Tree Data Structure There are many basic data structures that can be used to solve application problems. Array is a good static data structure that can be accessed randomly and is fairly easy to implement. Linked Lists on the other hand is dynamic and is ideal for application that requires frequent operations such as add, delete, and update.

- One drawback of linked list is that data access is sequential.
- Then there are other specialized data structures like, stacks and queues that allows us to solve complicated problems ( eg : Maze traversal) using these restricted data structures.
- One other data structure is the hash table that allows users to program applications that require frequent search and updates.

They can be done in O( 1) in a hash table. One of the disadvantages of using an array or linked list to store data is the time necessary to search for an item. Since both the arrays and Linked Lists are linear structures the time required to search a “linear” list is proportional to the size of the data set.

For example, if the size of the data set is n, then the number of comparisons needed to find (or not find) an item may be as bad as some multiple of n. So imagine doing the search on a linked list (or array) with n = 10 6 nodes. Even on a machine that can do million comparisons per second, searching for m items will take roughly m seconds.

This not acceptable in today’s world where speed at which we complete operations is extremely important. Time is money. Therefore it seems that better (more efficient) data structures are needed to store and search data. In this chapter, we can extend the concept of linked data structure (linked list, stack, queue ) to a structure that may have multiple relations among its nodes.

- Such a structure is called a tree,
- A tree is a collection of nodes connected by directed (or undirected) edges.
- A tree is a nonlinear data structure, compared to arrays, linked lists, stacks and queues which are linear data structures.
- A tree can be empty with no nodes or a tree is a structure consisting of one node called the root and zero or one or more subtrees,

A tree has following general properties:

One node is distinguished as a root ; Every node (exclude a root) is connected by a directed edge from exactly one other node; A direction is: parent -> children

A is a parent of B, C, D, B is called a child of A, on the other hand, B is a parent of E, F, K In the above picture, the root has 3 subtrees, Each node can have arbitrary number of children. Nodes with no children are called leaves, or external nodes.

In the above picture, C, E, F, L, G are leaves. Nodes, which are not leaves, are called internal nodes. Internal nodes have at least one child. Nodes with the same parent are called siblings, In the picture, B, C, D are called siblings. The depth of a node is the number of edges from the root to the node.

The depth of K is 2. The height of a node is the number of edges from the node to the deepest leaf. The height of B is 2. The height of a tree is a height of a root. A General Tree A general tree is a tree where each node may have zero or more children (a binary tree is a specialized case of a general tree). Figure courtesy of www.washington.edu Implementation Since each node in a tree can have an arbitrary number of children, and that number is not known in advance, the general tree can be implemented using a first child/next sibling method. Each node will have TWO pointers: one to the leftmost child, and one to the rightmost sibling. The following picture illustrates this

Figure courtesy of The following Java code may be used to define a general tree node. public class TNode } Binary Trees We will see that dealing with binary trees, a tree where each node can have no more than two children is a good way to understand trees.

Here is a Java prototype for a tree node: public class BNode public BNode (Object data) } A binary tree in which each node has exactly zero or two children is called a full binary tree, In a full tree, there are no nodes with exactly one child. A complete binary tree is a tree, which is completely filled, with the possible exception of the bottom level, which is filled from left to right. Binary Search Trees Given a binary tree, suppose we visit each node (recursively) as follows. We visit left child, then root and then the right child. For example, visiting the following tree In the order defined above will produce the sequence which we call flat(T). A binary search tree (BST) is a tree, where flat( T) is an ordered sequence. In other words, a binary search tree can be “searched” efficiently using this ordering property. A “balanced” binary search tree can be searched in O( log n) time, where n is the number of nodes in the tree.

Contents

- 0.1 Which data structure suits the most in the tree construction Why?
- 0.2 Which is the most suitable data structure?
- 1 What type of data structure is a tree?
- 2 What is AVL tree in data structure?
- 3 Why do we need tree data structure?
- 4 How trees are stored in data structure?
- 5 Which data structure is likely to be used by a tree map?
- 6 In which type of database information is represented in the form of tree structure?
- 7 Which is the most suitable data structure to represent a heap?
- 7.1 Which of these is the most efficient data structure used to implement?
- 7.2 What tree structure is drawn to decide the best solution for a problem?
- 7.3 Which data structure is used most commonly to represent a binary tree?
- 7.4 Which data structure is likely to be used by a tree map?
- 7.5 Which data structure is most suitable for implementing best first branch and bound strategy *?

