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Implement special cases here: (define (delete t v) (let ((path (find t v))) (cond (( empty? t ) ) ((empty? (bst-root t)) ) ((not ( = v (node-value (car path))) ) (( > (node-count (car path)) 1) decrement count) ((equal? (car path) (bst-root t)) ;node were trying to delete (cond ; nest conditiona; ( (let-AND right (car path) empty) ; case 0.1 root <- null ((let-root empty, right empty) ; case 1 root <- left car path ; case 1.1 ((left-empty, right not empty) ; case 1.2 root <- right car path (else (delete-node path)) (else (delete-node path)) ) ) ) ) ) ) ) ) ) Special cases Top-Level Function: Delete Value from BST: (delete t v) The first parameter t is a reference to a bst, and the second parameter v is a value to find and delete. Like the insert function, delete will directly resolve a few special cases. For the general cases, it will call (find t v) to obtain a list of nodes that represent a path from the root to the node to be deleted, and will then call a helper function (delete-node path) to handle the rest of the work. In the case of delete the helper function will further rely on secondary helper functions to resolve cases and subcases. Deletion logically breaks down into cases based on how many child nodes the node to delete has. Each of those cases has subcases. The large number of cases implies the need for a correspondingly larger set of test cases: a test case to trigger each deletion case. Delete Cases Before we look at the detailed code for delete in Racket, lets look at the general approach. As for some of the other functions, it will be convenient to create a top-level function (delete t v) and several helper functions that manage specific detailed cases. There will be some initial special cases that should be managed separately, before launching any lower level helper function. Special cases for (delete t v): Tree t is empty: end the function because there is nothing to do. At this point, call (find t v) to create the path from root to node to delete if it is present. Assume the list returned is bound to a symbol named path. The node of interest will be the first node in the list: (car path) By examining node (car path), you can determine if the value to delete is present or not. Value v is not in the tree: end the function because there is nothing to do. Value v is in the tree: o Is the count field > 1? Dont delete the node, simply decrement its count field. o Is the count field = 1? In this case, we must move forward to actually delete the node. Is the node to delete the root of the tree? Does the node have 0 or 1 child nodes? This corresponds to delete cases 0.1, 1.1, and 1.2. Delete the node and update the root of the tree. o If we reach this pointvalue v is in the tree, count field is 1, node is not the root if it has 0 or 1 child nodes then the general delete case applies, call (delete-node path) The remaining delete cases will be covered by the (delete-node path) helper function. Some general considerations for node n (.

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TREES.pptx

This document provides an overview of data structures and trees. It defines trees and their properties like hierarchical structure, parent-child relationships, and representation using arrays and linked lists. It describes binary trees and their properties. It also covers binary search trees, operations on binary trees like insertion, deletion and traversal, and balanced binary search trees like AVL trees.

Q

1. Hash tables are good for random access of elements but not sequential access. When records need to be accessed sequentially, hashing can be problematic because elements are stored in random locations instead of consecutively.
2. To find the successor of a node in a binary search tree, we take the right child. This operation has a runtime complexity of O(1).
3. When comparing operations like insertion, deletion, and searching between different data structures, arrays generally have the best performance for insertion and searching, while linked lists have better performance for deletion and allow for easy insertion/deletion anywhere. Binary search trees fall between these two.

(a) There are three ways to traverse a binary tree pre-order, in-or.docx

The document discusses three topics: (1) in-order tree traversal, (2) B-tree data structures, and (3) open addressing for hash collisions. It provides code for in-order traversal and explains that B-trees allow for efficient searching, insertion and deletion of large blocks of sorted data, keeping the tree balanced. Open addressing resolves collisions by probing alternate array locations using techniques like linear, quadratic or double hashing until finding an empty slot.

Lecture notes data structures tree

The document discusses different types of tree data structures, including general trees, binary trees, binary search trees, and their traversal methods. General trees allow nodes to have any number of children, while binary trees restrict nodes to having 0, 1, or 2 children. Binary search trees organize nodes so that all left descendants are less than the parent and all right descendants are greater. Common traversal orders for trees include preorder, inorder, and postorder, which differ in whether they process the root node before or after visiting child nodes.

Trees in data structure

This document provides information about different tree data structures including binary trees, binary search trees, AVL trees, red-black trees, splay trees, and B-trees. Binary search trees allow for fast searching and maintain an ordered structure. AVL and red-black trees are self-balancing binary search trees that ensure fast search, insert, and delete times by keeping the tree balanced. B-trees are multiway search trees that allow for efficient storage and retrieval of data in databases and file systems.

Data Structures

This document discusses data structures and binary trees. It begins with basic terminology used in trees such as root, node, degree, levels, and traversal methods. It then explains different types of binary trees including strictly binary trees and complete binary trees. Next, it covers binary tree representations using arrays and linked lists. Finally, it discusses operations that can be performed on binary search trees including insertion, searching, deletion, and traversing nodes using preorder, inorder and postorder traversal methods.

Binary tree

These slides are part of a full series of slides which covers almost all the basic concepts of data structures and algorithms.
Part 11

Leftlist Heap-1.pdf

1. A leftist heap is a type of priority queue that is implemented using a variant of a binary heap. It attempts to be very unbalanced in contrast to a binary heap, which is always a complete binary tree.
2. Key operations on a leftist heap like insert, delete minimum, and merge have O(logN) time complexity. Merge is particularly efficient compared to a binary heap which has O(N) time complexity for merging.
3. Properties of a leftist heap include the minimum key property and the property that the right descendant of every node has a smaller s-value (distance to the nearest leaf). These properties allow leftist heaps to efficiently support merge in O(log

TREES.pptx

This document provides an overview of data structures and trees. It defines trees and their properties like hierarchical structure, parent-child relationships, and representation using arrays and linked lists. It describes binary trees and their properties. It also covers binary search trees, operations on binary trees like insertion, deletion and traversal, and balanced binary search trees like AVL trees.

Q

1. Hash tables are good for random access of elements but not sequential access. When records need to be accessed sequentially, hashing can be problematic because elements are stored in random locations instead of consecutively.
2. To find the successor of a node in a binary search tree, we take the right child. This operation has a runtime complexity of O(1).
3. When comparing operations like insertion, deletion, and searching between different data structures, arrays generally have the best performance for insertion and searching, while linked lists have better performance for deletion and allow for easy insertion/deletion anywhere. Binary search trees fall between these two.

(a) There are three ways to traverse a binary tree pre-order, in-or.docx

The document discusses three topics: (1) in-order tree traversal, (2) B-tree data structures, and (3) open addressing for hash collisions. It provides code for in-order traversal and explains that B-trees allow for efficient searching, insertion and deletion of large blocks of sorted data, keeping the tree balanced. Open addressing resolves collisions by probing alternate array locations using techniques like linear, quadratic or double hashing until finding an empty slot.

