Project Eueler: problem18
問題
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 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 23NOTE: 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)
テスト
require "p18.rb"
pil4 = <<"PIL4"
3
7 4
2 4 6
8 5 9 3
PIL4
pil15 = <<"PIL15"
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
PIL15
describe "max" do
it "pil4" do
calcMax(pil4) == 23
end
it "pil15" do
calcMax(pil15) == 1074
end
end
回答
$ar = Array.new
def sum(col,row,cache)
return cache[col][row] if cache[col][row]
if $ar.size-1 <= col
return cache[col][row] = $ar[col][row]
end
lnode, rnode = sum(col+1,row,cache), sum(col+1,row+1,cache)
if lnode >= rnode
return cache[col][row] = lnode + $ar[col][row]
else
return cache[col][row] = rnode + $ar[col][row]
end
end
def calcMax(pil)
cnt = 0
pil.each do |line|
$ar[cnt] = line.chomp!.split(/ /).map{|x| x.to_i}
cnt += 1
end
cache = Array.new(cnt)
0.upto(cnt-1){|x| cache[x] = Array.new(x+1)}
p rslt = sum(0,0,cache)
return rslt
end
