Project Euler problem 67: find maximum cost path in 100-row triangle

Question

In Project Euler\'s problem 67 there is a triangle given and it contains 100 rows. For e.g.

        5
      9  6
    4   6  8
  0   7  1   5

I.e. 5 + 9 + 6 + 7          


        

Answer 1

To build off of @Matt Wilson's answer, using a two-dimensional array to hold the numbers would be a fairly simple solution. In your case, you would encode the triangle

      5
    9  6
  4   6  8
0   7  1   5

as the array

[5][ ][ ][ ]
[9][6][ ][ ]
[4][6][8][ ]
[0][7][1][5]

From here, a node at position (i, j) has children at (i + 1, j) and (i + 1, j + 1) and parents at position (i - 1, j) and (i - 1, j - 1), assuming those indices are valid.

The advantage of this approach is that if your triangle has height N, the space required for this approach is N², which is just less than twice the N(N + 1) / 2 space required to actually store the elements. A linked structure like an explicit graph would certainly use more memory than that.