The Diameter of a Binary Tree

Problem: Given a binary tree, there is a path connecting any two nodes u,v in the tree. Among all the possible paths, the longest path is considered as the diameter of the binary tree. Find out this path.

Solution: We can use recursion to solve this problem. We need to be careful than this longest path can just reside in one of the sub-tree of the root. The code for this algorithm is as follow:

int height(TreeNode * root)
{
   if(!root) return 0;
   
   return 1+max(height(root->left), height(root->right));


int Diameter(TreeNode *root)
{
   if(!root) return 0;

   int h_left = height(root->left);
   int h_right = height(root->right);
   
   return max(1+h_left+h_right, max(Diameter(root->left), Diameter(root->right)));

}

Memorization might be used to avoid repeated calculation.