let calcUpperBound problem =
    let N = problem.nodeCount
    let findEdge = getEdge problem.graph

    let rec loop tour unvisitedNodes includedEdges =
        match tour with
        | [] -> failwith "Empty list is bad"
        | xs when xs.Length = N -> tour
        | current :: xs ->
            let f = List.tryFind (fun f -> f.node1 = current || f.node2 = current) includedEdges
            match f with
            | Some(edge) ->
                let next =
                    if edge.node1 = current then edge.node2
                    else edge.node1
                loop (next :: tour) (removeFirst current unvisitedNodes) (removeFirst edge includedEdges)
            | None ->
                let next =
                    List.map (fun x -> (x, findEdge current x |> edgeWeight)) unvisitedNodes
                    |> List.minBy (fun (_, weight) -> weight)
                    |> fst
                loop (next :: tour) (removeFirst current unvisitedNodes) includedEdges

    let allNodes = [ 0..problem.nodeCount - 1 ]

    let makeTour i =
        let t = loop [ i ] (removeFirst i allNodes) (List.ofSeq problem.includedEdges)

        let tour: Graph.Tour =
            { nodes = t
              totalWeight = tourWeight problem.graph t }
        tour
    let results = List.map makeTour allNodes
    List.minBy (fun (f: Graph.Tour) -> f.totalWeight) results