Problem Statement

Class Name:  TriTravel
Method Name:  bestWayDown
Parameters: int[]
Returns: int

Implement a class TriTravel, which contains a method bestWayDown.  The
method analyzes a set of Integers organized as a triangle and finds the path
from the top to the bottom of the triangle with the maximum possible sum of
numbers passed on route (including both the starting and ending number).  The
method returns an int that is this maximum sum.  The method is passed an int[]
that contains the elements in the triangle.  The elements of the int[]
correspond to the triangle as follows.  The numbers in this triangle are the
index of the elements in the int[]:
        0
      1     2
    3     4     5
  6     7     8     9
10    11    .  .  .  .  . 
     .     .     .
     .     .     .
     .     .     .
For example, the triangle
    1
  6  7
 4 -1 6
5 8  9 0
is represented by the int[]{1,6,7,4,-1,6,5,8,9,0}
The path starts at the element in the top row.  Each step in the path is
either diagonally down one row to the right or diagonally down one row to the
left.  For instance, given the triangle above, the maximum sum route down is 1
-> 7 -> 6 -> 9 and the method returns the sum, 23.

Here is the method signature:
public int bestWayDown(int[] triValues);
*triValues is an int[] of elements between -100 and 100, inclusive.
*The number of elements in triValues represents a triangle perfectly. (that is,
it has 1 or 3 or 6 or 10 or 15 or ... elements).
*triValues has at least 1 element (a 1 row triangle).
*triValues has at most 45 elements (a 9 row triangle).

Examples:
*If triValues = {5, 4, 1, 2, 8, -1}, the path 5->4->8 yeilds the maximum sum
and the method returns the sum: 17.

Definition