Problem 008: Largest product in a series

From Project Euler:

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

This one was pretty straightforward. You could technically do it using string manipulation, but it's easy and fast to do it with numeric manipulation. First step was just to copy-paste the giant number into a file, and load it into a constant:

(def N
  (read-string (clojure.string/replace (slurp "big_number.txt") "\n" "")))

I also wrote a few helper functions. Some of these are available through libraries, but setting up a Leiningen project for everything is a bit tedious for functions that are small:

(defn pow [a b] (reduce * 1 (repeat b a)))

(defn prod [n]
  "Multiply the digits of `n` together."
  (if (< n 10)
    n
    (* (mod n 10) (prod (quot n 10)))))

Once you do that, you can just loop across $N$, chopping off the last $k$ digits and seeing if the product of those digits is bigger than anything you've seen before:

(defn top [_n num-digits]
  (let [mask (pow 10 num-digits)]
    (loop [n _n best 0]
      (if (== n 0)
        best
        (recur (quot n 10)
               (max (prod (mod n mask))
                    best))))))

(println (top N 13))

This runs pretty quick (remember it takes ~1.5s for the JVM to start up):

$ time clj 8.clj 
23514624000N

real 0m1.569s
user 0m3.196s
sys 0m0.111s