### Which data structure suits the most in the tree construction Why?

Which data structure suits the most in the tree construction? Depending on the type of tree, you can use multiple data structures to present a tree, if it is a segment tree or a fenwick tree, you can use an array data structure. If it is a type of N-ary tree, you can use a LinkedList type of data structure.

It depends on the data, and what you use the data for.A simple binary tree allows a discriminate to select one of two sub trees.A b+ tree allows a discriminate to select one of a number of sub trees.

Then there is sometimes the need to have a linear ordering of the tree (such as when the tree discriminate is priority). To quickly find the first entry you can look at the root of the tree – which then has a pointer to the leftmost leaf node. That leaf node then has two pointers – one to its parent, and one to the next entry.

Thus quick to find, and easy to remove and relatively quick to insert. Then there are radix trees where the discriminate may be something like text – the left tree contains all words starting with “a”. The next entry (if in a b+ tree), would be words with b all the way up to “z”. The next level repeats with the next input (so the left tree would represent “aa” through “az”.

And left tree would be “aaa” through “aaz”. It can make a dictionary search relatively fast. : Which data structure suits the most in the tree construction?

### Which is the most suitable data structure?

Arrays – An array is the simplest and most widely used data structure. Other data structures like stacks and queues are derived from arrays. Here’s an image of a simple array of size 4, containing elements (1, 2, 3 and 4). Each data element is assigned a positive numerical value called the Index, which corresponds to the position of that item in the array. The majority of languages define the starting index of the array as 0. The following are the two types of arrays:

- One-dimensional arrays (as shown above)
- Multi-dimensional arrays (arrays within arrays)

