A Practical Introduction to Data Structures and Algorithm Analysis

200 Chap. 5 Binary Treesprints the root, then all nodes of level 1, then all nodes of level 2, and soon. Hint: Preorder traversals make use of a stack through recursive calls.Consider making use of another data structure to help implement the levelordertraversal.5.8 Write a recursive function that returns the height of a binary tree.5.9 Write a recursive function that returns a count of the number of leaf nodes ina binary tree.5.10 Assume that a given BST stores integer values in its nodes. Write a recursivefunction that sums the values of all nodes in the tree.5.11 Assume that a given BST stores integer values in its nodes. Write a recursivefunction that traverses a binary tree, and prints the value of every node who’sgrandparent has a value that is a multiple of five.5.12 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.