# Efficiently finding the min-cost path of an AVL tree

It seems that in a full AVL tree, the left edge is always the minimum-cost path. For example, take the following full AVL tree:

The min-cost path would be 8-6-5. However this is not the case with other AVL trees. Take the previous tree with an additional 4 inserted:

Here the min-cost path would be 8-6-7 rather than 8-6-5-4.

What is the most efficient algorithm to find the min-cost path in any AVL tree? Given the characteristics of AVL trees, is this algorithm faster than it would be for a standard BST?

• I'd prefer an explicit definition of minimum-cost path over what I glean from the examples (sum of node labels on a path between root an leaf). The node labels are in strictly ascending order - 1) is that guaranteed? 2) any additional conditions? – greybeard Mar 4 '20 at 6:11