## Problem:

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)

1074

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}
/*
* Solution to Project Euler problem 18
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/

public final class p018 implements EulerSolution {

public static void main(String[] args) {
System.out.println(new p018().run());
}

public String run() {
for (int i = triangle.length - 2; i >= 0; i--) {
for (int j = 0; j < triangle[i].length; j++)
triangle[i][j] += Math.max(triangle[i + 1][j], triangle[i + 1][j + 1]);  // Dynamic programming
}
return Integer.toString(triangle[0][0]);
}

private int[][] triangle = {
{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, 9,70,98,73,93,38,53,60,04,23}
};

}