Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 19.3, Problem 1E
Program Plan Intro
Argue that it doesn’t matter to the analysis that x is marked, even though it is not a root that first linked to another node and then lost one child.
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Create a binary linked tree, and traverse the tree by using the recursive function.
The structure of the tree is as follows:
//check pic//
You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space.
Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes.
Count the height of the tree.
Hints:
Header file
typedef char ElemType;
typedef struct node//define the type of binary tree node
{
}BTnode;
Source file
#include <stdio.h>
#include <stdlib.h>
#include "tree.h"
BTnode * createTree()//create the binary tree,return the root
{
BTnode *tnode;// tnode is the root
char elem;
;//input the character
//if the input is a space,set the pointer as NULL
Else// if the input is not a space,generate the binary node and create its left…
Consider the implementation of disjoint
sets using forests. Assume the union is
done by weight, i.e., the root of the tree
with lesser nodes points to the root of the
tree with more nodes: The following
operations are applied on an initial set of
elements {x, x2, X3, X4, X5} : union (x, x2);
union (x1, x3); union (x4, xg); union
(x4, x1). Show the forest after each
operation.
Given a binary tree, find the lowest common ancestor
(LCA) of two given nodes in the tree.
According to the definition of LCA on Wikipedia:
"The lowest common ancestor is defined between two nodes
v and w as the lowest node in T that has both v and w as
descendants
(where we allow a node to be a descendant of itself)."
/
6
1
2
1
0
1
8
7 4
For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3.
Another example is LCA of nodes 5 and 4 is 5,
since a node can be a descendant of itself according to the LCA definition.
Chapter 19 Solutions
Introduction to Algorithms
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- Use the recursive strategy described in the chapter to implement a binary tree. Each node in this method is a binary tree. Thus, a binary tree includes references to its left and right subtrees in addition to the element stored at its root.You could also wish to make mention of its progenitor.arrow_forwardImplement a graphical system for employee management that includes an employee id, employee name, and years of service. Employees should be stored in the system using a B-tree of order 7, and they should be able to be added and removed. Your system must refresh a sorted list of workers sorted by name on the screen after each operation. Implement a graphical system for employee management that includes an employee id, employee name, and years of service. Employees should be stored in the system using a B-tree of order 7, and they should be able to be added and removed. Your system must refresh a sorted list of workers sorted by name on the screen after each operation.arrow_forwardUse the recursive strategy described in the chapter to implement a binary tree. Each node in this method is a binary tree. Thus, a binary tree includes references to its left and right subtrees in addition to the element stored at its root. You could also wish to make mention of its progenitor.arrow_forward
- What scenario is possible for a node-based situation in computer science. Please explainin set of 9 nodes, every node has 3 branches In a set of 9 nodes, one node has two branches, and the rest have exactly three.arrow_forwardImplement a function to verify if a binary tree is balanced. A balanced tree, for the purposes of this question, is one in which the heights of the two subtrees of any node never differ by more than one.arrow_forwardThe BST remove algorithm traverses the tree from the root to find the node to remove. When the node being removed has 2 children, the node's successor is found and a recursive call is made. One node is visited per level, and in the worst-case scenario, the tree is traversed twice from the root to a leaf. A BST with N nodes has at least log2N levels and at most N levels. Therefore, the runtime complexity of removal is best case O(logN) and worst case O(N). Two pointers are used to traverse the tree during removal. When the node being removed has 2 children, a third pointer and a copy of one node's data are also used, and one recursive call is made. Thus, the space complexity of removal is always O(1)." I have to explain this clearly! and the advantages of the BST algorithimarrow_forward
- 7 4 2 4 2 Tree #1 1 5 Tree #2 6 3 6 8 8 9 5 7 9 1 For parts a through g, implement the given method and demonstrate the method working with the two trees provided earlier. All code implemented in this assignment should be in a class called Homework 6. You may use the data structures and algorithm code from the lecture notes. Hint: Consider using recursion. To do so implement a private helper method that takes a Node and then recursively calls itself to traverse the tree. The public method would call the private method passing the tree's root as the Node.arrow_forwardUse a triply linked structure as opposed to an array when implementing a priority list using a heapordered binary tree. Each component will require three links: two to move up the tree and one to move down it. Even if the utmost size of the priority queue is unknown at the outset, your implementation should still ensure logarithmic running times for each action.arrow_forwardUse a triply linked structure as opposed to an array for implementing a priority queue using a heapordered binary tree. Each node will require three links: two to move up the tree and one to move down it. Even if the maximum size of the priority queue is unknown at the outset, your solution should nonetheless provide logarithmic running times for each operation.arrow_forward
- Implement a priority queue using a heapordered binary tree, however instead of using an array, use a triply linked structure. Three connections are needed for each node: two for climbing the tree and one for descending it. Your solution should offer logarithmic running durations for each operation, even if there isn't a set maximum priority-queue size.arrow_forwardYour system consists of nodes connected in a full binary search tree of height 6. If a node has failed, it is unreachable, as are all of its descendants, as shown in the figure below (the node with the red star has failed). You randomly select a node from the tree, and want to traverse from the root of the tree to your selected node. You are unaware that one node (you don't know which one) has failed, potentially causing your traversal to fail, depending on which node you're looking for and which node failed. All nodes are equally likely to fail. Assuming that exactly one node has failed, which of the following statements is true? Pick ONE option The likelihood of success is between 90-100% The likelihood of success is between 80-89.99%. The likelihood of success is between 70-79.99%. The likelihood of success is between 60-69.99%. The likelihood of success is between 50-59.99%.arrow_forwardImplement a binary tree by utilising the chapter's recursive method. In this technique, each node is a binary tree. Therefore, in addition to the element stored at its root, a binary tree also contains pointers to its left and right subtrees. You could also want to discuss its ancestor.arrow_forward
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