(ns ConnectedGraph)

(def input1 #{[1 2] [2 3] [3 1] [4 5] [5 6] [6 4]})

;(def candidate (first (first input1)))

;(println candidate)

;(def nodes (into [] (disj (reduce #(into %1 %2) #{} input1) candidate)))

;(println nodes)

;(defn getNext [s x] (into s (filter #(some #{x} %1) input1)))

;(defn nextLevel [level visited] (apply disj (into #{} (flatten (reduce getNext [] level))) (into level visited)))

;(defn connectedPair? [root cand graph] (loop [visited #{cand} next #{cand}] (cond

; (empty? (nextLevel next visited)) false

; (some #{root} (nextLevel next visited)) true

; :default (recur (into visited next) (nextLevel next visited)))))

(defn connected? [graph] (let [candidate (first (first graph))

nodes (into [] (disj (reduce #(into %1 %2) #{} graph) candidate))

getNext (fn [s x] (into s (filter #(some #{x} %1) graph)))

nextLevel (fn [level visited] (apply disj (into #{} (flatten (reduce getNext [] level))) (into level visited)))

connectedPair? (fn [root cand] (loop [visited #{cand} next #{cand}] (cond

(empty? (nextLevel next visited)) false

(some #{root} (nextLevel next visited)) true

:default (recur (into visited next) (nextLevel next visited)))))

] (if (= 1 (count graph)) true (every? #(connectedPair? candidate %1) nodes))))

(println (connected? input1))