performance of the linked binary tree implementation to summarize the efficiencies of the linked structure representationwe analyze the running times of the linkedbinarytree methodsincluding derived methods that are inherited from the tree and binarytree classesthe len methodimplemented in linkedbinarytreeuses an instance variable storing the number of nodes of and takes ( time method is emptyinherited from treerelies on single call to len and thus takes ( time the accessor methods rootleftrightparentand num children are implemented directly in linkedbinarytree and take ( time the sibling and children methods are derived in binarytree based on constant number of calls to these other accessorsso they run in ( time as well the is root and is leaf methodsfrom the tree classboth run in ( timeas is root calls root and then relies on equivalence testing of positionswhile is leaf calls left and right and verifies that none is returned by both methods depth and height were each analyzed in section the depth method at position runs in ( time where is its depththe height method on the root of the tree runs in (ntime the various update methods add rootadd leftadd rightreplacedeleteand attach (that istheir nonpublic implementationseach run in ( timeas they involve relinking only constant number of nodes per operation table summarizes the performance of the linked structure implementation of binary tree operation lenis empty rootparentleftrightsiblingchildrennum children is rootis leaf depth(pheight add rootadd leftadd rightreplacedeleteattach running time ( ( ( ( (no( table running times for the methods of an -node binary tree implemented with linked structure the space usage is (