## Project Euler : Problem 018

Project Euler problems in Oforth . Feel free to post your own code.

### Project Euler : Problem 018

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)

Code: Select all
`ListBuffer new[ 75 ] over add[95, 64 ] over add[17, 47, 82 ] over add[18, 35, 87, 10 ] over add[20, 04, 82, 47, 65 ] over add[19, 01, 23, 75, 03, 34 ] over add[88, 02, 77, 73, 07, 63, 67 ] over add[99, 65, 04, 28, 06, 16, 70, 92 ] over add[41, 41, 26, 56, 83, 40, 80, 70, 33 ] over add[41, 48, 72, 33, 47, 32, 37, 16, 94, 29 ] over add[53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14 ] over add[70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57 ] over add[91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48 ] over add[63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31 ] over add[04, 62, 98, 27, 23, 09, 70, 98, 73, 93, 38, 53, 60, 04, 23 ] over adddup freeze Constant new: TRIANGLE: pe018   // ( -- [n] ) : Sum for max path{| i t |   TRIANGLE size 1 -1 step: i [      TRIANGLE at(i)      // If not the last line, add it to the previous calculated one      i TRIANGLE size <> ifTrue: [ zipWith(#+) ] ->t      // If not the first line, calculates all max for 2 consecutive numbers      t i 1 == ifFalse: [ t t right(t size 1 -) zipWith(#max) ]      ]}`
Franck

Posts: 163
Joined: 29 Oct 2014 19:01