Trees & BST

The worst case running time to search for an element in a balanced binary search tree with $n2^n$ elements is

The height of a tree is defined as the number of edges on the longest path in the tree. The function shown in the pseudocode below is invoked as height(root) to compute the height of a binary tree rooted at the tree pointer root.

int height (treeptr n)
{ if (n == NULL) return -1;
  if (n -> left == NULL)
     if (n -> right == NULL) return 0;
     else return [B1] ;                    // Box 1
  else { h1 = height (n -> left);
         if (n -> right == NULL) return (1+h1);
         else { h2 = height (n -> right);
                return [B2] ;              // Box 2
              }
       }
}

The appropriate expressions for the two boxes B1 and B2 are