# Project Euler 18

Problem18を解きました．

• Maximum path sum I

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)

https://projecteuler.net/problem=18

```data = Array.new()
File.open("data.txt") do |file|
file.each_line do |numStr|
numStr.chomp!
array = numStr.split(" ")
for i in 0..array.length - 1 do
array[i] = array[i].to_i
end
data.push(array)
end
end

def max2(num1, num2)
if num1 < num2 then
return num2
end
return num1
end

(data.length - 1).downto(1) do |i|
k = i - 1
for j in 0..data[k].length - 1 do
data[k][j] += max2(data[k + 1][j], data[k + 1][j + 1])
end
end

p data[0][0]
```

プログラム簡単化のため，以下のdata.txtを用意しました．

• data.txt
```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```

ボトムアップからの動的計画法で求めました．
Problem 67も同様に解けます．