#### What is tree construction in data structure?

- Introduction to Tree – Data Structure and Algorithm Tutorials A is a and a hierarchy consisting of a collection of nodes such that each node of the tree stores a value and a list of references to other nodes (the “children”). This data structure is a specialized method to organize and store data in the computer to be used more effectively. It consists of a central node, structural nodes, and sub-nodes, which are connected via edges. We can also say that tree data structure has roots, branches, and leaves connected with one another. Introduction to Tree – Data Structure and Algorithm Tutorials A tree consists of a root, and zero or more subtrees T 1, T 2,, T k such that there is an edge from the root of the tree to the root of each subtree. The data in a tree are not stored in a sequential manner i.e, they are not stored linearly. Instead, they are arranged on multiple levels or we can say it is a hierarchical structure. For this reason, the tree is considered to be a non-linear data structure.
- Parent Node: The node which is a predecessor of a node is called the parent node of that node. is the parent node of,
- Child Node: The node which is the immediate successor of a node is called the child node of that node. Examples: are the child nodes of,
- Root Node: The topmost node of a tree or the node which does not have any parent node is called the root node. is the root node of the tree. A non-empty tree must contain exactly one root node and exactly one path from the root to all other nodes of the tree.
- Leaf Node or External Node: The nodes which do not have any child nodes are called leaf nodes. are the leaf nodes of the tree.
- Ancestor of a Node: Any predecessor nodes on the path of the root to that node are called Ancestors of that node. are the ancestor nodes of the node
- Descendant: Any successor node on the path from the leaf node to that node. are the descendants of the node,
- Sibling: Children of the same parent node are called siblings. are called siblings.
- Level of a node: The count of edges on the path from the root node to that node. The root node has level 0,
- Internal node: A node with at least one child is called Internal Node.
- Neighbour of a Node: Parent or child nodes of that node are called neighbors of that node.
- Subtree : Any node of the tree along with its descendant.
- Number of edges: An edge can be defined as the connection between two nodes. If a tree has N nodes then it will have (N-1) edges. There is only one path from each node to any other node of the tree.
- Depth of a node: The depth of a node is defined as the length of the path from the root to that node. Each edge adds 1 unit of length to the path. So, it can also be defined as the number of edges in the path from the root of the tree to the node.
- Height of a node: The height of a node can be defined as the length of the longest path from the node to a leaf node of the tree.
- Height of the Tree: The height of a tree is the length of the longest path from the root of the tree to a leaf node of the tree.
- Degree of a Node: The total count of subtrees attached to that node is called the degree of the node. The degree of a leaf node must be 0, The degree of a tree is the maximum degree of a node among all the nodes in the tree.
- Traversing in a tree is done by depth first search and breadth first search algorithm.
- It has no loop and no circuit
- It has no self-loop
- Its hierarchical model.
- Node : the node is an entity in a tree data structure that contains a key or a value and pointers to its child nodes.
- Child node : A child node is the descendant of any node.
- Leaf nodes: The nodes which don’t have any child nodes and are the bottom-most node in a tree. They are also called the external nodes.
- Parent node: This node is located directly above a node. It is the principal in the hierarchy. For example, 50 is the parent node of 60, 70, and 80.
- Root : It is the topmost point of a tree.
- Internal node : The node having at least one child node.
- Edge: An edge refers to the connection between any two nodes in a tree.
- Height of a node: Number of edges from the node to the deepest leaf.
- Depth of a node : Number of edges from the root to the node. The root node’s depth is zero. Any other node’s depth is the number of edges it derives from the root node.
- Degree of a tree: It denotes the maximum of all the probable degrees of its nodes.
- Number of edges: If a tree has n nodes, the number of edges would be n-1. Excluding the root node, all other nodes in the tree possess a minimum of one incoming edge.
- Height of a tree : Height of the root node. It is the path length from a specific node to the extreme leaf node. It is always calculated from bottom to top. Hence, each leaf’s height is 0.
- Degree of a node : Total number of branches to that node.
- Forest: A collection of disjoint trees.
- Subtree: It denotes children in the tree. Every child is either a leaf node or a subtree.
- Generation: Nodes existing at the same level of the tree are called a generation. For instance, 60, 70, and 80 belong to the same generation.
- Ancestor: Suppose there are two nodes, A and B, and there is a path from A to B, then A is the ancestor of B. It is common terminology used in various trees in data structure.
- Descendent: It is the reverse of an ancestor.
- Sibling: Two nodes with the same parent are called siblings. Suppose 70, 80, and 90 are siblings and 100 is the parent.
- Subtree: It denotes children in the tree. Every child is either a leaf node or a subtree.
- Generation: Nodes existing at the same level of the tree are called a generation. For instance, 60, 70, and 80 belong to the same generation.
- Ancestor: Suppose there are two nodes, A and B, and there is a path from A to B, then A is the ancestor of B. It is common terminology used in various trees in data structure.
- Descendent: It is the reverse of an ancestor.
- Sibling: Two nodes with the same parent are called siblings. Suppose 70, 80, and 90 are siblings and 100 is the parent.
- Levels: The root node exists at level zero, and its children exist at level one. Level one’s children exist at level two.
- Arrays are best for storing multiple values in a single variable
- Arrays are better at processing many values easily and quickly
- Sorting and searching the values is easier in arrays
- If we organize keys in form of a tree (with some ordering e.g., BST), we can search for a given key in moderate time (quicker than Linked List and slower than arrays). Self-balancing search trees like AVL and Red-Black trees guarantee an upper bound of O(Logn) for search.
- We can insert/delete keys in moderate time (quicker than Arrays and slower than Unordered Linked Lists). Self-balancing search trees like AVL and Red-Black trees guarantee an upper bound of O(Logn) for insertion/deletion.
- Like Linked Lists and unlike Arrays, Pointer implementation of trees don’t have an upper limit on number of nodes as nodes are linked using pointers.
- Each element in the array represents a node of the heap, and
- The parent / child relationship is defined implicitly by the elements’ indices in the array.
- Insertion: Add the new element at the end of the heap, in the first available free space. If this will violate the heap property, sift up the new element ( swim operation) until the heap property has been reestablished.
- Extraction: Remove the root and insert the last element of the heap in the root. If this will violate the heap property, sift down the new root ( sink operation) to reestablish the heap property.
- Replacement: Remove the root and put the new element in the root and sift down. When compared to extraction followed by insertion, this avoids a sift up step.
- Linked list
- Binary heap
- Arrays
- Binary search tree
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- Like Article
- The recursion is completed when the subset at a node all has the same value of the target variable, or when splitting no longer adds value to the predictions.
- The construction of a decision tree classifier does not require any domain knowledge or parameter setting, and therefore is appropriate for exploratory knowledge discovery.
- Lowest cost branch and bound helps us find the lowest cost path.3.
- Which data structure is used for implementing a LIFO branch and bound strategy? a) stack b) queue c) array d) linked list View Answer Answer: a Explanation: Stack is the data structure is used for implementing LIFO branch and bound strategy.
- Both LIFO branch and bound strategy and backtracking leads to depth first search.
- A) true b) false View Answer Answer: a Explanation: Both backtrackings as well as branch and bound are problem solving algorithms.
- Both LIFO branch and bound strategy and backtracking leads to depth first search.10.
- Choose the correct statement from the following.