Lecture notes data structures tree

The document discusses different types of tree data structures, including general trees, binary trees, binary search trees, and their traversal methods. General trees allow nodes to have any number of children, while binary trees restrict nodes to having 0, 1, or 2 children. Binary search trees organize nodes so that all left descendants are less than the parent and all right descendants are greater. Common traversal orders for trees include preorder, inorder, and postorder, which differ in whether they process the root node before or after visiting child nodes.

Trees in data structure

This document provides information about different tree data structures including binary trees, binary search trees, AVL trees, red-black trees, splay trees, and B-trees. Binary search trees allow for fast searching and maintain an ordered structure. AVL and red-black trees are self-balancing binary search trees that ensure fast search, insert, and delete times by keeping the tree balanced. B-trees are multiway search trees that allow for efficient storage and retrieval of data in databases and file systems.

Data Structures

This document discusses data structures and binary trees. It begins with basic terminology used in trees such as root, node, degree, levels, and traversal methods. It then explains different types of binary trees including strictly binary trees and complete binary trees. Next, it covers binary tree representations using arrays and linked lists. Finally, it discusses operations that can be performed on binary search trees including insertion, searching, deletion, and traversing nodes using preorder, inorder and postorder traversal methods.

Binary tree

These slides are part of a full series of slides which covers almost all the basic concepts of data structures and algorithms.
Part 11

Leftlist Heap-1.pdf

1. A leftist heap is a type of priority queue that is implemented using a variant of a binary heap. It attempts to be very unbalanced in contrast to a binary heap, which is always a complete binary tree.
2. Key operations on a leftist heap like insert, delete minimum, and merge have O(logN) time complexity. Merge is particularly efficient compared to a binary heap which has O(N) time complexity for merging.
3. Properties of a leftist heap include the minimum key property and the property that the right descendant of every node has a smaller s-value (distance to the nearest leaf). These properties allow leftist heaps to efficiently support merge in O(log

(a)PreOrder, PostOrder and Inorder are three ways you can iterate .pdf

(a)
PreOrder, PostOrder and Inorder are three ways you can iterate a binary tree. The way these
three are different is in order of root,left child and right child.
Pre Order: root is printed first then lefy child and in last right child.
Given: TreeNode is class which have data part, left child and right child.
TreeNode root is root element of binary tree
Recursive algorithm of Preorder traversal
(A)void printPreorder(TreeNode root)
{
if (root == null) //Exit case if Tree is empty
return;
/* first print data of root because in preorder root is printed first */
System.out.println(root.value ); //recursive calling
/* then recur on left subtree of root*/
printPreorder(root.left); //recursive calling
/* now recur on right subtree of root*/
printPreorder(root.right); //recursive calling
}
Explanation: Here first we check If tree is exist or not. If exist we print root of tree and then
move to left part of current node and apply same process again untill left part is completed. After
that move to right sub tree and do same process again.
(b)
T(n) = T(k) + T(n โ k โ 1) + c
Where k is the number of nodes on one side of root and n-k-1 on the other side.
Letโs do analysis of boundary conditions
Case 1:left subtree is empty then all the n-1 nodes present in right part only. SO k=0
T(n) = T(0) + T(n-1) + c -(1)
Putting value of T(n-1) in equation 1
T(n) = 2T(0) + T(n-2) + 2c -(2)
Similarly puting value of T(n-3) in equation 2
T(n) = 3T(0) + T(n-3) + 3c
Similarly
T(n) = 4T(0) + T(n-4) + 4c
T(n) = (n-1)T(0) + T(1) + (n-1)c
T(n) = nT(0)-T(0) + (n)c-c
Value of T(0) will be some constant say d.
T(n)= n(d+c)-(c+d)
T(n)=(n-1)(c+d)
T(n) = Theta of n
Case 2: Both left and right subtrees have equal number of nodes.
T(n) = 2T(n/2) + c
which clearly shows T(n)= theta(n)
(c)
void printPreorder(TreeNode root)
{
if (root == null) //Exit case if Tree is empty
return;
/*print left subtree of root*/
printPreorder(root.left); //recursive calling
/* print data of root because in Inorder root is printed in middle */
System.out.println(root.value ); //recursive calling
/* now recur on right subtree of root*/
printPreorder(root.right); //recursive calling
}
(d)
void printPreorder(TreeNode root)
{
if (root == null) //Exit case if Tree is empty
return;
/*print left subtree of root*/
printPreorder(root.left); //recursive calling
/* now recur on right subtree of root*/
printPreorder(root.right); //recursive calling
/* print data of root because in postorder root is printed in last */
System.out.println(root.value ); //recursive calling
}
Solution
(a)
PreOrder, PostOrder and Inorder are three ways you can iterate a binary tree. The way these
three are different is in order of root,left child and right child.
Pre Order: root is printed first then lefy child and in last right child.
Given: TreeNode is class which have data part, left child and right child.
TreeNode root is root element of binary tree
Recursive algorithm of Preorder traversal
(A)void printPreorder(TreeNode root)
{
if .

Unit8 C

The document discusses tree data structures and binary trees. It provides definitions for key tree terminology like root, child, parent, leaf nodes, and discusses tree traversal methods like preorder, inorder, and postorder traversal. It also covers implementing binary trees using linked lists and building binary search trees with functions for insertion, searching, and deletion of nodes.

THREADED BINARY TREE AND BINARY SEARCH TREE

The document discusses threaded binary trees. It begins by defining a regular binary tree. It then explains that in a threaded binary tree, null pointers are replaced by threads (pointers) to other nodes. Threading rules specify that a null left/right pointer is replaced by a pointer to the inorder predecessor/successor. Boolean fields distinguish threads from links. Non-recursive traversals are possible by following threads. Insertion and deletion of nodes may require updating threads. Threaded binary trees allow efficient non-recursive traversals without a stack.

2 4 Tree

1. A (2,4)-tree is a type of multiway search tree where each node has between 2 and 4 children and all external nodes are at the same depth, maintaining the tree's balanced structure.
2. Insertion of a new key into a (2,4)-tree is done through searching, then inserting the key and splitting overflowed nodes, maintaining the structure properties. Deletion is done by searching, then deleting and fusing or transferring nodes to resolve underflows.
3. Both insertion and deletion take O(logn) time through splitting or fusing a constant number of nodes per operation while searching takes O(logn) time, maintaining the optimal O(logn

Binary Search Tree

The document discusses binary search trees and AVL trees. It defines binary search trees as binary trees where all left descendants of a node are less than or equal to the node and all right descendants are greater than or equal. Search, insertion and deletion operations in binary search trees have logarithmic time complexity. AVL trees are binary search trees where the heights of left and right subtrees differ by at most one, ensuring logarithmic time operations. The document outlines algorithms for insertion, deletion and balancing rotations in AVL trees.

