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;;
;; helper methods for euler.clj - trying to learn some clojure
;; by working through some of the problems in http://www.projecteuler.net
;;
(ns euler
  (:use clojure.contrib.math))

;; Fibonacci value calculation - using tail recursion!
;; used in: prob-2.
;; TODO: simplify using (loop ..)
(defn fib
  "return the fibonacci value for a given number"
  ([nn] (fib nn 0 1))
  ([nn cur nxt]
   (if (= nn 0)
     cur
     (recur (- nn 1) nxt (+ cur nxt)))))


;; calculate the factorial of a positive integer
(defn fact
  "Factorial of a number"
  ([nn] (fact nn 1))
  ([nn acc]
   (if (zero? nn)
     acc
     (recur (- nn 1) (* acc nn)))))

;; Test if a given number is a prime one
(defn prime?
  "Uses Wilson's theorem to determine if a number is prime. Not too efficient."
  [nn]
  (if (or (= 0 nn) (= 1 nn))
    false
    (if (or (= 2 nn) (= 3 nn))
      true
      (=
        (mod (fact (dec nn)) nn)
        (dec nn)))))


;; list of primes up to given nn. Uses the Sieve of Eratosthenes
;; algorithm.
(defn primes
  "return a list of all prime numbers up to given value"
  [nn]
  (loop [i 0 lst (range 2 nn)]
    (let [value (nth lst i)
          multiple? #(and (not= % value) (= 0 (mod % value)))]
      (if (or (>= value nn) (= value (last lst)))
        lst
        (recur (+ i 1) (filter #(not (multiple? %)) lst))))))

;; get the max prime factor for a given number
(defn max-prime
  "Given a number nn, determine the largest prime factor"
  [nn]
  ;; the list of primes is sorted in ascending order -
  ;; start from the end (max value) and check to see
  ;; if it divides by the given number. If not, proceed
  ;; to the next largest.
  (loop [values (primes (ceil (sqrt nn)))]
    (let [tail (last values)]
      (do ;;(println values) (println tail)
        (if (= 0 (mod nn tail))
          tail
          (recur (drop-last values)))))))