Question

For a 2-3 tree containing real numbers, design an algorithm for computing the range (i.e., the difference between the largest and smallest numbers in the tree) and determine its worst-case efficiency.

Answer 1

Sols =)* 2-3" Trees The 2-3 trees are called balanced trees. > All nodes have equal_height sub-trees. so, it forms perfect balance tree. It contains or three nodes. that is 2 nodes contain oore children and two 3 nodes contain o or a children. - 2-3 tree ee algorithm e-3trees cycot).' lefnode =rig-node =root. while (Enode.left != null). lef-node = lef- nodde, jeft. while (riganode.right != null). rig-mode=rig-node, right- retuin rignode Value -lef_node. Value. =) Explanation : In the above 2-3 algorithm. search the root node. - Initially 个个 the thode ande fnode is check whether Equal to yoot. execute the while loop untill the left of the mode is Equal to null

- assign the inode left node.. Exeaute while untill the right of te huil. the mode is not Equal Assign the mode as right node. Return the difference Value blie the mode and knode. worst case Efficiency; In the above algorithm the left most and right most nodes appear on the lasti level of the tree. the soi in this algorithm ito search. is takes node ollogn)" time leftnost takes. and for right most mode it orlogn) time. . The worst case for searching up both the left and right most nodes 2-3 trees is eling )