Biary search Tree.docx

A binary search tree (BST) is a tree data structure where each node has a maximum of two children, and the values of left descendant nodes are less than the current node, which is less than the values of right descendant nodes. This structure allows for fast lookup, insertion, and removal of nodes in O(log n) time on average. However, in a worst case scenario where the tree is unbalanced, these operations can take O(n) time. Common operations on a BST include creating an empty tree, searching for a node, inserting a new node, and deleting an existing node.

Binary Tree - Algorithms

The document discusses various tree traversal algorithms and operations on binary trees. It explains breadth-first traversal, depth-first traversal including preorder, inorder and postorder. It also covers searching, inserting and checking if two trees are the same in binary trees. Other topics covered include finding the size, height, root-to-leaf sums, checking if a tree is a binary search tree, and level order traversal. Iterative algorithms for postorder, preorder and inorder traversal using stacks are also presented.

VCE Unit 05.pptx

This document discusses different tree and graph data structures and algorithms. It begins by defining trees and their key properties like nodes, roots, parents, children, levels. It then discusses binary trees and their representations. Next, it covers binary search trees, their properties and operations like search, insert, delete. It also discusses different tree traversals. Finally, it discusses heaps, graphs and their representations and operations.

Unit 3.ppt

This document discusses trees and binary trees. It defines key terminology like root, leaf nodes, internal nodes, and provides examples of different types of binary trees including full, complete, balanced, and binary search trees. It also covers different representations of binary trees using arrays and linked lists as well as common traversal techniques for binary trees like preorder, inorder and postorder traversal.

Trees

The document discusses deletion operations in B+ trees. It explains that deleting a key from a leaf node may cause the leaf to have too few keys, requiring a merge with a sibling leaf. If the sibling also has too few keys, their parent node may need to be split or merged to maintain the B+ tree properties. The process of replacing deleted internal keys and potentially merging/splitting nodes is similar to the insertion procedure.

Tree

The document discusses binary tree traversal methods. It defines key binary tree terminology like nodes, edges, root, and provides examples of different types of binary trees like strictly binary, complete, and almost complete binary trees. It also explains the three common traversal techniques for binary search trees - in-order, pre-order and post-order traversals - and provides pseudocode algorithms and examples for each traversal method.

Trees unit 3

The document discusses binary tree representation and traversal methods. It provides two main representations of binary trees - array and linked representations. It also describes different types of binary trees like full, complete, left-skewed, and right-skewed trees. The document then explains three common traversal techniques for binary trees - inorder, preorder, and postorder traversals. Algorithms and code snippets are given for each traversal. Finally, applications of binary tree traversals are discussed along with expression trees and converting infix to postfix notation using a stack.

Chap 5 Tree.ppt

The document discusses trees and graphs data structures. It begins with introducing different types of trees like binary trees, binary search trees, threaded binary trees, and their various traversal algorithms like inorder, preorder and postorder traversals. It then discusses tree operations like copying trees, testing for equality. It also covers the satisfiability problem and how binary trees can be used to represent logical expressions to solve this problem. Finally, it discusses threaded binary trees where null links in a binary tree are replaced with threads, and how this allows for efficient inorder traversal in linear time.

Trees

This document discusses binary trees, including their basic definitions, traversal methods, node representations, and functions. It describes binary trees as having a root node that partitions the tree into two disjoint subsets, left and right subtrees. Traversal methods like preorder, inorder, and postorder are explained recursively. Applications of binary search trees for sorting and searching arrays are also covered.

Tree and Binary Search tree

Tree and Binary search tree in data structure.
The complete explanation of working of trees and Binary Search Tree is given. It is discussed such a way that everyone can easily understand it. Trees have great role in the data structures.

Red black 1

Red black trees are binary search trees where each node is colored red or black. Properties of red black trees include: (1) the root and external nodes are black, (2) no two consecutive nodes on any path from the root to an external node are red, and (3) all paths from the root to an external node contain the same number of black nodes. Insertion and deletion of nodes may violate these properties and require rebalancing through rotations and recoloring of nodes.

computer notes - Deleting a node

As is common with many data structures, the hardest operation is deletion. Once we have found the node to be deleted, we need to consider several possibilities. If the node is a leaf, it can be deleted immediately.

Master of Computer Application (MCA) โ Semester 4 MC0080

This document describes several sorting algorithms and asymptotic analysis techniques. It discusses bubble sort, selection sort, insertion sort, shell sort, heap sort, merge sort, and quick sort as sorting algorithms. It then explains asymptotic notation such as Big-O, Big-Omega, and Theta to describe the time complexity of algorithms. Finally, it asks questions about Fibonacci heaps, binomial heaps, Strassen's matrix multiplication algorithm, and formalizing a greedy algorithm.

L 17 ct1120

Class lecture of Data Structure and Algorithms and Python.
Stack, Queue, Tree, Python, Python Code, Computer Science, Data, Data Analysis, Machine Learning, Artificial Intellegence, Deep Learning, Programming, Information Technology, Psuedocide, Tree, pseudocode, Binary Tree, Binary Search Tree, implementation, Binary search, linear search, Binary search operation, real-life example of binary search, linear search operation, real-life example of linear search, example bubble sort, sorting, insertion sort example, stack implementation, queue implementation, binary tree implementation, priority queue, binary heap, binary heap implementation

DS MCQS.pptx

The document contains questions and answers related to binary search trees and graphs. It discusses finding the minimum element in a binary search tree, different tree traversals like preorder, inorder and postorder, properties of binary search trees like the increasing order of inorder traversal and complexity, balance factors of binary trees, cut vertices in graphs, and properties of complete graphs.

In a study on the retirement savings plans of young Canadian.pdf

In a study on the retirement savings plans of young Canadians, a sample of 400 Canadians
between the ages of 25 and 34 revealed that only 14 made regular personal contributions to an
RRSP. Based on this result, construct a 99% confidence interval for the true proportion of young
Canadians (aged 25-34) who make regular personal contributions to an RRSP. (3 marks).

In a spreadsheet decompose the change in the debt ratio fro.pdf

In a spreadsheet, decompose the change in the debt ratio from 2020 to 2025 into its key drivers
using the equation for debt accumulation that we studied in class (shown above) and data from
Budget 2023 Economic & Fiscal Outlook. (ii) Construct a table summarising how each of the three
components of the equation contributed to changes in the debt ratio during the COVID-19
pandemic as well as their expected contributions in the years ahead. (iii) Comment briefly on how
each of these drivers have contributed to changes in the debt ratio during the pandemic and in the
years ahead..

