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use std::cmp::PartialEq;
use std::fmt::Display;
use std::ops::{Add, AddAssign, Mul, Sub};

#[derive(Debug, Clone)]
/// Polynomials
pub struct Pol(Vec<f64>);

impl Pol {
    /// Create polynomials form vector
    pub fn new(input: Vec<f64>) -> Pol {
        if input.is_empty() {
            return Pol(vec![0.]);
        }
        Pol(input)
    }
}

impl Display for Pol {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        let mut result = String::new();

        for (i, el) in self.0.iter().enumerate() {
            if *el != 0. {
                let el_str = (el.abs()).to_string();
                let i_str = i.to_string();

                result += &format!(
                    "{} {}{}{}{} ",
                    if *el > 0. { "+" } else { "-" },
                    if *el != 1. && *el != -1. { &el_str } else { "" },
                    if i != 0 { "x" } else { "" },
                    if i != 0 && i != 1 { "^" } else { "" },
                    if i != 1 { &i_str } else { "" }
                );
            }
        }

        write!(f, "{}", result)
    }
}

impl Add for Pol {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        let mut result: Vec<f64> = vec![
            0.;
            if self.0.len() >= other.0.len() {
                self.0.len()
            } else {
                other.0.len()
            }
        ];

        for (i, el) in result.iter_mut().enumerate() {
            let first = if i < self.0.len() { self.0[i] } else { 0. };
            let second = if i < other.0.len() { other.0[i] } else { 0. };

            *el = first + second;
        }

        Pol(result)
    }
}

impl AddAssign for Pol {
    fn add_assign(&mut self, rhs: Self) {
        if self.0.len() >= rhs.0.len() {
            for (i, el) in rhs.0.iter().enumerate() {
                self.0[i] += el;
            }
        } else {
            for (i, el) in self.0.iter_mut().enumerate() {
                *el += rhs.0[i];
            }

            for i in self.0.len()..rhs.0.len() {
                self.0.push(rhs.0[i]);
            }
        }
    }
}

impl Sub for Pol {
    type Output = Self;

    fn sub(self, other: Self) -> Self {
        let mut result: Vec<f64> = vec![
            0.;
            if self.0.len() >= other.0.len() {
                self.0.len()
            } else {
                other.0.len()
            }
        ];

        for (i, el) in result.iter_mut().enumerate() {
            let first = if i < self.0.len() { self.0[i] } else { 0. };
            let second = if i < other.0.len() { other.0[i] } else { 0. };

            *el = first - second;
        }

        Pol(result)
    }
}

impl Mul for Pol {
    type Output = Self;

    fn mul(self, rhs: Self) -> Self {
        let mut result = Pol(vec![0.; self.0.len() + rhs.0.len() - 1]);

        for (i, s_el) in self.0.iter().enumerate() {
            let mut inter = vec![0.; i];
            for r_el in rhs.0.iter() {
                inter.push(s_el * r_el);
            }

            result += Pol(inter);
        }

        result
    }
}
impl<'a> Mul<&'a Pol> for &'a Pol {
    type Output = Pol;

    fn mul(self, rhs: Self) -> Self::Output {
        let mut result = Pol(vec![0.; self.0.len() + rhs.0.len() - 1]);

        for (i, s_el) in self.0.iter().enumerate() {
            let mut inter = vec![0.; i];
            for r_el in rhs.0.iter() {
                inter.push(s_el * r_el);
            }

            result += Pol(inter);
        }

        result.clone()
    }
}

impl<'a> Mul<&'a Pol> for Pol {
    type Output = Pol;

    fn mul(self, rhs: &'a Pol) -> Self::Output {
        let mut result = Pol(vec![0.; self.0.len() + rhs.0.len() - 1]);

        for (i, s_el) in self.0.iter().enumerate() {
            let mut inter = vec![0.; i];
            for r_el in rhs.0.iter() {
                inter.push(s_el * r_el);
            }

            result += Pol(inter);
        }

        result.clone()
    }
}

impl PartialEq for Pol {
    fn eq(&self, other: &Self) -> bool {
        if self.0.len() != other.0.len() {
            return false;
        } else {
            for i in 0..self.0.len() {
                if self.0[i] != other.0[i] {
                    return false;
                }
            }
        }

        true
    }
}