sales domestic international canada america africa overseas europe (aasia australia sales domestic international canada america overseas africa europe asia australia (bfigure (atree (bindented parenthetic representation of - the indented parenthetic representation of tree is variation of the parenthetic representation of (see code fragment that uses indentation and line breaks as illustrated in figure give an algorithm that prints this representation of tree - let be binary tree with positions define roman position to be position in such that the number of descendants in ' left subtree differ from the number of descendants in ' right subtree by at most describe linear-time method for finding each position of such that is not roman positionbut all of ' descendants are roman - let be tree with positions define the lowest common ancestor (lcabetween two positions and as the lowest position in that has both and as descendants (where we allow position to be descendant of itself given two positions and qdescribe an efficient algorithm for finding the lca of and what is the running time of your algorithmc- let be binary tree with positionsandfor any position in let denote the depth of in the distance between two positions and in is dq da where is the lowest common ancestor (lcaof and the diameter of is the maximum distance between two positions in describe an efficient algorithm for finding the diameter of what is the running time of your algorithmc- suppose each position of binary tree is labeled with its value (pin level numbering of design fast method for determining (afor the lowest common ancestor (lca)aof two positions and in given (pand (qyou do not need to find position ajust value (ac- give an alternative implementation of the build expression tree method of the expressiontree class that relies on recursion to perform an implicit euler tour of the tree that is being built