Modify Figs. 21.15 and 21.16 to allow the binary tree to contain duplicates.

Fig. 21.15

Fig. 21.16

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I // Fig. 21.15: Tree.java 2 // TreeNode and Tree class declarations for a binary search tree. 3 package com.deitel.datastructures; 4 5 // class TreeNode definition 6 class TreeNode { 7 8 9 10 IL 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 } 42 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 // package access members TreeNode leftNode; 99 100 101 } E data; // node value TreeNode rightNode; // constructor initializes data and makes this a leaf node public TreeNode (E nodeData) { data nodeData; leftNode= rightNode = null; // node has no children } // locate insertion point and insert new node; ignore duplicate values public void insert (E insertValue) { // insert in left subtree } if (insertValue.compareTo (data) < 0) { // insert new TreeNode } } if (leftNode == null) { leftNode = new TreeNode (insertValue); } else { // continue traversing left subtree recursively leftNode.insert(insertValue); } // insert in right subtree else if (insertValue.compareTo (data) > 0) { // class Tree definition public class Tree { private TreeNode root; } // constructor initializes an empty Tree of integers public Tree() {root = null;} // insert new TreeNode. if (rightNode == null) { rightNode = new TreeNode (insertValue); } else { // continue traversing right subtree recursively rightNode.insert(insertValue); } // insert a new node in the binary search tree public void insertNode (E insertValue) { if (root == nul1) { root = new TreeNode (insertValue); // create root node } } } else { root.insert(insertValue); // call the insert method // begin preorder traversal public void preorderTraversal() {preorderHelper (root); } // recursive method to perform preorder traversal private void preorderHelper (TreeNode node) { if (node == null) { return; } System.out.printf("%s", node.data); // output node data preorderHelper (node.leftNode); // traverse left subtree preorderHelper(node.rightNode); // traverse right subtree } // begin inorder traversal public void inorderTraversal() {inorderHelper (root); } // recursive method to perform inorder traversal private void inorderHelper (TreeNode node) { if (node = null) { return; } inorderHelper (node.leftNode); // traverse left subtree System.out.printf("%s ", node.data); // output node data inorderHelper (node.rightNode); // traverse right subtree } // begin postorder traversal public void postorderTraversal() [postorderHelper (root); } // recursive method to perform postorder traversal private void postorderHelper (TreeNode node) { if (node null) { return; } postorderHelper (node.leftNode); // traverse left subtree postorderHelper (node.rightNode); // traverse right subtree System.out.printf("%s", node.data); // output node data