solution to euler 18 problem

output

problem18> (solve)
14 [4 62 98 27 23 9 70 98 73 93 38 53 60 4 23] [63 66 4 68 89 53 67 30 73 16 69 87 40 31]
13 (125 164 102 95 112 123 165 128 166 109 122 147 100 54) [91 71 52 38 17 14 91 43 58 50 27 29 48]
12 (255 235 154 150 140 179 256 209 224 172 174 176 148) [70 11 33 28 77 73 17 78 39 68 17 57]
11 (325 246 187 178 256 329 273 302 263 242 193 233) [53 71 44 65 25 43 91 52 97 51 14]
10 (378 317 231 321 354 372 393 354 360 293 247) [41 48 72 33 47 32 37 16 94 29]
9 (419 365 393 387 419 425 430 376 454 322) [41 41 26 56 83 40 80 70 33]
8 (460 434 419 475 508 470 510 524 487) [99 65 4 28 6 16 70 92]
7 (559 499 479 536 514 526 594 616) [88 2 77 73 7 63 67]
6 (647 501 613 609 533 657 683) [19 1 23 75 3 34]
5 (666 614 636 684 660 717) [20 4 82 47 65]
4 (686 640 766 731 782) [18 35 87 10]
3 (704 801 853 792) [17 47 82]
2 (818 900 935) [95 64]
1 (995 999) [75]
0 (1074) nil
1074

problem18.clj

;; By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

;; 3
;; 7 4
;; 2 4 6
;; 8 5 9 3

;; That is, 3 + 7 + 4 + 9 = 23.

;; Find the maximum total from top to bottom of the triangle below:

;; 75
;; 95 64
;; 17 47 82
;; 18 35 87 10
;; 20 04 82 47 65
;; 19 01 23 75 03 34
;; 88 02 77 73 07 63 67
;; 99 65 04 28 06 16 70 92
;; 41 41 26 56 83 40 80 70 33
;; 41 48 72 33 47 32 37 16 94 29
;; 53 71 44 65 25 43 91 52 97 51 14
;; 70 11 33 28 77 73 17 78 39 68 17 57
;; 91 71 52 38 17 14 91 43 58 50 27 29 48
;; 63 66 04 68 89 53 67 30 73 16 69 87 40 31
;; 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

;; NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

(ns problem18
  (:require [clojure.zip :as z]))

;;    3
;;   7 4
;;  2 4 6
;; 8 5 9 3

;; (def test-tree
;;         [[3]
;;         [7 4]
;;        [2 4 6]
;;       [8 5 9 3]])

;; (def test-tree
;;      [[5]
;;       [9 6]
;;       [4 6 9]
;;       [0 7 1 9]])

(def test-tree
     [[75]
      [95 64]
      [ 17 47 82]
      [ 18 35 87 10]
      [ 20 4 82 47 65]
      [ 19 1 23 75 03 34]
      [ 88 2 77 73 07 63 67]
      [ 99 65 04 28 06 16 70 92]
      [41 41 26 56 83 40 80 70 33]
      [41 48 72 33 47 32 37 16 94 29]
      [53 71 44 65 25 43 91 52 97 51 14]
      [70 11 33 28 77 73 17 78 39 68 17 57]
      [91 71 52 38 17 14 91 43 58 50 27 29 48]
      [63 66 04 68 89 53 67 30 73 16 69 87 40 31]
      [04 62 98 27 23 9 70 98 73 93 38 53 60 04 23]])

(defn row
  [n]
  (get test-tree n))

(defn reduce-pair
  [[a b]]
  (let [a-sum (apply + a)
        b-sum (apply + b)]
    (if (> a-sum b-sum) a-sum b-sum)))

(defn solve
  []
  (loop [n (dec (count test-tree))
        current-row (row n)
         above-row (row (dec n))]
    (prn n current-row above-row)
    (if (zero? n)
      (first current-row)
        (recur
         (dec n)
         (->> (interleave current-row (conj above-row 0))
              (partition 2 1)
              (partition 2)
              (map reduce-pair))
         (row (- n 2))))))