Maximum path sum II
2014-09-13
Problem 067: Maximum path sum II
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 3That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom in triangle.txt (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with one-hundred rows.
NOTE: This is a much more difficult version of [Problem 18]. It is not possible to try every route to solve this problem, as there are 299 altogether! If you could check one trillion (1012) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)
Solution:
>"d" 00p00g1-20p010p>10g3*:20g1+g"0"-55+*\1+20g1+g"0"-+10g20g1+p10g1+:10p20g-1-#v_20g:1-20p010p#v_v
59 ^ < < v
73 41 v <
52 40 09 > $v
26 53 06 34 >00g2-:10p 20p > 10g20g1+g 10g20g2+g : 10g1+20g2+g -:0`>#^_-> + 10g20g1+ p 10g:1-10p#v_20g:1-:20p10p#v_ 01g.@
10 51 87 86 81 ^ < <
61 95 66 57 25 68
90 81 80 38 92 67 73
30 28 51 76 81 18 75 44
84 14 95 87 62 81 17 78 58
... ... ...
59 ^ < < v
73 41 v <
52 40 09 > $v
26 53 06 34 >00g2-:10p 20p > 10g20g1+g 10g20g2+g : 10g1+20g2+g -:0`>#^_-> + 10g20g1+ p 10g:1-10p#v_20g:1-:20p10p#v_ 01g.@
10 51 87 86 81 ^ < <
61 95 66 57 25 68
90 81 80 38 92 67 73
30 28 51 76 81 18 75 44
84 14 95 87 62 81 17 78 58
... ... ...
Explanation:
see [Problem-018]
| Interpreter steps: | 650 537 |
| Execution time (BefunExec): | 266ms (2.45 MHz) |
| Program size: | 299 x 101 |
| Solution: | 7273 |
| Solved at: | 2014-09-13 |