greplin-challenge-solution

(ns clojure-scratch.gettysburg
  (:require [clojure.contrib.lazy-seqs :as ls]
            [clojure.contrib.combinatorics :as comb]))

;; level-one

(def level-one "FourscoreandsevenyearsagoourfaathersbroughtforthonthiscontainentanewnationconceivedinzLibertyanddedicatedtothepropositionthatallmenarecreatedequalNowweareengagedinagreahtcivilwartestingwhetherthatnaptionoranynartionsoconceivedandsodedicatedcanlongendureWeareqmetonagreatbattlefiemldoftzhatwarWehavecometodedicpateaportionofthatfieldasafinalrestingplaceforthosewhoheregavetheirlivesthatthatnationmightliveItisaltogetherfangandproperthatweshoulddothisButinalargersensewecannotdedicatewecannotconsecratewecannothallowthisgroundThebravelmenlivinganddeadwhostruggledherehaveconsecrateditfaraboveourpoorponwertoaddordetractTgheworldadswfilllittlenotlenorlongrememberwhatwesayherebutitcanneverforgetwhattheydidhereItisforusthelivingrathertobededicatedheretotheulnfinishedworkwhichtheywhofoughtherehavethusfarsonoblyadvancedItisratherforustobeherededicatedtothegreattdafskremainingbeforeusthatfromthesehonoreddeadwetakeincreaseddevotiontothatcauseforwhichtheygavethelastpfullmeasureofdevotionthatweherehighlyresolvethatthesedeadshallnothavediedinvainthatthisnationunsderGodshallhaveanewbirthoffreedomandthatgovernmentofthepeoplebythepeopleforthepeopleshallnotperishfromtheearth")

(defn palindrone? [w]
  (= w (apply str (reverse w))))

(defn longest-palindrone-in [s]
  (loop [l 2
         winner ""]
    (if (= l (count s))
      winner
      (let [words (map #(apply str %) (partition l 1 s))
            palindrones (filter palindrone? words)]
        (recur (inc l)
               (or (first palindrones)
                   winner))))))

(time
 (println (longest-palindrone-in level-one))) ;; answer = ranynar

;; level-two

(defn prime? [n]
  (loop [i (int (Math/sqrt n))]
    (if (<= i 1)
      true
      (if (= 0 (mod n i))
        false
        (recur (dec i))))))

(defn prime-fibs []
  (filter prime? (ls/fibs)))

(time (println (first (filter #(> % 227000) (prime-fibs))))) ;; 514229

(defn prime-divisors [n]
  (distinct (filter (fn [p] 
                      (= (mod n p) 0))
                    (take-while (fn [p] (<= (* p p) n)) 
                                ls/primes))))

(time (println (apply + (prime-divisors 514230)))) ;; 352

;; level-three

(def numbers [3 4 9 14 15 19 28 37 47 50 54 56 59 61 70 73 78 81 92 95 97 99])

(defn largest-is-sum-of-others? [l]
  (let [l (reverse (sort l))
        largest (first l)
        others (rest l)]
    (= largest (apply + others))))

(defn solve [n]
  (loop [res []
         i 3]
    (if (> i (count n))
      (count res)
      (recur (into res
                   (filter largest-is-sum-of-others?
                           (comb/combinations n i)))
             (inc i)))))

(time println (solve numbers)) ;; 179