solution.clj

(defn get-topic-children [topics topic-id]
  (map first (filter #(= topic-id (:parent (second %))) topics)))

(defn get-routes [topics topic-id & [slug-so-far]]
  (let [children (get-topic-children topics topic-id)
        newslug (if (= topic-id :root) ""
                    (str slug-so-far "/" (:slug (get topics topic-id))))]
    (if children
      (into (if (= topic-id :root) {} {topic-id newslug})
            (map #(get-routes topics % newslug) children))
      {topic-id newslug})))

(let [topics {1 {:parent :root, :slug "lovely"}
              2 {:parent 1, :slug "lovelier"}
              3 {:parent 1, :slug "loveliest"}
              4 {:parent :root, :slug "cool"}}
  (get-routes topics :root))