Project Euler 18

Your problem is that your algorithm is a greedy algorithm, always finding local maxima. Unfortunately that causes it to miss higher numbers down below because they are directly below lower numbers. For example, if the triangle were only 3 levels, your algorithm would pick 75 + 95 + 47 = 217, while the correct answer is 75 + 64 + 82 = 221.

The correct algorithm will either try every path and choose the one with the highest total, or compute paths from the bottom up (which allows you to avoid trying every one, thus being much faster). I should add that working from the bottom-up is not only much faster (O(n^2) instead of O(2^n)!), but also much easier to write (I did it in about 3 lines of code).

Here is a graphical description:

Here's what the bottom up method belisarius describes--using the trivial triangle given in problem 18--looks like, just in case the image in his post is confusing to anyone else.

      03
    07  04
  02  04  06
08  05  09  03

      03
    07  04
  02  04  06
08  05  09  03
^^^^^^

      03
    07  04
  10  04  06
08  05  09  03
    ^^^^^^

      03
    07  04
  10  13  06
08  05  09  03
        ^^^^^^

      03
    07  04
  10  13  15
  ^^^^^^
08  05  09  03

      03
    20  04
  10  13  15
      ^^^^^^
08  05  09  03

      03
    20  04
  10  13  15
      ^^^^^^
08  05  09  03

      03
    20  19
    ^^^^^^
  10  13  15
08  05  09  03

      23
      ^^
    20  19
  10  13  15
08  05  09  03

You've written a greedy algorithm, which I don't think fits the requirements here. Here's a quick example to demonstrate that point:

  1
 2 1
1 1 100 

Using your algorithm you'll reach a sum of 4, although the optimal solution is 102.