Project Euler > Problem 18 > Maximum path sum I (Java Solution)

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)

Solution:

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}
 };
 
}