(a)PreOrder, PostOrder and Inorder are three ways you can iterate .pdf

(a)
PreOrder, PostOrder and Inorder are three ways you can iterate a binary tree. The way these
three are different is in order of root,left child and right child.
Pre Order: root is printed first then lefy child and in last right child.
Given: TreeNode is class which have data part, left child and right child.
TreeNode root is root element of binary tree
Recursive algorithm of Preorder traversal
(A)void printPreorder(TreeNode root)
{
if (root == null) //Exit case if Tree is empty
return;
/* first print data of root because in preorder root is printed first */
System.out.println(root.value ); //recursive calling
/* then recur on left subtree of root*/
printPreorder(root.left); //recursive calling
/* now recur on right subtree of root*/
printPreorder(root.right); //recursive calling
}
Explanation: Here first we check If tree is exist or not. If exist we print root of tree and then
move to left part of current node and apply same process again untill left part is completed. After
that move to right sub tree and do same process again.
(b)
T(n) = T(k) + T(n โ k โ 1) + c
Where k is the number of nodes on one side of root and n-k-1 on the other side.
Letโs do analysis of boundary conditions
Case 1:left subtree is empty then all the n-1 nodes present in right part only. SO k=0
T(n) = T(0) + T(n-1) + c -(1)
Putting value of T(n-1) in equation 1
T(n) = 2T(0) + T(n-2) + 2c -(2)
Similarly puting value of T(n-3) in equation 2
T(n) = 3T(0) + T(n-3) + 3c
Similarly
T(n) = 4T(0) + T(n-4) + 4c
T(n) = (n-1)T(0) + T(1) + (n-1)c
T(n) = nT(0)-T(0) + (n)c-c
Value of T(0) will be some constant say d.
T(n)= n(d+c)-(c+d)
T(n)=(n-1)(c+d)
T(n) = Theta of n
Case 2: Both left and right subtrees have equal number of nodes.
T(n) = 2T(n/2) + c
which clearly shows T(n)= theta(n)
(c)
void printPreorder(TreeNode root)
{
if (root == null) //Exit case if Tree is empty
return;
/*print left subtree of root*/
printPreorder(root.left); //recursive calling
/* print data of root because in Inorder root is printed in middle */
System.out.println(root.value ); //recursive calling
/* now recur on right subtree of root*/
printPreorder(root.right); //recursive calling
}
(d)
void printPreorder(TreeNode root)
{
if (root == null) //Exit case if Tree is empty
return;
/*print left subtree of root*/
printPreorder(root.left); //recursive calling
/* now recur on right subtree of root*/
printPreorder(root.right); //recursive calling
/* print data of root because in postorder root is printed in last */
System.out.println(root.value ); //recursive calling
}
Solution
(a)
PreOrder, PostOrder and Inorder are three ways you can iterate a binary tree. The way these
three are different is in order of root,left child and right child.
Pre Order: root is printed first then lefy child and in last right child.
Given: TreeNode is class which have data part, left child and right child.
TreeNode root is root element of binary tree
Recursive algorithm of Preorder traversal
(A)void printPreorder(TreeNode root)
{
if .

Unit8 C

The document discusses tree data structures and binary trees. It provides definitions for key tree terminology like root, child, parent, leaf nodes, and discusses tree traversal methods like preorder, inorder, and postorder traversal. It also covers implementing binary trees using linked lists and building binary search trees with functions for insertion, searching, and deletion of nodes.

THREADED BINARY TREE AND BINARY SEARCH TREE

The document discusses threaded binary trees. It begins by defining a regular binary tree. It then explains that in a threaded binary tree, null pointers are replaced by threads (pointers) to other nodes. Threading rules specify that a null left/right pointer is replaced by a pointer to the inorder predecessor/successor. Boolean fields distinguish threads from links. Non-recursive traversals are possible by following threads. Insertion and deletion of nodes may require updating threads. Threaded binary trees allow efficient non-recursive traversals without a stack.

2 4 Tree

1. A (2,4)-tree is a type of multiway search tree where each node has between 2 and 4 children and all external nodes are at the same depth, maintaining the tree's balanced structure.
2. Insertion of a new key into a (2,4)-tree is done through searching, then inserting the key and splitting overflowed nodes, maintaining the structure properties. Deletion is done by searching, then deleting and fusing or transferring nodes to resolve underflows.
3. Both insertion and deletion take O(logn) time through splitting or fusing a constant number of nodes per operation while searching takes O(logn) time, maintaining the optimal O(logn

Binary Search Tree

The document discusses binary search trees and AVL trees. It defines binary search trees as binary trees where all left descendants of a node are less than or equal to the node and all right descendants are greater than or equal. Search, insertion and deletion operations in binary search trees have logarithmic time complexity. AVL trees are binary search trees where the heights of left and right subtrees differ by at most one, ensuring logarithmic time operations. The document outlines algorithms for insertion, deletion and balancing rotations in AVL trees.

Biary search Tree.docx

A binary search tree (BST) is a tree data structure where each node has a maximum of two children, and the values of left descendant nodes are less than the current node, which is less than the values of right descendant nodes. This structure allows for fast lookup, insertion, and removal of nodes in O(log n) time on average. However, in a worst case scenario where the tree is unbalanced, these operations can take O(n) time. Common operations on a BST include creating an empty tree, searching for a node, inserting a new node, and deleting an existing node.

Binary Tree - Algorithms

The document discusses various tree traversal algorithms and operations on binary trees. It explains breadth-first traversal, depth-first traversal including preorder, inorder and postorder. It also covers searching, inserting and checking if two trees are the same in binary trees. Other topics covered include finding the size, height, root-to-leaf sums, checking if a tree is a binary search tree, and level order traversal. Iterative algorithms for postorder, preorder and inorder traversal using stacks are also presented.

VCE Unit 05.pptx

This document discusses different tree and graph data structures and algorithms. It begins by defining trees and their key properties like nodes, roots, parents, children, levels. It then discusses binary trees and their representations. Next, it covers binary search trees, their properties and operations like search, insert, delete. It also discusses different tree traversals. Finally, it discusses heaps, graphs and their representations and operations.

Unit 3.ppt

This document discusses trees and binary trees. It defines key terminology like root, leaf nodes, internal nodes, and provides examples of different types of binary trees including full, complete, balanced, and binary search trees. It also covers different representations of binary trees using arrays and linked lists as well as common traversal techniques for binary trees like preorder, inorder and postorder traversal.

