Question

I have written code for finding the diameter of binary tree. But I am unable to figure out where is it going wrong . The two functions that I have written and their definition are as follows :-

    int btree::diameteroftree(node* leaf)
    { 
     if (leaf==NULL) 
     return 0;

     int lheight = hieghtoftree(leaf->left);
     int rheight = hieghtoftree(leaf->right);

     int ldiameter = diameteroftree(leaf->left);
     int rdiameter = diameteroftree(leaf->right);

     return max(lheight + rheight + 1,max(ldiameter,rdiameter));
   }


   int btree::hieghtoftree(node* leaf)
   {
    int left=0,right=0;
    if(leaf==NULL)
    return -1;
    else
    {
     left=hieghtoftree(leaf->left);
     right=hieghtoftree(leaf->right);
     if(left > right)
     return left +1;
     else
     return right+1;   
    }
   }

I am unable to figure out where am I going wrong here . Can someone let me know …

Answer 1

You want to return the number of nodes on the longest path. Therefore, the problem in your algorithm is this line:

return max(lheight + rheight + 1,max(ldiameter,rdiameter));

where

rootDiameter = lheight + rheight + 1

is the length of the path from the deepest node of the left tree to the deepest node of the right tree. However, this calculation is not correct. A single node returns a height of 0, so it will not be counted. You have two options:

1. Change hieghtoftree to return the number of nodes on the deepest path and not the number of “hops”
2. Address this problem in your summation

.

return max(lheight + rheight + 3,max(ldiameter,rdiameter));