Is the depth counted in nodes or in edges?

Nodes: a single node has depth 1 and null has depth 0, so [4, 2, 7, null, null, 6, 9, 5] gives 4. A height counted in edges is one less for every non-empty tree and -1 for the empty one; change the 0 branch to -1 in the recursive version to get it.

Why copy queue.size into a var before the inner loop?

Children are enqueued on the same queue while the level is processed, so queue.size grows during the loop. Reading it once into n and counting down dequeues exactly the nodes of the current level, which is what makes depth += 1 count levels. for (_ <- 0 until queue.size) also works, because the range is built once, as long as the body never needs a return.

Is the return 0 at the top of the BFS version allowed in Scala 3?

Yes. A return directly in the method body is an ordinary return. Scala 3 only warns about a return inside a lambda, such as a foreach body or a for comprehension, because that would be a non-local return, which it no longer supports. If you wanted to stop early inside such a loop, for example at the first leaf for a minimum depth, wrap the body in boundary and call break(depth).

Will the recursive version throw StackOverflowError?

Only on very deep trees. Each level adds one JVM frame on the thread stack, whose size is fixed when the thread starts, so a one-sided chain of tens of thousands of nodes can throw StackOverflowError. @tailrec cannot fix it: the method makes two calls and adds one to their maximum, so neither is in tail position. The cases here stay within 500 levels, so both versions pass.

How do I get the minimum depth instead?

Not by swapping math.max for math.min: a node with one child is not a leaf, and on [10, null, 20, null, 30] the swap returns 1 (the missing left child counts as a path of zero) instead of 3. Match on the children: when one is null, return one plus the other side's depth. In the queue loop, stop at the first node whose left and right are both null.

Maximum Depth of a Binary Tree in Scala: Recursive and BFS Solutions

Q: Is the return 0 at the top of the BFS version allowed in Scala 3?

Yes. A return directly in the method body is an ordinary return. Scala 3 only warns about a return inside a lambda, such as a foreach body or a for comprehension, because that would be a non-local return, which it no longer supports. If you wanted to stop early inside such a loop, for example at the first leaf for a minimum depth, wrap the body in boundary and call break(depth).

Q: Will the recursive version throw StackOverflowError?

Only on very deep trees. Each level adds one JVM frame on the thread stack, whose size is fixed when the thread starts, so a one-sided chain of tens of thousands of nodes can throw StackOverflowError. @tailrec cannot fix it: the method makes two calls and adds one to their maximum, so neither is in tail position. The cases here stay within 500 levels, so both versions pass.

Q: How do I get the minimum depth instead?

Not by swapping math.max for math.min: a node with one child is not a leaf, and on [10, null, 20, null, 30] the swap returns 1 (the missing left child counts as a path of zero) instead of 3. Match on the children: when one is null, return one plus the other side's depth. In the queue loop, stop at the first node whose left and right are both null.

max_depth.scala

Scala 3.6

Not run yet

+ 7 hidden

Input

root = [4, 2, 7, null, null, 6, 9, 5]

Expected

The longest path is 4 → 7 → 6 → 5, four nodes. The branch through 2 ends after two, and 9 after three.

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue

1 · Recursive DFS: one more than the deeper subtree

2 · Iterative BFS: count the levels with a queue