Week 1 - problem #2

gistfile1.clj

(ns codelesson.week1
    (:require [clojure.math.combinatorics :as mc]))

(defn add-up [coeffs terms]
  "ax + by + cz + ...
   this adds up a Specific set of coefficients for terms(coins)"
  (reduce + (map #(* %1 %2) coeffs terms)))

(defn coeffs [dollar coin]
  "return a sequence of coeffs from 0 to the divisor of the dollar amt by the coin
   this is the range of possible coefficients for a given coin!"
   (vec (range (inc (/ dollar coin)))))

(defn coeffs-for-all-terms [dollar coins]
  "creates a map of coins to their range of possible coefficients that add up to dollar"
  (loop [coin (first coins)
         rcoins (rest coins)
         allcoeffs (array-map coin (coeffs dollar coin)) ]
        (if-not (empty? rcoins)
                (recur (first rcoins) (rest rcoins) (assoc allcoeffs (first rcoins) ( coeffs dollar (first rcoins))))
                allcoeffs)))

(defn coeff-seq [dollar coins]
  "A sequence of possible coeffecients for the coins to add up to dollar
  may need lazy seq...this is huge!"
  (apply mc/cartesian-product (vals (coeffs-for-all-terms dollar (sort coins)))))

(defn less-brutal-binomnoms [coins dollar]
  (let [massive-possibilities (coeff-seq dollar coins)]
    (count
      (filter #(= dollar (add-up % coins)) massive-possibilities))))