use std::ops;

fn det(m: &[f64], x: usize) -> f64 {
    if x == 1 {
        m[0]
    } else if x == 2 {
        m[0] * m[3] - m[1] * m[2]
    } else {
        let mut d = 0.0;

        for n in 0..x {
            let ms = m
                .iter()
                .enumerate()
                .skip(x)
                .filter(|(i, _)| (i % x) != n)
                .map(|(_, v)| *v)
                .collect::<Vec<_>>();

            d += (-1.0f64).powi(n as i32) * m[n] * det(&ms, x - 1);
        }

        d
    }
}

#[derive(Clone, Debug)]
pub struct Matrix {
    data: Box<[f64]>,
    height: usize,
    width: usize,
}

impl Matrix {
    pub fn new(height: usize, width: usize) -> Matrix {
        Matrix {
            data: vec![0.0; height * width].into_boxed_slice(),
            height,
            width,
        }
    }

    pub fn transpose(&self) -> Matrix {
        let mut matrix = Matrix::new(self.width, self.height);

        for c in 0..self.width {
            for r in 0..self.height {
                matrix[(c, r)] = self[(r, c)];
            }
        }

        matrix
    }

    pub fn minor(&self, row_n: usize, col_n: usize) -> Matrix {
        let mut matrix = Matrix::new(self.height - 1, self.width - 1);

        let mut nr = 0;

        for r in 0..self.height {
            if r == row_n {
                continue;
            }

            let mut nc = 0;

            for c in 0..self.width {
                if c == col_n {
                    continue;
                }

                matrix[(nr, nc)] = self[(r, c)];

                nc += 1;
            }

            nr += 1;
        }

        matrix
    }

    pub fn determinant(&self) -> f64 {
        debug_assert!(self.width == self.height);

        det(&self.data, self.width)
    }

    pub fn adjugate(&self) -> Matrix {
        debug_assert!(self.width == self.height);

        let mut matrix = Matrix::new(self.height, self.width);

        if matrix.height == 2 {
            matrix[(0, 0)] = self[(1, 1)];
            matrix[(0, 1)] = -self[(0, 1)];
            matrix[(1, 0)] = -self[(1, 0)];
            matrix[(1, 1)] = self[(0, 0)];
        } else {
            for r in 0..matrix.height {
                for c in 0..matrix.width {
                    let sign = if (r + c) % 2 == 0 { 1.0 } else { -1.0 };

                    matrix[(r, c)] = self.minor(r, c).determinant() * sign;
                }
            }
        }

        matrix
    }

    pub fn inverse(&self) -> Matrix {
        let mut matrix = Matrix::new(self.width, self.height);

        if self.height == self.width && self.height == 1 {
            matrix[(0, 0)] = 1.0 / self[(0, 0)];
        } else {
        }

        matrix
    }
}

impl ops::Index<(usize, usize)> for Matrix {
    type Output = f64;

    fn index(&self, pos: (usize, usize)) -> &Self::Output {
        &self.data[(self.width * pos.0) + pos.1]
    }
}

impl ops::IndexMut<(usize, usize)> for Matrix {
    fn index_mut(&mut self, pos: (usize, usize)) -> &mut Self::Output {
        &mut self.data[(self.width * pos.0) + pos.1]
    }
}

impl<'a> ops::Mul<&'a Matrix> for f64 {
    type Output = Matrix;

    fn mul(self, rhs: &'a Matrix) -> Matrix {
        let mut matrix = Matrix::new(rhs.height, rhs.width);

        for r in 0..rhs.height {
            for c in 0..rhs.width {
                matrix[(r, c)] = self * rhs[(r, c)];
            }
        }

        matrix
    }
}

impl<'a> ops::Mul<&'a Matrix> for Matrix {
    type Output = Matrix;

    fn mul(self, rhs: &'a Matrix) -> Matrix {
        let mut matrix = Matrix::new(self.height, rhs.width);

        for r in 0..matrix.height {
            for c in 0..matrix.width {
                let mut value = 0.0;

                for x in 0..self.width {
                    value += self[(r, x)] * rhs[(x, c)];
                }

                matrix[(r, c)] = value;
            }
        }

        matrix
    }
}

impl<'a> ops::Mul<&'a Matrix> for &'a Matrix {
    type Output = Matrix;

    fn mul(self, rhs: &'a Matrix) -> Matrix {
        let mut matrix = Matrix::new(self.height, rhs.width);

        for r in 0..matrix.height {
            for c in 0..matrix.width {
                let mut value = 0.0;

                for x in 0..self.width {
                    value += self[(r, x)] * rhs[(x, c)];
                }

                matrix[(r, c)] = value;
            }
        }

        matrix
    }
}

impl<'a> ops::Add<&'a Matrix> for &'a Matrix {
    type Output = Matrix;

    fn add(self, rhs: &'a Matrix) -> Matrix {
        let mut matrix = Matrix::new(self.height, self.width);

        for r in 0..matrix.height {
            for c in 0..matrix.width {
                matrix[(r, c)] = self[(r, c)] + rhs[(r, c)];
            }
        }

        matrix
    }
}