize(query)?;
    let sanitized_tokens = sanitize_tokens(tokens)?;
    let ast = build_ast(sanitized_tokens);

    Ok(ast)
}

fn print_reduced_form(equation: &Vec<f64>) {
    let mut string = String::from("Reduced form: ");

    for (i, n) in equation.iter().enumerate() {
        let mut n = *n;
        if n < 0. {
            string += " - ";
            n *= -1.;
        } else if i != 0 {
            string += " + ";
        }
        string.push_str(&n.to_string());
        string.push_str(" * X^");
        string.push_str(&i.to_string());
    }
    string += " = 0";

    println!("{string}");
}

fn sqrt(n: f64) -> f64 {
    let mut z = 1.;

    for _ in 0..10 {
        z -= (z * z - n) / (2. * z);
    }

    z
}

fn solve_degree_0(equation: Vec<f64>) {
    if equation[0] == 0. {
        println!("Each real number is a solution.");
    } else {
        println!("There are no solutions to this equation");
    }
}

fn solve_degree_1(equation: Vec<f64>) {
    println!("The solution is:");
    println!("{}", -1. * equation[0] / equation[1]);
}

fn solve_degree_2(equation: Vec<f64>) {
    let delta = equation[1] * equation[1] - 4. * equation[2] * equation[0];

    if delta > 0. {
        let sqrt_delta = sqrt(delta);
        let x1 = (-equation[1] - sqrt_delta) / (2. * equation[2]);
        let x2 = (-equation[1] + sqrt_delta) / (2. * equation[2]);
        println!("Discriminant is strictly positive, the two solutions are:");
        println!("{x1}");
        println!("{x2}");
    } else if delta < 0. {
        let sqrt_delta = sqrt(delta);
        let a = -equation[1] / (2. * equation[2]);
        let b = sqrt_delta / (2. * equation[2]);
        println!("Discriminant is strictly negative, the two complex solutions are:");
        println!("{a} + {b}i");
        println!("{a} - {b}i");
    } else {
        let x = -equation[1] / (2. * equation[2]);
        println!("Discriminant is zero, the solution is:");
        println!("{x}");
    }
}

pub fn solve(equation: Vec<f64>) {
    let degree = equation.len() - 1;

    print_reduced_form(&equation);
    println!("Polynomial degree: {degree}");
    match degree {
        0 => solve_degree_0(equation),
        1 => solve_degree_1(equation),
        2 => solve_degree_2(equation),
        _ if degree > 2 => println!("The polynomial degree is strictly greater than 2, I can't solve."),
        _ => unreachable!(),
    }
}