between two nodes and as the lowest node in that has both and as descendents (where we allow node to be descendent of itselfgiven two nodes and wdescribe an efficient algorithm for finding the lca of and what is the running time of your algorithmc- let be binary tree with nodesandfor any node in tlet denote the depth of in the distance between two nodes and in is where is the lowest common ancestor (lcau of and the diameter of is the maximum distance between two nodes in describe an efficient algorithm for finding the diameter of what is the running time of your algorithmc- suppose each node of binary tree is labeled with its value (vin level numbering of design fast method for determining (ufor the lowest common ancestor (lca)uof two nodes and in tgiven (vand (wyou do not need to find node ujust compute its level-numbering label - justify the bounds in table by providing detailed analysis of the running times of the methods of binary tree implemented with an array listswhere is realized by means of an array - justify table summarizing the running time of the methods of tree represented with linked structureby providingfor each methoda description of its implementationand an analysis of its running time - describe nonrecursive method for evaluating binary tree representing an arithmetic expression - let be binary tree with nodes define roman node to be node in tsuch that the number of descendents in ' left subtree differ from the number of descendents in ' right subtree by at most describe linear-time method for finding each node of tsuch that is not roman nodebut all of ' descendents are roman nodes -