Some more properties are:

## What type of data structure is a tree?

What is a Tree in Data Structure? – A tree is a type of data structure representing hierarchical data. It has a non-linear structure consisting of nodes connected by edges. Among the other types of data structures that perform operations in a linear data structure, the complexwebinarity increases with an increase in data size.

However, the tree data structure provides quicker access to the data which is non-linear. Availability of the various types of data structures and the algorithms associated with them, the task performance has become an easy and efficient way. Check out our free data science courses to get an edge over the competition.

The difference between the computing field tree and the real-world tree is that it is visualized as upside down with roots at the top and leaves at the bottom. In real-world applications, the tree data structure helps to demonstrate relationships between various nodes with the parent-child hierarchy.

It is alternatively known as a hierarchic data structure. It is highly popular for streamlining and accelerating sorting and searching tasks. It is one of the resilient and most innovative data structures. It represents the non-linear data structure. It can also represent various primitive or user-defined data types.

You can use classes connected lists, arrays, or other types of data structures to employ the tree. Its structure shows a group of interconnected nodes. These nodes are connected to the edges to depict the relationship. After understanding what is tree in data structure, let’s get familiar with some of its key terminologies.

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### Which of the following data structures is most suitable for MCQ?

Detailed Solution. Stack data structure is suitable for evaluating postfix expression.

### Which of the following data structure is efficient to implement tree?

Both sets and priority queue.

### Why array is best in data structure?

Why do we need arrays? – Here, are some reasons for using arrays in data structure:

#### What are the 2 main types of data structures?

Types of Data Structure – Basically, data structures are divided into two categories:

Linear data structure Non-linear data structure

Let’s learn about each type in detail.

## What is AVL tree in data structure?

AVL tree is a self-balancing binary search tree in which each node maintains extra information called a balance factor whose value is either -1, 0 or +1. AVL tree got its name after its inventor Georgy Adelson-Velsky and Landis.

## Why do we need tree data structure?

Why Tree to use Data Structure? – Unlike Array and Linked List, which are linear data structures, tree is hierarchical (or non-linear) data structure.

One reason to use trees might be because you want to store information that naturally forms a hierarchy. For example, the file system on a computer:

## How trees are stored in data structure?

Storing Hierarchical Data in a Database Storing hierarchical data in a database: two approaches for stable storage and fast reporting of tree data. Many times we need to store enormous amounts of —tree— or —hierarchical— data:

Hundreds of categories, sub-categories and sub-sub-categories in a single online storeNavigation menus of extremely complex sitemapsRelationship of members who are involved in affiliate marketing campaigns

Proper organization and indexing of this data will make it possible to easily:

Display results (how do you build a navigation tree?)Report on statistics (how many people are in this member’s affiliate down-line?)Extract a specific segment of the tree desired (do you want to show the sub-nav in the side bar of a category detail page?)

Adjacent List Model: the —parent-child— method The standard method of storing hierarchical data is simple parent-child relationship. Each record in the database includes a —parent id—, and a recursive query through the records build the children, siblings, and levels of the tree.

Adding a new record to the system only requires the ID of the parent, with no other indexing. The advantages of this method are the simplicity, and low-cost of entering new records. If you add a child record, you simply need to know the parent ID and everything else will build out fine. The cost comes to building out the tree, or running reports on the data when you get into larger data sets.

This might not be any big deal for a small navigation tree, but if you are trying to show the genealogy of an affiliate marketing team the numbers can get into the thousands, and the recursion through the data can be brutal. Parent Child Tree Parent – Child Relationship, the storage of the Parent ID Pros:

Easy to insert new data (no indexing required)Lightweight storage of data (only one field —parent id— required to build an entire affiliate tree)—levels of the tree— (how deep you are) is inherently obvious, as each level requires a new query.

