use std::cmp;

use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};

#[derive(PartialEq, Eq, Clone, Copy, Debug)]

pub struct Point {

    pub x: i32,

    pub y: i32,

}

impl Point {

    #[inline]

    pub fn new(x: i32, y: i32) -> Self {

        Self { x, y }

    }

    #[inline]

    pub fn zero() -> Self {

        Self::new(0, 0)

    }

    #[inline]

    pub fn signum(self) -> Self {

        Self::new(self.x.signum(), self.y.signum())

    }

    #[inline]

    pub fn abs(self) -> Self {

        Self::new(self.x.abs(), self.y.abs())

    }

    #[inline]

    pub fn dot(self, other: Point) -> i32 {

        self.x * other.x + self.y * other.y

    }

    #[inline]

    pub fn max_norm(self) -> i32 {

        std::cmp::max(self.x.abs(), self.y.abs())

    }

    #[inline]

    pub fn transform(self, matrix: &[i32; 4]) -> Self {

        Point::new(matrix[0] * self.x + matrix[1] * self.y,

                   matrix[2] * self.x + matrix[3] * self.y)

    }

}

macro_rules! bin_op_impl {

    ($op: ty, $name: tt) => {

        impl $op for Point {

            type Output = Self;

            #[inline]

            fn $name(self, rhs: Self) -> Self::Output {

                Self::new(self.x.$name(rhs.x), self.y.$name(rhs.y))

            }

        }

    };

}

macro_rules! bin_assign_op_impl {

    ($op: ty, $name: tt) => {

        impl $op for Point {

            #[inline]

            fn $name(&mut self, rhs: Self) {

                self.x.$name(rhs.x);

                self.y.$name(rhs.y);

            }

        }

    };

}

bin_op_impl!(Add, add);

bin_op_impl!(Sub, sub);

bin_op_impl!(Mul, mul);

bin_op_impl!(Div, div);

bin_assign_op_impl!(AddAssign, add_assign);

bin_assign_op_impl!(SubAssign, sub_assign);

bin_assign_op_impl!(MulAssign, mul_assign);

bin_assign_op_impl!(DivAssign, div_assign);

pub struct LinePoints {

    accumulator: Point,

    direction: Point,

    sign: Point,

    current: Point,

    total_steps: i32,

    step: i32,

}

impl LinePoints {

    pub fn new(from: Point, to: Point) -> Self {

        let dir = to - from;

        Self {

            accumulator: Point::zero(),

            direction: dir.abs(),

            sign: dir.signum(),

            current: from,

            total_steps: dir.max_norm(),

            step: 0,

        }

    }

}

impl Iterator for LinePoints {

    type Item = Point;

    fn next(&mut self) -> Option<Self::Item> {

        if self.step <= self.total_steps {

            self.accumulator += self.direction;

            if self.accumulator.x > self.total_steps {

                self.accumulator.x -= self.total_steps;

                self.current.x += self.sign.x;

            }

            if self.accumulator.y > self.total_steps {

                self.accumulator.y -= self.total_steps;

                self.current.y += self.sign.y;

            }

            self.step += 1;

            Some(self.current)

        } else {

            None

        }

    }

}

pub struct ArcPoints {

    point: Point,

    step: i32,

}

impl ArcPoints {

    pub fn new(radius: i32) -> Self {

        Self {

            point: Point::new(0, radius),

            step: 3 - 2 * radius,

        }

    }

}

impl Iterator for ArcPoints {

    type Item = Point;

    fn next(&mut self) -> Option<Self::Item> {

        if self.point.x < self.point.y {

            let result = self.point;

            if self.step < 0 {

                self.step += self.point.x * 4 + 6;

            } else {

                self.step += (self.point.x - self.point.y) * 4 + 10;

                self.point.y -= 1;

            }

            self.point.x += 1;

            Some(result)

        } else if self.point.x == self.point.y {

            self.point.x += 1;

            Some(self.point)

        } else {

            None

        }

    }

}

pub struct EquidistantPoints {

    vector: Point,

    iteration: u8,

}

impl EquidistantPoints {

    pub fn new(vector: Point) -> Self {

        Self {

            vector,

            iteration: if vector.x == vector.y { 4 } else { 8 },

        }

    }

}

impl Iterator for EquidistantPoints {

    type Item = Point;

    fn next(&mut self) -> Option<Self::Item> {

        if self.iteration > 0 {

            self.vector.x = -self.vector.x;

            if self.iteration & 1 == 0 {

                self.vector.y = -self.vector.y;

            }

            if self.iteration == 4 {

                std::mem::swap(&mut self.vector.x, &mut self.vector.y);

            }

            self.iteration -= 1;

            Some(self.vector)

        } else {

            None

        }

    }

}

#[cfg(test)]

mod tests {

    use super::*;

    fn get_points(coords: &[(i32, i32)]) -> Vec<Point> {

        coords.iter().map(|(x, y)| Point::new(*x, *y)).collect()

    }

    #[test]

    fn line_basic() {

        let line = LinePoints::new(Point::new(0, 0), Point::new(3, 3));

        let v = get_points(&[(0, 0), (1, 1), (2, 2), (3, 3), (123, 456)]);

        for (&a, b) in v.iter().zip(line) {

            assert_eq!(a, b);

        }

    }

    #[test]

    fn line_skewed() {

        let line = LinePoints::new(Point::new(0, 0), Point::new(5, -7));

        let v = get_points(&[

            (0, 0),

            (1, -1),

            (2, -2),

            (2, -3),

            (3, -4),

            (4, -5),

            (4, -6),

            (5, -7),

        ]);

        for (&a, b) in v.iter().zip(line) {

            assert_eq!(a, b);

        }

    }

    #[test]

    fn equidistant_full() {

        let n = EquidistantPoints::new(Point::new(1, 3));

        let v = get_points(&[

            (-1, -3),

            (1, -3),

            (-1, 3),

            (1, 3),

            (-3, -1),

            (3, -1),

            (-3, 1),

            (3, 1),

            (123, 456),

        ]);

        for (&a, b) in v.iter().zip(n) {

            assert_eq!(a, b);

        }

    }

    #[test]

    fn equidistant_half() {

        let n = EquidistantPoints::new(Point::new(2, 2));

        let v = get_points(&[(-2, -2), (2, -2), (-2, 2), (2, 2), (123, 456)]);

        for (&a, b) in v.iter().zip(n) {

            assert_eq!(a, b);

        }

    }

}