Trees

The document discusses deletion operations in B+ trees. It explains that deleting a key from a leaf node may cause the leaf to have too few keys, requiring a merge with a sibling leaf. If the sibling also has too few keys, their parent node may need to be split or merged to maintain the B+ tree properties. The process of replacing deleted internal keys and potentially merging/splitting nodes is similar to the insertion procedure.

Tree

The document discusses binary tree traversal methods. It defines key binary tree terminology like nodes, edges, root, and provides examples of different types of binary trees like strictly binary, complete, and almost complete binary trees. It also explains the three common traversal techniques for binary search trees - in-order, pre-order and post-order traversals - and provides pseudocode algorithms and examples for each traversal method.

Trees unit 3

The document discusses binary tree representation and traversal methods. It provides two main representations of binary trees - array and linked representations. It also describes different types of binary trees like full, complete, left-skewed, and right-skewed trees. The document then explains three common traversal techniques for binary trees - inorder, preorder, and postorder traversals. Algorithms and code snippets are given for each traversal. Finally, applications of binary tree traversals are discussed along with expression trees and converting infix to postfix notation using a stack.

Chap 5 Tree.ppt

The document discusses trees and graphs data structures. It begins with introducing different types of trees like binary trees, binary search trees, threaded binary trees, and their various traversal algorithms like inorder, preorder and postorder traversals. It then discusses tree operations like copying trees, testing for equality. It also covers the satisfiability problem and how binary trees can be used to represent logical expressions to solve this problem. Finally, it discusses threaded binary trees where null links in a binary tree are replaced with threads, and how this allows for efficient inorder traversal in linear time.

Trees

This document discusses binary trees, including their basic definitions, traversal methods, node representations, and functions. It describes binary trees as having a root node that partitions the tree into two disjoint subsets, left and right subtrees. Traversal methods like preorder, inorder, and postorder are explained recursively. Applications of binary search trees for sorting and searching arrays are also covered.

Tree and Binary Search tree

Tree and Binary search tree in data structure.
The complete explanation of working of trees and Binary Search Tree is given. It is discussed such a way that everyone can easily understand it. Trees have great role in the data structures.

Red black 1

Red black trees are binary search trees where each node is colored red or black. Properties of red black trees include: (1) the root and external nodes are black, (2) no two consecutive nodes on any path from the root to an external node are red, and (3) all paths from the root to an external node contain the same number of black nodes. Insertion and deletion of nodes may violate these properties and require rebalancing through rotations and recoloring of nodes.

computer notes - Deleting a node

As is common with many data structures, the hardest operation is deletion. Once we have found the node to be deleted, we need to consider several possibilities. If the node is a leaf, it can be deleted immediately.

Master of Computer Application (MCA) โ Semester 4 MC0080

This document describes several sorting algorithms and asymptotic analysis techniques. It discusses bubble sort, selection sort, insertion sort, shell sort, heap sort, merge sort, and quick sort as sorting algorithms. It then explains asymptotic notation such as Big-O, Big-Omega, and Theta to describe the time complexity of algorithms. Finally, it asks questions about Fibonacci heaps, binomial heaps, Strassen's matrix multiplication algorithm, and formalizing a greedy algorithm.

L 17 ct1120

Class lecture of Data Structure and Algorithms and Python.
Stack, Queue, Tree, Python, Python Code, Computer Science, Data, Data Analysis, Machine Learning, Artificial Intellegence, Deep Learning, Programming, Information Technology, Psuedocide, Tree, pseudocode, Binary Tree, Binary Search Tree, implementation, Binary search, linear search, Binary search operation, real-life example of binary search, linear search operation, real-life example of linear search, example bubble sort, sorting, insertion sort example, stack implementation, queue implementation, binary tree implementation, priority queue, binary heap, binary heap implementation

DS MCQS.pptx

The document contains questions and answers related to binary search trees and graphs. It discusses finding the minimum element in a binary search tree, different tree traversals like preorder, inorder and postorder, properties of binary search trees like the increasing order of inorder traversal and complexity, balance factors of binary trees, cut vertices in graphs, and properties of complete graphs.

(a)PreOrder, PostOrder and Inorder are three ways you can iterate .pdf

(a)PreOrder, PostOrder and Inorder are three ways you can iterate .pdf

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Unit8 C

Unit8 C

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THREADED BINARY TREE AND BINARY SEARCH TREE

THREADED BINARY TREE AND BINARY SEARCH TREE

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2 4 Tree

2 4 Tree

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Binary Search Tree

Binary Search Tree

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Biary search Tree.docx

Biary search Tree.docx

ย

Binary Tree - Algorithms

Binary Tree - Algorithms

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VCE Unit 05.pptx

VCE Unit 05.pptx

ย

Unit 3.ppt

Unit 3.ppt

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Trees

Trees

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Tree

Tree

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Trees unit 3

Trees unit 3

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Chap 5 Tree.ppt

Chap 5 Tree.ppt

ย

Trees

Trees

ย

Tree and Binary Search tree

Tree and Binary Search tree

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Red black 1

Red black 1

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computer notes - Deleting a node

computer notes - Deleting a node

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Master of Computer Application (MCA) โ Semester 4 MC0080

Master of Computer Application (MCA) โ Semester 4 MC0080

ย

L 17 ct1120

L 17 ct1120

ย

DS MCQS.pptx

DS MCQS.pptx

ย

In a study on the retirement savings plans of young Canadian.pdf

In a study on the retirement savings plans of young Canadians, a sample of 400 Canadians
between the ages of 25 and 34 revealed that only 14 made regular personal contributions to an
RRSP. Based on this result, construct a 99% confidence interval for the true proportion of young
Canadians (aged 25-34) who make regular personal contributions to an RRSP. (3 marks).

In a spreadsheet decompose the change in the debt ratio fro.pdf

In a spreadsheet, decompose the change in the debt ratio from 2020 to 2025 into its key drivers
using the equation for debt accumulation that we studied in class (shown above) and data from
Budget 2023 Economic & Fiscal Outlook. (ii) Construct a table summarising how each of the three
components of the equation contributed to changes in the debt ratio during the COVID-19
pandemic as well as their expected contributions in the years ahead. (iii) Comment briefly on how
each of these drivers have contributed to changes in the debt ratio during the pandemic and in the
years ahead..

In a school there are 5 sections of 10th standard with same.pdf

In a school, there are 5 sections of 10th standard with same number of students. Formation of
sections is based on the performance of students in 9th standard. To judge the IQ of 10th class
students, principal selected randomly 16 students from each section. What is the type of sampling
technique he used? Simple random Sampling Systematic Sampling Stratified Sampling.

