7.3. Topological Sorting

public List<Integer> topological_sort(boolean depth_first) {
    Deque<Integer> global = getVerticesWithNoIncomingEdges();
    List<Deque<Edge>> outgoingEdgesAll = getOutgoingEdges();
    List<Integer> order = new ArrayList<>();

    while (!global.isEmpty()) {
        Deque<Integer> local = new ArrayDeque<>();
        int vertex = global.poll();
        order.add(vertex);
        Deque<Edge> outgoingEdges = outgoingEdgesAll.get(vertex);
        
        while (!outgoingEdges.isEmpty()) {
            Edge edge = outgoingEdges.poll();

            //Remove edge in all incomingEdges of the target vertex
            List<Edge> incomingEdges = getIncomingEdges(edge.getTarget());
            incomingEdges.remove(edge);

            //If the vertex has no incoming edges, add it to the local queue awaited to be added to the global deque
            if (incomingEdges.isEmpty())
                local.add(edge.getTarget());
        }

        //Transfer all vertices in local to global
        while (!local.isEmpty())
            if (depth_first) global.addFirst(local.removeLast());
            else global.addLast(local.removeFirst());
    }

    if (!hasNoEdge()) throw new IllegalArgumentException("Cyclic graph.");
    return order;
}