Euler: Problem 106

pe_106.clj

(ns euler.pe_106
  (:require [clojure.math.combinatorics :as combo]))
;; Prablem 106
;; "Elapsed time: 456.3979 msecs"


(defn create-sets [basel m]
  (let [pair-a (combo/combinations basel m)]
    (reduce into #{}
            (for [pair pair-a]
              (let [reminder (sort (clojure.set/difference (set basel) (set pair)))]
                (->> (combo/combinations reminder m)
                     (map #(if (< (first pair) (first %))
                             (vector pair %)
                             (vector % pair)) ,,)))))))

(defn needs_verify? [[a b]]
  (let [comparison (map > a b)]
    (not
     (or (every? true? comparison)
         (every? false? comparison)))))

(defn part-size-list [N]
  (range 2 (+ 1 (quot N 2))))

(defn base-list [N]
  (range 1 (+ 1 N)))

(defn pe106-check [N]
  (let [basel (base-list N)
        m-list (part-size-list N)]
    (apply + 
           (for [m m-list]
             (->> (create-sets basel m)
                  (map needs_verify? ,,)
                  (filter true? ,,)
                  (count))))))