extern crate num;

use std::fmt;
use std::ops::Index;
use std::cmp::PartialOrd;

pub trait Zero {
    fn zero() -> Self;
}

impl<T: num::Zero> Zero for T {
    fn zero() -> Self {
        num::Zero::zero()
    }
}

/// A k-dimension kd tree
pub struct KdTree<T> {
    location: T,
    left:  Option<Box<KdTree<T>>>,
    right: Option<Box<KdTree<T>>>,
}

impl<T, U> KdTree<T> where T: Copy + Clone + Index<usize, Output = U> + Zero, U: PartialOrd {
    pub fn new(points: &mut [T], dimension: usize) -> KdTree<T> {
        KdTree::new_with_depth(points, dimension, 0)
    }

    fn new_with_depth(points: &mut [T], dimension: usize, depth: usize) -> KdTree<T> {

        // Select axis to work on
        let axis = depth % dimension;

        // Sort the points by axis
        points.sort_by(|p1, p2| p1[axis].partial_cmp(&p2[axis]).unwrap());

        // Find the median
        let len = points.len();
        let delimiter = points.len() / 2;
        let median = points[delimiter];

        let zero = Zero::zero();
        let mut left = vec![zero; delimiter];
        left.copy_from_slice(&points[0..delimiter]);

        let right = &mut points[delimiter + 1 .. len];

        if left.len() == 0 || right.len() == 0 {
            KdTree {
                location: median,
                left:  None,
                right: None,
            }
        } else {
            KdTree {
                location: median,
                left:  Some(Box::new(KdTree::new_with_depth(&mut left, dimension, depth + 1))),
                right: Some(Box::new(KdTree::new_with_depth(right, dimension, depth + 1))),
            }
        }
    }
}

impl<T: Zero + Copy + Clone + fmt::Display + Index<usize>> KdTree<T> {
    fn print(&self, formatter: &mut fmt::Formatter, indent: &str) -> fmt::Result {
        writeln!(formatter, "{}{}", indent, self.location)?;

        if let Some(left) = self.left.as_ref() {
            left.print(formatter, &format!("{}  ", indent))?;
        }

        if let Some(right) = self.right.as_ref() {
            right.print(formatter, &format!("{}  ", indent))?;
        }

        Ok(())
    }
}

impl<T: Zero + Copy + Clone + fmt::Display + Index<usize>> fmt::Display for KdTree<T> {
    fn fmt(&self, formatter: &mut fmt::Formatter) -> fmt::Result {
        self.print(formatter, "")
    }

}