title: Euler project #18 approach
body: <p>I am looking into an Euler project. Specifically #18.<br>
  To sum up, the idea is to find the max path from a triangle:  </p>
  
  <pre><code>   3
    7 4
   2 4 6  
  8 5 9 3
  </code></pre>
  
  <p>3 + 7 + 4 + 9 = 23.</p>
  
  <p>Reading for this, most people indicate that this is solved correctly by working bottom to top instead of using an algorithm that works "greedy" from top to bottom.  </p>
  
  <p>I can understand that starting from top and going down selecting the max you find is "shortsighted" and may not be the overall max.  </p>
  
  <p>But why is the approach of going from bottom to top any better?<br>
  It seems to me it suffers from the same problem.  </p>
  
  <p>For example in the triangle in the example we would get (starting from bottom):<br>
  9+6+4+3=22 &lt; 23  </p>
  
  <p>So why start from bottom-up?</p>