Lazy Squirrel Learns Programming #1

The length of each edge in the binary tree is given as a real number element of an array/list: $a=\left[a[0],a[1],\ldots,a[2^{n+1}-2]\right].$ At each of the $2^n$ leaves, there is an acorn. The squirrel is lazy and wants to travel the minimum possible distance to get 1 acorn, so the squirrel learns to program. What is the runtime of the best algorithm the squirrel can use to solve its problem?