Exercise Stair with Steps

exercise.php

<?php

class Tree {
    /**
     * @var Node[]
     */
    public $nodes;

    /**
     * @var Node
     */
    public $root;

    /**
     * @var integer
     */
    public $goal;

    public function __construct(int $goal)
    {
        $this->root = new Node(0);
        $this->nodes = [];
        $this->goal = $goal;
        $this->fillNodes();
    }

    public function fillNodes(): void
    {
        $nodesToAnalyze = $this->root->bornChildren();
        $this->nodes = array_merge($this->nodes, $nodesToAnalyze);
        while(sizeof($nodesToAnalyze) > 0){
            if($nodesToAnalyze[0]->canHaveChidren($this->goal)){
                $nodesBornt = $nodesToAnalyze[0]->bornChildren();
                $this->nodes = array_merge($this->nodes, $nodesBornt);
                $nodesToAnalyze = array_merge($nodesToAnalyze, $nodesBornt);
            }
            array_shift($nodesToAnalyze);
        }
    }

    public function nodesArrived(): int
    {
        $count = 0;
        foreach ($this->nodes as $node)
            if($node->hasArrivedTo($this->goal)) $count++;

        return $count;
    }
}

class Node {
    /**
     * @var integer
     */
    public $value;
    /**
     * @var Node[]
     */
    public $children;

    /**
     * @param Node
     */
    public $parent;

    public function __construct(int $value, ?Node $parent = null)
    {
        $this->value = $value;
        $this->children = [];
        $this->parent = $parent;
    }

    public function addChild(Node $child)
    {
        if(sizeof($this->children) < 2 )
            $this->children[] = $child;
        else
            throw new Exception("Cannot add more than 2 childs to the node.");
    }

    public function canHaveChidren(int $value)
    {
        return !$this->hasArrivedTo($value) && !$this->hasPass($value);
    }

    public function bornChildren()
    {
        $this->addChild(new Node(1, $this));
        $this->addChild(new Node(2, $this));

        return $this->children;
    }

    public function inheritedValue()
    {
        if(!$this->parent) return $this->value;
        return $this->value + $this->parent->inheritedValue();
    }

    public function hasArrivedTo(int $value)
    {
        return $this->inheritedValue() === $value;
    }

    public function hasPass(int $value)
    {
        return $this->inheritedValue() > $value;
    }

}

$tree = new Tree(15);
echo $tree->nodesArrived();