Cons:

Very intensive overhead to report

Example: “Show all child records of a single node” Given parent “A”, build a tree of all members of the affiliate downline:

First show all records with Parent ID = “A”For each of these records, find the records that have the corresponding parent IDRinse and repeat. (one query per level, but if you want to get the granularity, you may have to run one query per each child record)

You can see how quickly the queries add up, and come at a heavy cost. Nested Sets to the rescue! Another technique is to build an index for each record using nested sets. In a nested set, each record contains two indices, a “left” and “right” index number. But, view the data set from the TOP and the brilliance shines through. Each node, in essence, is a container holding the indexes of each of the child nodes below. The left and right index numbers now line up from left to right. If there are any child records, the left and right indexes of the children will be a number larger then the left of the parent, and smaller than the right. Pros

Reporting is easy and lightweightQuick selection of downline sets

Cons

Adding or removing records requires a re-index of the entire treeReport details (such as finding the number of levels in the child-set of records) can require complex queries

Example: “how many children are below node A”? Because of the pre-indexing of the nodes, you only need to take the difference between the left and right nodes, subtract 1 and divide by 2 to get the total number of children of a given node. This can be done without any queries involving the children themselves.

Node AIndex “left” = 1Index “right” = 16((Right – Left) – 1) / 2 = Total Number of Children((16 – 1) – 1)/2 = 8 nodes

: Storing Hierarchical Data in a Database

### What is an example of tree data structure?

7.2. Examples of Trees — Problem Solving with Algorithms and Data Structures Now that we have studied linear data structures like stacks and queues and have some experience with recursion, we will look at a common data structure called the tree, Trees are used in many areas of computer science, including operating systems, graphics, database systems, and computer networking. Tree data structures have many things in common with their botanical cousins. A tree data structure has a root, branches, and leaves. The difference between a tree in nature and a tree in computer science is that a tree data structure has its root at the top and its leaves on the bottom. Before we begin our study of tree data structures, let’s look at a few common examples. Our first example of a tree is a classification tree from biology. shows an example of the biological classification of some animals. From this simple example, we can learn about several properties of trees. The first property this example demonstrates is that trees are hierarchical. By hierarchical, we mean that trees are structured in layers with the more general things near the top and the more specific things near the bottom. The top of the hierarchy is the Kingdom, the next layer of the tree (the “children” of the layer above) is the Phylum, then the Class, and so on. However, no matter how deep we go in the classification tree, all the organisms are still animals. Figure 1: Taxonomy of Some Common Animals Shown as a Tree Notice that you can start at the top of the tree and follow a path made of circles and arrows all the way to the bottom. At each level of the tree we might ask ourselves a question and then follow the path that agrees with our answer. For example we might ask, “Is this animal a Chordate or an Arthropod?” If the answer is “Chordate” then we follow that path and ask, “Is this Chordate a Mammal?” If not, we are stuck (but only in this simplified example). When we are at the Mammal level we ask, “Is this Mammal a Primate or a Carnivore?” We can keep following paths until we get to the very bottom of the tree where we have the common name. A second property of trees is that all of the children of one node are independent of the children of another node. For example, the Genus Felis has the children Domestica and Leo. The Genus Musca also has a child named Domestica, but it is a different node and is independent of the Domestica child of Felis. This means that we can change the node that is the child of Musca without affecting the child of Felis. A third property is that each leaf node is unique. We can specify a path from the root of the tree to a leaf that uniquely identifies each species in the animal kingdom; for example, Animalia \(\rightarrow\) Chordate \(\rightarrow\) Mammal \(\rightarrow\) Carnivora \(\rightarrow\) Felidae \(\rightarrow\) Felis \(\rightarrow\) Domestica. Another example of a tree structure that you probably use every day is a file system. In a file system, directories, or folders, are structured as a tree. illustrates a small part of a Unix file system hierarchy. Figure 2: A Small Part of the Unix File System Hierarchy The file system tree has much in common with the biological classification tree. You can follow a path from the root to any directory. That path will uniquely identify that subdirectory (and all the files in it). Another important property of trees, derived from their hierarchical nature, is that you can move entire sections of a tree (called a subtree ) to a different position in the tree without affecting the lower levels of the hierarchy. For example, we could take the entire subtree staring with /etc/, detach etc/ from the root and reattach it under usr/. This would change the unique pathname to httpd from /etc/httpd to /usr/etc/httpd, but would not affect the contents or any children of the httpd directory. A final example of a tree is a web page. The following is an example of a simple web page written using HTML. shows the tree that corresponds to each of the HTML tags used to create the page. < html xmlns = "http://www.w3.org/1999/xhtml" xml : lang = "en" lang = "en" > < head > < meta http - equiv = "Content-Type" content = "text/html; charset=utf-8" /> < title > simple < body > < h1 > A simple web page < ul > < li > List item one < li > List item two < h2 >< a href = "http://www.cs.luther.edu" > Luther CS < h2 > Figure 3: A Tree Corresponding to the Markup Elements of a Web Page The HTML source code and the tree accompanying the source illustrate another hierarchy. Notice that each level of the tree corresponds to a level of nesting inside the HTML tags. The first tag in the source is and the last is All the rest of the tags in the page are inside the pair.

