algorithm - Print the Longest leaf-to-leaf path in a binary tree along with its length -

i solving problem in have find longest leaf-to-leaf path in binary tree along length.

for example, if binary tree follows:

                  /\         b c       /   / \      d   e  f      / \      \    g  h      p        \         k

the longest leaf-to-leaf path k-h-d-b-a-c-f-p of length 8.

i calculating length recursively finding length of left , right sub-tree , return height_left + height_right + 1 . concept correct?.

also how should print longest leaf-to-leaf path? want idea proceed.

it seems me algorithm close finding diameter of binary tree. diameter of tree number of nodes on longest path between 2 leaves in tree.

i think can here implementation: http://www.geeksforgeeks.org/diameter-of-a-binary-tree/ , adapt or optimize it's time complexity if want. think o(n) enough.

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