Question

I’m currently trying to solve problem 18 of project Euler. The goal is:

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

I tried to solve it with the following algorithm:

public static void main(String[] args) throws NumberFormatException, IOException {

        int[][] values = readFile();
        int depth = values.length - 2;

        while ( depth >= 0) {
            for (int j = 0; j < depth; j++) {
                values[depth][j] += Math.max( values[depth+1][j], values[depth+1][j+1]);
            }
            depth += -1;
        }

        values[0][0] += Math.max(values[1][0], values[1][1]);

            System.out.println("The maximum path sum is: " + values[0][0]);
    }

The array values contains all the numbers from the triangle where values[0][0] is the element in the top row and values[n][n] is the last element in the last row.

The algorithm uses the approach that if for example I start in the last row and have the choice between 04 + 63 and 62 + 63, the sum of the field in which 63 was will be set to 125 because this is the highest amount. This algorithm works for the small triangle, but for the big triangle it seems to fail. I’m not sure why and would appreciate every hint.

Answer 1

I believe that the line:

for (int j = 0; j < depth; j++) {

should be

for (int j = 0; j <= depth; j++) {

because right now you aren’t visiting the last element on each row. Of course, then you don’t need the line

values[0][0] += Math.max(values[1][0], values[1][1]);

because it is already done in the loop.