I think, my output for my first test case is correct according to the problem description:

A tree is an almost well-balanced tree if at each node the depths of the subtrees rooted at its children are the same or differ at most by 1. The depth of a tree is 1 if the tree is a single leaf, or 1 plus the maximum of the depths of subtrees rooted at the children of its root.

So here is how the test case looks like as a tree:

1 2 2 1 3 2 4 1 5 0 6 0 9 2 8 1 7 0 10 0

So nodes 5, 6, 7 and 10 have depth 1, nodes 4,8 depth 2, nodes 3 and 9 depth 3, node 2 depth 4, node 1 depth 5.

For node 1, the depth of subtrees is 4 (for node 2) and 3 (node 9).

and the subtrees with node 2 as root or node 9 as node are obviously almost well-balanced, so the tree is almost well balanced.

This test case is an example for that the given definition is not equivalent to the definition: all leaves should occur at depths that differ at most by one.

Which definition for almost well balanced did you use to get Accepted and to get as result for my test case "0" ?