Return Maximum number of turns in a tree from root to lead node

First clarify the wording: it likely means the maximum number of left-to-right or right-to-left direction changes on a path from the root to a leaf. Confirm whether the first edge counts as a turn and whether a turn means a change of direction rather than simply taking a left or right edge. With that definition, run DFS carrying (previousDirection, turnsSoFar). When taking a left child, add one only if the previous direction was right; when taking a right child, add one only if the previous direction was left. At each leaf, maximize the answer.

The recursion state captures exactly the information the next edge needs, so no full path array is required. Start at the root with a neutral previous direction, which prevents the first edge from being counted as a change. A postorder return can also carry the best result, but a shared maximum is simpler if recursion depth is safe. Test a root-only tree, an all-left chain with zero changes, a zigzag path where every edge after the first changes direction, and multiple leaves with different counts. Every node is visited once, yielding O(n) time and O(h) call-stack space, where h is tree height.