## Which data structure is likely to be used by a tree map?

Internal Working of TreeMap – Like HashMap and LikedHasMap it does not use hashing for storing key-value pairs. Internally, it uses a data structure called the Red-Black Tree, In other words, it sorts the TreeMap object keys using the Red-Black Tree algorithm. For understanding the internal working of TreeMap, we must understand the Red-Black Tree algorithm.

## In which type of database information is represented in the form of tree structure?

Hierarchical database model is a data model in which data are organised into a tree-like structure.

#### Which is the efficient data structure in tree construction Mcq?

Linked list is the suitable efficient data structure.

#### Which of the following is more suitable for representing binary tree?

2. Linked List Representation of Binary Tree – We use a double linked list to represent a binary tree. In a double linked list, every node consists of three fields. First field for storing left child address, second for storing actual data and third for storing right child address.In this linked list representation, a node has the following structure. The above example of the binary tree represented using Linked list representation is shown as follows. : Data Structures Tutorials – Binary Tree Representations with an example

## Which is the most suitable data structure to represent a heap?

Implementation – Heaps are usually implemented with an array, as follows:

Example of a complete binary max-heap with node keys being integers from 1 to 100 and how it would be stored in an array. For a binary heap, in the array, the first index contains the root element. The next two indices of the array contain the root’s children. and, and its parent is at index ⌊( i −1)/2⌋, This simple indexing scheme makes it efficient to move “up” or “down” the tree. Balancing a heap is done by sift-up or sift-down operations (swapping elements which are out of order). As we can build a heap from an array without requiring extra memory (for the nodes, for example), heapsort can be used to sort an array in-place.

Construction of a binary (or d -ary) heap out of a given array of elements may be performed in linear time using the classic Floyd algorithm, with the worst-case number of comparisons equal to 2 N − 2 s 2 ( N ) − e 2 ( N ) (for a binary heap), where s 2 ( N ) is the sum of all digits of the binary representation of N and e 2 ( N ) is the exponent of 2 in the prime factorization of N,

### Which of these is the most efficient data structure used to implement?

Implementation of the Priority Queue in Data Structure – You can implement the priority queues in one of the following ways:

The binary heap is the most efficient method for implementing the priority queue in the data structure, The below tables summarize the complexity of different operations in a priority queue.

Operation | Unordered Array | Ordered Array | Binary Heap | Binary Search Tree |

Insert | 0(1) | 0(N) | 0(log(N)) | 0(log(N)) |

Peek | 0(N) | 0(1) | 0(1) | 0(1) |

Delete | 0(N) | 0(1) | 0(log (N)) | 0(log(N)) |

### What tree structure is drawn to decide the best solution for a problem?

Decision Tree – GeeksforGeeks

Decision Tree is the most powerful and popular tool for classification and prediction. A Decision tree is a flowchart-like tree structure, where each internal node denotes a test on an attribute, each branch represents an outcome of the test, and each leaf node (terminal node) holds a class label. A decision tree for the concept PlayTennis. Construction of Decision Tree: A tree can be “learned” by splitting the source set into subsets based on an attribute value test. This process is repeated on each derived subset in a recursive manner called recursive partitioning,

Decision trees can handle high-dimensional data. In general decision tree classifier has good accuracy. Decision tree induction is a typical inductive approach to learn knowledge on classification. Decision Tree Representation: Decision trees classify instances by sorting them down the tree from the root to some leaf node, which provides the classification of the instance.

An instance is classified by starting at the root node of the tree, testing the attribute specified by this node, then moving down the tree branch corresponding to the value of the attribute as shown in the above figure. This process is then repeated for the subtree rooted at the new node. The decision tree in above figure classifies a particular morning according to whether it is suitable for playing tennis and returns the classification associated with the particular leaf.(in this case Yes or No).

