We will be solving a problem on trees together! Here's the problem statement: Given the root of a binary tree, invert the tree, and return its root. Function definition for Java: public TreeNode invertTree (TreeNode root) { } Function definition for Python: def invertTree(self, root): #Your code here Announced Test Cases: Test Case 1: Input: Output: 2 3 5 6 8 1 6 5 4 2 Explanation: 1's children are flipped, so 2,8 become 8,2. Their children are also respectively flipped so 5,6 becomes 6,5, and 3,4 becomes 4,3.
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- Written in Java The diameter D of a binary tree is defined as the number of nodes on the longest path between any two nodes in the tree. The path may pass through the root, but does not have to. For a given diameter, there may be more than one path which has the longestlength. For example, the following tree has diameter of 5:I am having trouble determining time complexity when it comes to finding the runtime of a method or function. I need to know what the runtime for the following methods are. Any further explanation would also be helpful. All of these methods are dealing with a binary search tree in java. 1. public String getAllValues() - return a String that contains the elementsof the tree in ascending order. All elements are separated by a space. 2. public int numberNodes() - return the total number of nodes in the tree. 3. public void insertList(int[] list) - insert all of the values from list intothe tree. Note: My Method just goes through an array calling working insert() method on all the values in the list[] array. 4. public int removeLessThan(int value) - this method removes all integers strictly less than value from the tree. It also returns the number of nodes itremoved. Note: In this method I first call a method to count nodes less than I call another method to recursively remove by…Write a program named ProblemA.cpp that implements the followingfunctions using recursion. Make a menu-based implementation so that you can call each function basedon the user input. • insert: insert a new node in the BSTNode* insert (Node* root, int key); • print: prints the values of all items in the tree, using inorder traversal techniquevoid inorder (Node* root); • search: search a node with a value in the BSTNode* insert (Node* root, int key); • findMinimum: returns the element with the minimum value in the BSTNode* findMinimum (Node* root); • findMaximum: returns the element with the maximum value in the BSTNode* findMaximum (Node* root); • delete: delete a node from the BSTNode* delete (Node* root, int key);
- import java.util.*;public class BST { // instance variables private BSTNode m_root; private int m_size; // constructor public BST() { m_root = null; m_size = 0; } // This method returns the number of elements in the tree. // Do not make any changes to this method! public int size() { return m_size; } // This method clears the content of the tree. // Do not make any changes to this method! public void clear() { m_root = null; m_size = 0; } // This non-recursive method takes a string and inserts it into the binary // search tree, keeping the tree ordered. public void add(String value) { // TODO: implement this method using a non-recursive solution } // This non-recursive method returns a string that represents the in-order traversal // of the binary search tree. public String inOrder() { // TODO: implement this method using a…Write a recursive function that increments by one the value for every node in the binary tree pointed at by root, then returns the modified tree. Assume that nodes store integer values. Here are methods that you can use on the BinNode objects: interface BinNode { public int value(); public void setValue(int v); public BinNode left(); public BinNode right(); public boolean isLeaf(); } public BinNode BTinc(BinNode root){ }write a python function that will return the leaves of a binary tree with (t) being the root of the binary tree. the function must use recursion Starting code: def leaves(t): return [t.key]
- How to answer the following question screenshot shows our binary search tree For the binary search trees, the public method, size, calls the private recursive method, recSize, and passes it a reference to the root of the tree, returning to the caller whatever is returned to it by recSize. Critique the following implementation of recSize assuming its parameter variable is node: if (node == null) return 0; else if ((node.getLeft() == null) && (node.getRight() == null)) return 1; else if ((node.getLeft() == null)) return (1 + recSize(node.getRight())); else return (1 + recSize(node.getLeft())); A. The code will throw a "null pointer exception" under certain circumstances. B. The code will return an incorrect result under certain circumstances. C. The code works correctly but could be simpler. D. The code works correctly. If an application uses the remove method on an Iterator object returned by our binary search tree: A. a TreeUnderflowException is…python: In a binary search tree, write another way of function that takes in a root, p, and checks whether the tree rooted in p is a binary search tree or not. What is the time complexity of your function? def is_bst(self, p): root=p def helper(root, l, r): if not root: return True if not (left<root.val and root.val<right): return False return helper(root.l, l, root.val) and helper(root.r, root.val, r) return helper(root, float('-inf'), float('inf'))Java Programming In your program, you will demonstrate an understanding of all these concepts by developing your own priority queue, node, binary tree, array and/or linked list, and use of recursion to support the Huffman Code encryption algorithm. Read through the theory of the Huffman Code in the text and then write a program that can take a String and encrypt it. For example, given a String “Hello World”, the program should apply the Huffman Code algorithm on that String to create the corresponding encrypted code sequence. In addition, you must be able to show the various components that support creating the encrypted String. For the Huffman Code, this requires the following: Creating a frequency table for each character of the String (I suggest this to be an array but can be done as a linked list) Creating a Huffman Tree from the frequency table (This will require use of a priority queue and a binary tree) Creating the Huffman Code table (This should be an array and will…
- Given a binary tree with integer data at all nodes (including leaves), your task is to create a pretty printer. Each node in the tree can have 0, 1, or 2 children in python3. constructor that takes a required int argument for the data stored in the node, and two optional Node arguments for the left and right children, respectively. __str__(self) -> str: returns a string representation of the subtree rooted at the self node [must use recursion] compute_height(self) -> int: returns the height of the current node. The height is the distance of the longest path between a leaf node and the current node. [must use recursion] pretty_print(self, indent: int): prints a formatted tree string with each node on a separate line, using the format value: height, and making sure that sibling and cousin nodes (i.e., those at the same distance from the root node) are indented using the same number of spaces (see example below). The root is indented 0 spaces, the children of the root are indented…Hey please answer the 0-1 knapsack problem using recursion. Provide the full code in java and ensure it is well commented. The solution must use the method public static int RecursiveKnap (final int W, final int[] wt, final int[] Val). You should also provide the time complexity and the auxilary space complexity with your answer. The answer must be orginal, if you repost code from another chegg answer or from geeksforgeeks, stack overflow etc. I will dislike your answerJAVA For the given binary tree, write a java program to print the parent of allleaf nodesThe output for the above binary tree is 3,4, 5, 2