In a recent year grade 10 Washington State public school st.pdf

In a recent year, grade 10 Washington State public school students taking a mathematics
assessment test are normally distributed, with a mean score of 276.1 and a standard deviation of
34.4. Are you more likely to randomly select one student with a test score greater than 300 or are
you more likely to select a sample of 16 students with a mean test score greater than 300?.

In a recent poll the Gallup Organization found that 45 of.pdf

In a recent poll, the Gallup Organization found
that 45% of adult Americans believe that the overall state of
moral values in the United States is poor. Suppose a survey of a
random sample of 25 adult Americans is conducted in which
they are asked to disclose their feelings on the overall state of
moral values in the United States.
(a) Find and interpret the probability that exactly 15 of those
surveyed feel the state of morals is poor.
(b) Find and interpret the probability that no more than 10 of
those surveyed feel the state of morals is poor.
(c) Find and interpret the probability that more than 16 of those
surveyed feel the state of morals is poor.
(d) Find and interpret the probability that 13 or 14 believe the
state of morals is poor.
(e) Would it be unusual to find 20 or more adult Americans
who believe the overall state of moral values is poor in the
United States? Why?.

In a random sample of UTC students 50 indicated they are b.pdf

In a random sample of UTC students, 50% indicated they are business majors, 40% engineering
majors, and 10% other majors. Of the business majors, 60% were females, whereas 30% of
engineering majors were females. Finally, 20% of the other majors were female. Given that a
person is female, what is the probability that she is an engineering major? ( 4 Decimal format =
0.0000 ).

In a previous yeac the weights of the members of the San Fra.pdf

In a previous yeac the weights of the members of the San Francisco 4 Gers and the Dallss
Cowbors were published in the San Jose Mercury News. The fsctual dies are compled into she
foltowing fatle fer the folowing, supene that you randomly select one pibyer from the 49ers or
Combont. et Panc(a)Suppose that P(A)=0.4 and P(B)=0.1. If events A and B are independent, find
these probabilities. (a) P(AB) (b) P(AB).

In a questionnaire for 100 pernens the gender distribution .pdf

In a questionnaire for 100 pernens, the gender distribution (V) was 40 Nale (Mls and ou feumas
(E). Question: Do jou watch Foorball on TV? The answers X were Yes (1) or No (0). The number
of reypurses is given in the showa kahlo..

In a normal distribution what is the probability that a ran.pdf

In a normal distribution, what is the probability that a random sample of 204 with population
proportion 0.17 has a sample proportion of less than 0,16 ? Level of difficulty =1 of 3 Please
format to 3 decimal places. Answer:.

In 2019 scientists conducted a research study about spicy f.pdf

In 2019, scientists conducted a research study about spicy food as a potential risk factor for
gastroesophageal reflux disease (GERD). Scientists enrolled 500 patients with GERD. An
additional 1,000 persons without GERD were also enrolled, matched on gender to patients with
GERD. Participants self-reported their recent spicy foods consumption. What study design did the
scientists use to answer their research question?
a. Case-control study b. Cross-sectional study c. Prospective cohort study X d. Randomized
clinical trial X.

In a holiday gathering two families family 1 and family 2 .pdf

In a holiday gathering, two families: family 1 and family 2 play a game repeatedly and
independently until one of them win. A given game ends in a tie with probability of 0.2 . The
probability that family 1 wins an individual game is 0.35 , while probability that family 2 wins an
individual game is 0.45 . What is the probability that family 1 is eventual winner..

in 2019 facebook Announced is Plan 70 pon out a nea stablec.pdf

Facebook announced plans in 2019 for a stablecoin called Libra, which was later renamed to Diem in 2020 after failing to gain approval from U.S. regulators. Regulators had major concerns about the stablecoin, and in 2022 Meta decided to shut down the Diem project due to an inability to address these regulatory concerns.

In a city of half a million there are initially 400 cases o.pdf

In a city of half a million, there are initially 400 cases of a particularly virulent strain of flu. The
Centers for Disease Control and Prevention in Atlanta claims that the cumulative number of
infections of this flu strain will increase by 40% per week if there are no limiting factors. Make a
logistic model of the potential cumulative number of cases of flu as a function of weeks from initial
outbreak, and determine how long it will be before 100,000 people are infected..

In a 10year graph with an explanation of Idaho Panhandle H.pdf

In a 10-year graph with an explanation of Idaho Panhandle: Hypothetically speaking A forested
region with regular annual prescribed fire(RX), has a creek running through it. In a semi-arid
region, during the months of winter, which are typically wet each year and dry each year in the
summer. What would the results be in year 7, the month of July of the watershed when a wildfire
hits (2 months before full suppression) during the summertime? In terms of the watershed, what
would happen with runoff, local ecology, streamflow, changes in sediment, animal wildlife
activities, etcetera)..

In 2D let xx1x2 Write down the explicit cubic feature.pdf

In 2-D, let x=[x1,x2]. Write down the explicit cubic feature mapping (x) as a vector; i.e., (x)=[f1(x1,x
2),,fN(x1,x2)] Hint Hint: (x) should be a 10-dimensional vector. (x)= You have used 0 of 20
attempts The cubic_features function in features.py is already implemented for you. That function
can handle input with an arbitrary dimension and compute the corresponding features for the cubic
Kernel. Note that here we don't leverage the kernel properties that allow us to do a more efficient
computation with the kernel function (without computing the features themselves). Instead, here
we do compute the cubic features explicitly and apply the PCA on the output features..

In 2018 Tirana Trucks had a retum on equity of 180 and a.pdf

In 2018, Tirana Trucks had a retum on equity of 18.0%, and a financial leverage multiplier of 3.0 .
What was the return on assets? Enter your answer as a decimal, rounded to 4 decimal places (
.0000).

In 2021 California passed a law to provide all public schoo.pdf

In 2021, California passed a law to provide all public school children with free lunch and breakfast.
Public health professionals have asked the state to make sure the meals are healthy and
nutritious, to reduce the chance the program might contribute to childhood obesity. What are
public health professionals asking California to consider?
Balance the interests of the state and schools
Maximize the benefits over harms
Manage a tragedy of the commons
Interpret the general welfare clause broadly.

import yfinance as yf yfTickerstickersAAPL TSLA.pdf

import yfinance as yf
(yf.Tickers(tickers=['AAPL', 'TSLA']).history(period='max', auto_adjust=False,
progress=False).assign(Date = lambda
x:x.index.tz_localize(None)).set_index('Date').rename_axis(columns=['Variable',
'Ticker']).to_csv('yahoo.csv'))
Read the daily returns data for AAPL and TSLA saved in file yahoo.csv Calculate the decimal daily
returns for AAPL and TSLA from July 2010 through February 2023 (inclusive) and assign to data
frame returns..

