The diameter of an N-ary tree is the longest path present between any two nodes of the tree. These two nodes must be two leaf nodes. The following examples have the longest path[diameter] shaded.
Prerequisite : Diameter of a binary tree.
The path can either start from one of the node and goes up to one of the LCAs of these nodes and again come down to the deepest node of some other subtree or can exist as a diameter of one of the child of the current node.
The solution will exist in any one of these:
I] Diameter of one of the children of the current node
II] Sum of Height of highest two subtree + 1
Optimizations to above solution :
We can make a hash table to store heights of all nodes. If we precompute these heights, we don’t need to call depthOfTree() for every node.
A different optimized solution :
Longest path in an undirected tree
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