use num_traits::Float;

mod parser;

/*
 * NOTES
 * - each alternative should appear only once in a tree. need to figure out a
 *   way to enforce this.
 * - looks like this is like quite difficult to do through the type system
 */

#[derive(PartialEq, Eq, Debug)]
pub struct Alternative<T: Eq> {
  name: T
}

#[derive(PartialEq, Eq, Debug)]
pub struct Edge<T: Eq, U: Float> {
  weight: U,
  destination: Tree<T, U>
}

#[derive(PartialEq, Eq, Debug)]
pub enum Vertex<T: Eq, U: Float> {
  NonTerminal(Box<Edge<T, U>>, Box<Edge<T, U>>),
  Terminal(Alternative<T>),
}

#[derive(PartialEq, Eq, Debug)]
pub struct Tree<T: Eq, U: Float> {
  root: Vertex<T, U>
}

impl<T: Eq, U: Float> Tree<T, U> {
  fn left_edge_weights(&self) -> U {
    match &self.root {
      Vertex::NonTerminal(a, _) => {
        let left = &*a;
        left.weight
          + left.destination.left_edge_weights()
          + left.destination.right_edge_weights()
      },
      Vertex::Terminal(_) => U::zero()
    }
  }

  fn right_edge_weights(&self) -> U {
    match &self.root {
      Vertex::NonTerminal(_, b) => {
        let right = &*b;
        right.weight
          + right.destination.left_edge_weights()
          + right.destination.right_edge_weights()
      },
      Vertex::Terminal(_) => U::zero()
    }
  }

  pub fn choice_probability(&self, alternative: &T) -> U {
    match &self.root {
      Vertex::Terminal(alt) => {
        if alt.name == *alternative { U::one() } else { U::zero() }
      },
      Vertex::NonTerminal(a, b) => {
        let left = &*a;
        let right = &*b;
        let left_edge_weights = self.left_edge_weights();
        let right_edge_weights = self.right_edge_weights();
        let left_choice_probability =
          left.destination.choice_probability(alternative);
        let right_choice_probability =
          right.destination.choice_probability(alternative);
        (
          left_edge_weights * left_choice_probability
            + right_edge_weights * right_choice_probability
        )
          /(left_edge_weights + right_edge_weights)
      }
    }
  }
}

fn main() {
  unimplemented!();
}

#[cfg(test)]
mod test;