Data Structures and Algorithm Analysis - Computer Science at ...

190 Chap. 5 Binary Trees5.12 Write a recursive function that traverses a binary tree, and prints the value ofevery node which has at least four great-grandchildren.5.13 Compute the overhead fraction for each of the following full binary tree implementations.(a) All nodes store data, two child pointers, and a parent pointer. The datafield requires four bytes and each pointer requires four bytes.(b) All nodes store data and two child pointers. The data field requiressixteen bytes and each pointer requires four bytes.(c) All nodes store data and a parent pointer, and internal nodes store twochild pointers. The data field requires eight bytes and each pointer requiresfour bytes.(d) Only leaf nodes store data; internal nodes store two child pointers. Thedata field requires eight bytes and each pointer requires four bytes.5.14 Why is the BST Property defined so that nodes with values equal to the valueof the root appear only in the right subtree, rather than allow equal-valuednodes to appear in either subtree?5.15 (a) Show the BST that results from inserting the values 15, 20, 25, 18, 16,5, and 7 (in that order).(b) Show the enumerations for the tree of (a) that result from doing a preordertraversal, an inorder traversal, and a postorder traversal.5.16 Draw the BST that results from adding the value 5 to the BST shown inFigure 5.13(a).5.17 Draw the BST that results from deleting the value 7 from the BST of Figure5.13(b).5.18 Write a function that prints out the node values for a BST in sorted orderfrom highest to lowest.5.19 Write a recursive function named smallcount that, given the pointer tothe root of a BST and a key K, returns the number of nodes having keyvalues less than or equal to K. Function smallcount should visit as fewnodes in the BST as possible.5.20 Write a recursive function named printRange that, given the pointer tothe root of a BST, a low key value, and a high key value, prints in sortedorder all records whose key values fall between the two given keys. FunctionprintRange should visit as few nodes in the BST as possible.5.21 Write a recursive function named checkBST that, given the pointer to theroot of a binary tree, will return true if the tree is a BST, and false if it isnot.5.22 Describe a simple modification to the BST that will allow it to easily supportfinding the Kth smallest value in Θ(log n) average case time. Then writea pseudo-code function for finding the Kth smallest value in your modifiedBST.