In 2020 Natural Selection a nationwide computer dating se.pdf

In 2020, Natural Selection, a nationwide computer dating service has $508 million assets and
$204 million of liabilities. Earnings before interests and taxes were $124 million, interest expense
was $28.5million, the tax rate was 40%, principal payment requirements were $23.9 million, and
annual dividends were 20% per share on $20 million share outstanding. Calculate the following for
natural selection:
liabilities-to-equity ratio
times-interest-earned ratio
times burden covered.

In 2017 Americans spent a recordhigh 91 billion on Hallo.pdf

In 2017, Americans spent a record-high $9.1 billion on Halloween-related purchases (the balance
website). Sample data showing the amount, in dollars, 16 adults spent on a Halloween costume
are as follows. a. What is the estimate of the population mean amount adults spend on a
Halloween costume (to 2 decimals)? $ b. What is the sample standard deviation (to 2 decimals)? $
c. Provide a 95% confidence interval estimate of the population standard deviation for the amount
adults spend on a Halloween costume (to 2 decimals). Use Table 11.1 $$.

In a study on the retirement savings plans of young Canadian.pdf

In a study on the retirement savings plans of young Canadian.pdf

ย

In a spreadsheet decompose the change in the debt ratio fro.pdf

In a spreadsheet decompose the change in the debt ratio fro.pdf

ย

In a school there are 5 sections of 10th standard with same.pdf

In a school there are 5 sections of 10th standard with same.pdf

ย

In a recent year grade 10 Washington State public school st.pdf

In a recent year grade 10 Washington State public school st.pdf

ย

In a recent poll the Gallup Organization found that 45 of.pdf

In a recent poll the Gallup Organization found that 45 of.pdf

ย

In a random sample of UTC students 50 indicated they are b.pdf

In a random sample of UTC students 50 indicated they are b.pdf

ย

In a previous yeac the weights of the members of the San Fra.pdf

In a previous yeac the weights of the members of the San Fra.pdf

ย

In a questionnaire for 100 pernens the gender distribution .pdf

In a questionnaire for 100 pernens the gender distribution .pdf

ย

In a normal distribution what is the probability that a ran.pdf

In a normal distribution what is the probability that a ran.pdf

ย

In 2019 scientists conducted a research study about spicy f.pdf

In 2019 scientists conducted a research study about spicy f.pdf

ย

In a holiday gathering two families family 1 and family 2 .pdf

In a holiday gathering two families family 1 and family 2 .pdf

ย

in 2019 facebook Announced is Plan 70 pon out a nea stablec.pdf

in 2019 facebook Announced is Plan 70 pon out a nea stablec.pdf

ย

In a city of half a million there are initially 400 cases o.pdf

In a city of half a million there are initially 400 cases o.pdf

ย

In a 10year graph with an explanation of Idaho Panhandle H.pdf

In a 10year graph with an explanation of Idaho Panhandle H.pdf

ย

In 2D let xx1x2 Write down the explicit cubic feature.pdf

In 2D let xx1x2 Write down the explicit cubic feature.pdf

ย

In 2018 Tirana Trucks had a retum on equity of 180 and a.pdf

In 2018 Tirana Trucks had a retum on equity of 180 and a.pdf

ย

In 2021 California passed a law to provide all public schoo.pdf

In 2021 California passed a law to provide all public schoo.pdf

ย

import yfinance as yf yfTickerstickersAAPL TSLA.pdf

import yfinance as yf yfTickerstickersAAPL TSLA.pdf

ย

In 2020 Natural Selection a nationwide computer dating se.pdf

In 2020 Natural Selection a nationwide computer dating se.pdf

ย

In 2017 Americans spent a recordhigh 91 billion on Hallo.pdf

In 2017 Americans spent a recordhigh 91 billion on Hallo.pdf

ย

Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum

(๐๐๐ ๐๐๐) (๐๐๐ฌ๐ฌ๐จ๐ง ๐)-๐๐ซ๐๐ฅ๐ข๐ฆ๐ฌ
๐๐ข๐ฌ๐๐ฎ๐ฌ๐ฌ ๐ญ๐ก๐ ๐๐๐ ๐๐ฎ๐ซ๐ซ๐ข๐๐ฎ๐ฅ๐ฎ๐ฆ ๐ข๐ง ๐ญ๐ก๐ ๐๐ก๐ข๐ฅ๐ข๐ฉ๐ฉ๐ข๐ง๐๐ฌ:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
๐๐ฑ๐ฉ๐ฅ๐๐ข๐ง ๐ญ๐ก๐ ๐๐๐ญ๐ฎ๐ซ๐ ๐๐ง๐ ๐๐๐จ๐ฉ๐ ๐จ๐ ๐๐ง ๐๐ง๐ญ๐ซ๐๐ฉ๐ซ๐๐ง๐๐ฎ๐ซ:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.

RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students

Physical pharmaceutics notes for B.pharm students

Leveraging Generative AI to Drive Nonprofit Innovation

In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)

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Plenary presentation at the NTTC Inter-university Workshop, 18 June 2024, Manila Prince Hotel.

Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"

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This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.ย

How Barcodes Can Be Leveraged Within Odoo 17

In this presentation, we will explore how barcodes can be leveraged within Odoo 17 to streamline our manufacturing processes. We will cover the configuration steps, how to utilize barcodes in different manufacturing scenarios, and the overall benefits of implementing this technology.

Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt

The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,

Pharmaceutics Pharmaceuticals best of brub

First year pharmacy
Best for u

CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx

Slides from a Capitol Technology University webinar held June 20, 2024. The webinar featured Dr. Donovan Wright, presenting on the Department of Defense Digital Transformation.

Bonku-Babus-Friend by Sathyajith Ray (9)

Bonku-Babus-Friend by Sathyajith Ray for class 9 ksb

How to Manage Reception Report in Odoo 17

A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.

NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx

Revision on Paper 1 - Question 1

HYPERTENSION - SLIDE SHARE PRESENTATION.

IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.

How to Predict Vendor Bill Product in Odoo 17

This slide will guide us through the process of predicting vendor bill products based on previous purchases from the vendor in Odoo 17.

CHUYรN ฤแป รN TแบฌP Vร PHรT TRIแปN CรU HแปI TRONG ฤแป MINH HแปA THI TแปT NGHIแปP THPT ...

