Interview Question for Software Development Engineer Intern at Amazon.com:

I found the path to each node from the root, and stored that path in an array. The shortest path would then be the path from the end of one array (which contains a one of the nodes), up to the 'pivot point' of the array, and then from the 'pivot point' of the next array, to the node. You merge the two arrays at the 'pivot point' and the result is the shortest path.

That was my solution. it works, but I didn't have time to look into any special cases, debugging, optimization, etc. I'm sure there is a much simpler/efficient way.

Dijkstra's Algorithm came to mind, but I couldn't remember it in detail off of the top of my head at that moment.

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The shortest path would be from a node to the common ancestor (of the two nodes) to the other node -- right?

"The shortest path would be from a node to the common ancestor (of the two nodes) to the other node -- right?"

Yes, that's correct.