chap non-binary trees will use the ")symbolto indicate the end of child list all leaf nodes are followed by ")symbol because they have no children leaf node that is also the last child for its parent would indicate this by two or more successive ")symbols example for the general tree of figure we get the sequential representation rac) ) ))bf))( note that is followed by three ")marksbecause it is leafthe last node of ' rightmost subtreeand the last node of ' rightmost subtree note that this representation for serializing general trees cannot be used for binary trees this is because binary tree is not merely restricted form of general tree with at most two children every binary tree node has left and right childthough either or both might be empty for examplethe representation of example cannot let us distinguish whether node in figure is the left or right child of node further reading the expression logn cited in section is closely related to the inverse of ackermann' function for more information about ackermann' function and the cost of path compressionsee robert tarjan' paper "on the efficiency of good but not linear set merging algorithm[tar the article "data structures and algorithms for disjoint set union problemsby galil and italiano [gi covers many aspects of the equivalence class problem foundations of multidimensional and metric data structures by hanan samet [sam treats various implementations of tree structures in detail within the context of -ary trees samet covers sequential implementations as well as the linked and array implementations such as those described in this and while these books are ostensibly concerned with spatial data structuresmany of the concepts treated are relevant to anyone who must implement tree structures exercises write an algorithm to determine if two general trees are identical make the algorithm as efficient as you can analyze your algorithm' running time