CHUYรN ฤแป รN TแบฌP Vร PHรT TRIแปN CรU HแปI TRONG ฤแป MINH HแปA THI TแปT NGHIแปP THPT ...Nguyen Thanh Tu Collection

https://app.box.com/s/qspvswamcohjtbvbbhjad04lg65waylfย

Standardized tool for Intelligence test.

ASSESSMENT OF INTELLIGENCE USING WITH STANDARDIZED TOOL

Wound healing PPT

This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the bodyโs response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.

MDP on air pollution of class 8 year 2024-2025

mdp on air polution

Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...

Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.

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Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum

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RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students

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Leveraging Generative AI to Drive Nonprofit Innovation

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Educational Technology in the Health Sciences

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Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"

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How Barcodes Can Be Leveraged Within Odoo 17

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Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt

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Pharmaceutics Pharmaceuticals best of brub

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CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx

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Bonku-Babus-Friend by Sathyajith Ray (9)

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How to Manage Reception Report in Odoo 17

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NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx

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HYPERTENSION - SLIDE SHARE PRESENTATION.

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The basics of sentences session 7pptx.pptx

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How to Predict Vendor Bill Product in Odoo 17

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CHUYรN ฤแป รN TแบฌP Vร PHรT TRIแปN CรU HแปI TRONG ฤแป MINH HแปA THI TแปT NGHIแปP THPT ...

CHUYรN ฤแป รN TแบฌP Vร PHรT TRIแปN CรU HแปI TRONG ฤแป MINH HแปA THI TแปT NGHIแปP THPT ...

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Standardized tool for Intelligence test.

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Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...

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- 1. Implement special cases here: (define (delete t v) (let ((path (find t v))) (cond (( empty? t ) ) ((empty? (bst-root t)) ) ((not ( = v (node-value (car path))) ) (( > (node-count (car path)) 1) decrement count) ((equal? (car path) (bst-root t)) ;node were trying to delete (cond ; nest conditiona; ( (let-AND right (car path) empty) ; case 0.1 root <- null ((let-root empty, right empty) ; case 1 root <- left car path ; case 1.1 ((left-empty, right not empty) ; case 1.2 root <- right car path (else (delete-node path)) (else (delete-node path)) ) ) ) ) ) ) ) ) ) Special cases Top-Level Function: Delete Value from BST: (delete t v) The first parameter t is a reference to a bst, and the second parameter v is a value to find and delete. Like the insert function, delete will directly resolve a few special cases. For the general cases, it will call (find t v) to obtain a list of nodes that represent a path from the root to the node to be deleted, and will then call a helper function (delete-node path) to handle the rest of the work. In the case of delete the helper function will further rely on secondary helper functions to resolve cases and subcases. Deletion logically breaks down into cases based on how many child nodes the node to delete has. Each of those cases has subcases. The large number of cases implies the need for a correspondingly larger set of test cases: a test case to trigger each deletion case. Delete Cases Before we look at the detailed code for delete in Racket, lets look at the general approach. As for some of the other functions, it will be convenient to create a top-level function (delete t v) and several helper functions that manage specific detailed cases. There will be some initial special
- 2. cases that should be managed separately, before launching any lower level helper function. Special cases for (delete t v): Tree t is empty: end the function because there is nothing to do. At this point, call (find t v) to create the path from root to node to delete if it is present. Assume the list returned is bound to a symbol named path. The node of interest will be the first node in the list: (car path) By examining node (car path), you can determine if the value to delete is present or not. Value v is not in the tree: end the function because there is nothing to do. Value v is in the tree: o Is the count field > 1? Dont delete the node, simply decrement its count field. o Is the count field = 1? In this case, we must move forward to actually delete the node. Is the node to delete the root of the tree? Does the node have 0 or 1 child nodes? This corresponds to delete cases 0.1, 1.1, and 1.2. Delete the node and update the root of the tree. o If we reach this pointvalue v is in the tree, count field is 1, node is not the root if it has 0 or 1 child nodes then the general delete case applies, call (delete-node path) The remaining delete cases will be covered by the (delete-node path) helper function. Some general considerations for node n (node to delete), node p (parent of n), and node c (child of n). Is node n the left or right child of node p? If node n only has one child, node c, is node c the left child or right child of node n? If node n has two children, we will use an additional procedure to find the in-order predecessor of n, node iop. We will locate node iop, physically delete it, and copy its value and count fields into the original node, node n. This results in a logical but not physical delete of node n. Below is a detailed enumeration of all delete cases based on child count. Subcases 0.1, 1.1, and 1.2 will be handled as special cases by the top-level delete function because these cases cause the root of the tree to change. Since we are maintaining the result of (find t v) in path we can make the following assumptions for all remaining cases: Node to delete: (car path) Parent of node to delete: (car (cdr path)) = (cadr path) Child nodes of node to delete, if they exist: o (node-left(carpath)) o (node-right(carpath)) Path from n to in-order predecessor node: ioppath (only needed if n has two child nodes) In-order predecessor node: (car ioppath) (only needed if node n has two child nodes) Dont confuse path (list of nodes from root of tree to n) with ioppath (list of nodes from n to iop) Case 0: Child Count = 0 Subcase 0.1: parent is null implying node is root (already covered in top-level function) o node being deleted is root of the tree and has 0 child nodes. Set root to null Subcase 0.2: node is left child of parent o set left child of parent to null Subcase 0.3: node is right child of parent o Set right child of parent to null, root doesnt change
- 3. Case 1: Child Count = 1 Subcase 1.1: parent is null and child is left child of node (already covered in top-level) o node is root ,set root to left child Subcase 1.2: parent is null and child is right child of node (already covered in top-level) o Node is root, set root to right child Subcase 1.3: node is left child of parent and child is left child of node o set left child of parent to left child of node Subcase 1.4: node is left child of parent and child is right child of node o set left child of parent to right child of node Subcase 1.5: node is right child of parent and child is left child of node o set right child of parent to left child of node Subcase 1.6: node is right child of parent and child is right child of node o set right child of parent to right child of node The cases and subcases are similar, but still differ in the specifics. Take care to identify the correct case and respond with the correct implementation for that case. In the above cases, note that the root is the only node with no parent (if parent of n is null, then n is the root). Also note the deletion cases that cause a change in the root of the tree (0.1, 1.1, and 1.2) are coded directly in the top- level function. Case 2: Child Count = 2 There is no easy way to delete a node with two child nodes. Instead we substitute the original problem with a problem that is easier to solve: Locate the in-order predecessor of the node to be deleted. Move the value and count fields from the in-order predecessor node to the original node, thereby erasing the previous value and count fields of the original node. This content substitution achieves a logical removal of the original node. Physically remove the in-order predecessor node o Case 2.1: predecessor node is left of parent o Case 2.2: predecessor node is right of paren