title: Is there an algorithm to find the minimum cost path in a directed rooted tree (arborescence)?
body: <p>To be more specific : I have a rooted tree which represents the different paths of a matrix from its first element to its last, with only right, down and diagonal down movements allowed. Hence, every node can have up to 3 children. The tree will have the first element of the matrix as its root and every last node will be the last element of the matrix. Every node represents a cost. </p>
  
  <p>Here's an example of what kind of tree I'm talking about : <a href="https://i.stack.imgur.com/XV25e.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/XV25e.png" alt="enter image description here"></a> </p>
  
  <p>Here the minimum cost path would be : <strong>1 -> 2 -> 9</strong> or <strong>[0,0,2]</strong> in "coordinates"</p>
  
  <p>So is there any algorithm that is able to find the minimum cost path (I mean the path not the total cost of the minimum cost path) for this kind of tree ?<br>
  And if yes, is it possible to implement it in a recursive way ?</p>