# Euler 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:

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)

For this one you work backwards. Add up mini triangles starting from the bottom. When you get to the top, you have your answer.

import java.util.ArrayList;

public class Euler18
{
public static void main(String[] args)
{
System.out.print(“Problem 18:\n”);
Euler18 e = new Euler18();
System.out.print(“Answer = ” + e.Problem()+ “\n”);
}
public String Problem ()
{
ArrayList<int[]> tri = new ArrayList<int[]>();
tri.add (new int [] {95, 64});
tri.add (new int [] {17, 47, 82});
tri.add (new int [] {18, 35, 87, 10});
tri.add (new int [] {2, 4, 82, 47, 65});
tri.add (new int [] {19, 0, 23, 75, 3, 34});
tri.add (new int [] {88, 2, 77, 73, 7, 63, 67});
tri.add (new int [] {99, 65, 4, 28, 6, 16, 70, 92});
tri.add (new int [] {41, 41, 26, 56, 83, 40, 80, 70, 33});
tri.add (new int [] {41, 48, 72, 33, 47, 32, 37, 16, 94, 29});
tri.add (new int [] {53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14});
tri.add (new int [] {70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57});
tri.add (new int [] {91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48});
tri.add (new int [] {63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31});
tri.add (new int [] {4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23});
for (int i = 13; i >= 0; i–)
{
int [] row = new int [i+1];
for (int j = 0; j <= i; j++)
{
int sum1 = tri.get(i)[j] + tri.get(i+1)[j];
int sum2 = tri.get(i)[j] + tri.get(i+1)[j+1];
if (sum1 > sum2)
row[j] = sum1;
else
row[j] = sum2;
}
tri.remove(i);