/**
   * Runs the algorithm on the input graph and returns the match edge set.
   *
   * @return set of Edges
   */
  private Set<E> findMatch() {
    Set<E> result = new ArrayUnenforcedSet<>();
    match = new HashMap<>();
    path = new HashMap<>();
    contracted = new HashMap<>();

    for (V i : graph.vertexSet()) {
      // Any augmenting path should start with _exposed_ vertex
      // (vertex may not escape match-set being added once)
      if (!match.containsKey(i)) {
        // Match is maximal iff graph G contains no more augmenting paths
        V v = findPath(i);
        while (v != null) {
          V pv = path.get(v);
          V ppv = match.get(pv);
          match.put(v, pv);
          match.put(pv, v);
          v = ppv;
        }
      }
    }

    Set<V> seen = new HashSet<>();
    graph
        .vertexSet()
        .stream()
        .filter(v -> !seen.contains(v) && match.containsKey(v))
        .forEach(
            v -> {
              seen.add(v);
              seen.add(match.get(v));
              result.add(graph.getEdge(v, match.get(v)));
            });

    return result;
  }
  private V findPath(V root) {
    Set<V> used = new HashSet<>();
    Queue<V> q = new ArrayDeque<>();

    // Expand graph back from its contracted state
    path.clear();
    contracted.clear();

    graph.vertexSet().forEach(vertex -> contracted.put(vertex, vertex));

    used.add(root);
    q.add(root);

    while (!q.isEmpty()) {
      V v = q.remove();

      for (E e : graph.edgesOf(v)) {
        V to = graph.getEdgeSource(e);

        if (to.equals(v)) {
          to = graph.getEdgeTarget(e);
        }

        if ((contracted.get(v).equals(contracted.get(to))) || to.equals(match.get(v))) {
          continue;
        }

        // Check whether we've hit a 'blossom'
        if ((to.equals(root)) || ((match.containsKey(to)) && (path.containsKey(match.get(to))))) {
          V stem = lowestCommonAncestor(v, to);

          Set<V> blossom = new HashSet<>();

          markPath(v, to, stem, blossom);
          markPath(to, v, stem, blossom);

          graph
              .vertexSet()
              .stream()
              .filter(i -> contracted.containsKey(i) && blossom.contains(contracted.get(i)))
              .forEach(
                  i -> {
                    contracted.put(i, stem);
                    if (!used.contains(i)) {
                      used.add(i);
                      q.add(i);
                    }
                  });

          // Check whether we've had hit a loop (of even length (!) presumably)
        } else if (!path.containsKey(to)) {
          path.put(to, v);

          if (!match.containsKey(to)) {
            return to;
          }

          to = match.get(to);

          used.add(to);
          q.add(to);
        }
      }
    }
    return null;
  }