For example, the instance (Outlook = Sunny, Temperature = Hot, Humidity = High, Wind = Strong ) would be sorted down the leftmost branch of this decision tree and would therefore be classified as a negative instance. In other words, we can say that the decision tree represents a disjunction of conjunctions of constraints on the attribute values of instances.

### Which data structure is used most commonly to represent a binary tree?

2. Linked List Representation of Binary Tree – We use a double linked list to represent a binary tree. In a double linked list, every node consists of three fields. First field for storing left child address, second for storing actual data and third for storing right child address.In this linked list representation, a node has the following structure. The above example of the binary tree represented using Linked list representation is shown as follows. : Data Structures Tutorials – Binary Tree Representations with an example

### Which data structure is likely to be used by a tree map?

Internal Working of TreeMap – Like HashMap and LikedHasMap it does not use hashing for storing key-value pairs. Internally, it uses a data structure called the Red-Black Tree, In other words, it sorts the TreeMap object keys using the Red-Black Tree algorithm. For understanding the internal working of TreeMap, we must understand the Red-Black Tree algorithm.

### Which data structure is most suitable for implementing best first branch and bound strategy *?

Branch and Bound Multiple Choice Questions and Answers (MCQs)

This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Branch and Bound”.1. Branch and bound is a _ a) problem solving technique b) data structure c) sorting algorithm d) type of tree View Answer

Answer: a Explanation: Branch and bound is a problem solving technique generally used for solving combinatorial optimization problems. Branch and bound helps in solving them faster.2. Which of the following is not a branch and bound strategy to generate branches? a) LIFO branch and bound b) FIFO branch and bound c) Lowest cost branch and bound d) Highest cost branch and bound View Answer Answer: d Explanation: LIFO, FIFO and Lowest cost branch and bound are different strategies to generate branches.

This leads to depth first search as every branch is explored until a leaf node is discovered. Note: Join free Sanfoundry classes at or 4. Which data structure is used for implementing a FIFO branch and bound strategy? a) stack b) queue c) array d) linked list View Answer Answer: b Explanation: Queue is the data structure is used for implementing FIFO branch and bound strategy.

This leads to breadth first search as every branch at depth is explored first before moving to the nodes at greater depth.5. Which data structure is most suitable for implementing best first branch and bound strategy? a) stack b) queue c) priority queue d) linked list View Answer Answer: c Explanation: Priority Queue is the data structure is used for implementing best first branch and bound strategy.

Dijkstra’s algorithm is an example of best first search algorithm.6. Which of the following branch and bound strategy leads to breadth first search? a) LIFO branch and bound b) FIFO branch and bound c) Lowest cost branch and bound d) Highest cost branch and bound View Answer Answer: b Explanation: LIFO, FIFO and Lowest cost branch and bound are different strategies to generate branches.

FIFO branch and bound leads to breadth first search.7. Which of the following branch and bound strategy leads to depth first search? a) LIFO branch and bound b) FIFO branch and bound c) Lowest cost branch and bound d) Highest cost branch and bound View Answer Answer: a Explanation: LIFO, FIFO and Lowest cost branch and bound are different strategies to generate branches.

LIFO branch and bound leads to depth first search.8. Both FIFO branch and bound strategy and backtracking leads to depth first search. a) true b) false View Answer Answer: b Explanation: FIFO branch and bound leads to breadth first search. Whereas backtracking leads to depth first search.9.

a) branch and bound is more efficient than backtracking b) branch and bound is not suitable where a greedy algorithm is not applicable c) branch and bound divides a problem into at least 2 new restricted sub problems d) backtracking divides a problem into at least 2 new restricted sub problems View Answer Answer: c Explanation: Both backtracking as well as branch and bound are problem solving algorithms.

Branch and bound is less efficient than backtracking. Branch and bound divides a problem into at least 2 new restricted sub problems.11. Which of the following can traverse the state space tree only in DFS manner? a) branch and bound b) dynamic programming c) greedy algorithm d) backtracking View Answer Answer: d Explanation: Both backtracking as well as branch and bound are problem solving algorithms.

Branch and bound can traverse in DFS as well as BFS manner whereas backtracking only traverses in DFS manner. Sanfoundry Global Education & Learning Series – Data Structures & Algorithms. To practice all areas of Data Structures & Algorithms,, Next Steps:

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