# 1ae69146e0e2

`Problem 18`
author Steve Losh Mon, 13 Feb 2017 18:58:19 +0000 686f62d102f5 9d7ea7bf528b (none) euler.asd src/euler.lisp

## Changes

```--- a/euler.asd	Mon Feb 13 13:32:08 2017 +0000
+++ b/euler.asd	Mon Feb 13 18:58:19 2017 +0000
@@ -10,13 +10,9 @@

:depends-on (

-               :fare-quasiquote-optima
:fiveam
:iterate
:losh
-               :optima
-               :trivial-types

)
```
```--- a/src/euler.lisp	Mon Feb 13 13:32:08 2017 +0000
+++ b/src/euler.lisp	Mon Feb 13 18:58:19 2017 +0000
@@ -475,6 +475,44 @@
(sum (range 1 (1+ 1000))
:key #'silly-british-letters)))

+(defun problem-18 ()
+  ;; 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.
+  ;;
+  ;; 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)
+  (let ((triangle '((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))))
+    (car (reduce (lambda (last next)
+                   (mapcar #'+
+                           (mapcar #'max last (rest last))
+                           next))
+                 (reverse triangle)))))
+

;;;; Tests --------------------------------------------------------------------
(def-suite :euler)
@@ -497,6 +535,7 @@
(test p15 (is (= 137846528820 (problem-15))))
(test p16 (is (= 1366 (problem-16))))
(test p17 (is (= 21124 (problem-17))))
+(test p18 (is (= 1074 (problem-18))))

;; (run! :euler)```