ladder

ladder.cs

void Main()
{
    var N = 5;
    
    Node.Graph.Add(new Node());
    
    bool canExpand = true;
    while (canExpand)
    {  
        Func<int, IEnumerable<Move>> addNodes = steps => from c in Node.Graph
                                                         where c.IsLeaf && (c.Value + steps) <= N
                                                         select new Move { Node = c, Steps = steps };
        
        var moves = addNodes(1).Union(addNodes(2)).ToList();

        if(moves.Count > 0)
        {
            moves.ForEach(c => c.Node.AddChild(c.Steps));
        }
        else
        {
            canExpand = false;
        }
        
        Console.WriteLine (moves.Count);
       
    }

    foreach (var node in Node.Graph.Where(c => c.IsLeaf))
    { 
        node.GetSolution().Dump("Result");
    }
}

struct Move
{
    public Node Node { get; set; }
    public int Steps { get; set; }
}

struct Solution
{
    public int[] Steps { get; set; }
}

class Node
{
    public Node()
    {
        this.Children = new List<Node>();
        this.Id = ++NodeCount;
    }
    
    public Node(Node parent, int steps)
        : this()
    {
        this.Parent = parent;
        this.Steps = steps;
        this.Value = parent.Value + steps;
    }
    
    public void AddChild(int steps)
    {
        var node = new Node(this, steps);
        this.Children.Add(node);
        Graph.Add(node);
    }
    
    public Solution GetSolution()
    {
        var list = new LinkedList<int>();
        var parent = this;
        while (parent != null)
        {
            if(parent.Steps > 0)
            {
                list.AddFirst(parent.Steps);
            }
            parent = parent.Parent;
        }
        return new Solution { Steps = list.ToArray() };
    }
    
    public int Id { get; set; }
    
    public Node Parent { get; set; } 
    
    public List<Node> Children { get; set; } 
    
    public int Value { get; set; }
    
    public int Steps { get; set; }  
    
    public bool IsLeaf { get { return Children.Count == 0; } } 
    
    public static List<Node> Graph = new List<Node>();
    
    public static int NodeCount { get; set; }
}