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use std::cmp::Ordering::{Equal, Greater, Less};
use std::collections::HashSet;
use std::f64;

use Edge;
use graph::AnnotatedGraph;
use matching::Matching;

pub type Weight = f64;
pub type WeightedGraph = AnnotatedGraph<Weight>;

impl WeightedGraph {
    /// Returns a full matching with iteratively the maximum minimal weight edge.
    pub fn maximin_matching(&self) -> Option<Matching> {
        if self.is_empty() {
            return Some(Matching::new(&[]));
        }

        if self.full_matching().is_none() {
            return None;
        }

        let values: HashSet<_> = self.vertices()
            .iter()
            .flat_map(|&vertex| self.edges_from(vertex).1)
            .map(|x| x.to_bits())
            .collect();
        let mut values = values
            .into_iter()
            .map(Weight::from_bits)
            .collect::<Vec<_>>();
        values.sort_by(|&x, &y| {
            if y < x {
                Less
            } else if x.eq(&y) {
                Equal
            } else {
                Greater
            }
        });

        for value in values {
            let limited = self.limit(value);
            if let Some(matching) = limited.full_matching() {
                let mut edges: Vec<Edge> = matching
                    .edges()
                    .into_iter()
                    .filter(|edge| limited.weight(edge).eq(&value))
                    .collect();
                edges.sort_by_key(|&(v, w)| limited.vertices_from(v).min(limited.vertices_from(w)));
                let sub_matching = limited
                    .filter_vertices(|&v| v != edges[0].0 && v != edges[0].1)
                    .maximin_matching()
                    .unwrap();
                return Some(sub_matching.add(&Matching::new(&edges[0..1])));
            }
        }

        None
    }

    // Clone graph removing edges with weight less than given limit
    pub fn limit(&self, weight: Weight) -> WeightedGraph {
        self.filter_edges(|_, _, &w| w >= weight)
    }

    fn weight(&self, edge: &Edge) -> Weight {
        let (v, w) = self.edges_from(edge.0);
        *v.iter().zip(w.iter()).find(|t| *t.0 == edge.1).unwrap().1
    }
}

#[test]
fn find_match_sparse() {
    let g = [
        (0, (vec![2, 3], vec![0.1, 0.9])),
        (1, (vec![2, 3], vec![0.3, 0.2])),
        (2, (vec![0, 1], vec![0.1, 0.3])),
        (3, (vec![0, 1], vec![0.9, 0.2])),
    ].iter()
        .collect::<WeightedGraph>();
    let m = g.maximin_matching();
    assert!(m.is_some());
    if let Some(m) = m {
        assert_eq!(m.partner(0), 3);
        assert_eq!(m.partner(1), 2);
    }
}

#[test]
fn find_match_dense() {
    let g = [
        (0, (vec![1, 2, 3], vec![0.1, 0.3, 0.5])),
        (1, (vec![0, 2, 3], vec![0.1, 0.2, 0.6])),
        (2, (vec![0, 1, 3], vec![0.3, 0.2, 0.4])),
        (3, (vec![0, 1, 2], vec![0.5, 0.6, 0.4])),
    ].iter()
        .collect::<WeightedGraph>();
    let m = g.maximin_matching();
    assert!(m.is_some());
    if let Some(m) = m {
        assert_eq!(m.partner(0), 2);
        assert_eq!(m.partner(1), 3);
    }
}