For Tree Construction Which Is The Most Efficient Data Structure?

For Tree Construction Which Is The Most Efficient Data Structure
Linked list is the suitable efficient data structure.

Which data structure is most efficient for tree creation?

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.

  1. 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.
  2. So imagine doing the search on a linked list (or array) with n = 10 6 nodes.
  3. 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.

For Tree Construction Which Is The Most Efficient Data Structure 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. For Tree Construction Which Is The Most Efficient Data Structure 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 For Tree Construction Which Is The Most Efficient Data Structure 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.

Which is the most efficient data structure?

Arrays. An array is a linear data structure that holds an ordered collection of values. It’s the most efficient in storing and accessing a sequence of objects.

Which tree is best in data structure?

1. Binary Tree – A binary tree is a tree data structure where the following properties can be found.

Which tree traversal is most efficient?

Everything you need to know about tree traversal in 7 mins (with animations) – DFS & BFS Algorithms || Designed by Anand K Parmar If you are a pro programmer or working in the Software Industry for years then this topic may seem to you very trivial. But the use-cases of such algorithms and the different variants of that may create confusion in beginners mind.

  1. Tree Data Structure
  2. Tree Traversal — Introduction
  3. Let’s dive in — Practical Guide
  4. Inorder Traversal
  5. Preorder Traversal
  6. Postorder Traversal
  7. Level Order Traversal
  8. Final Notes

Before jumping into the tree traversal algorithms, let’s define Tree as a data structure first. That will help you to grasp the concepts in a meaningful way. Tree is a hierarchical data structure which stores the information naturally in the form of hierarchy unlike linear data structures like, Linked List, Stack, etc.

  • A tree contains nodes(data) and connections(edges) which should not form a cycle.
  • Following are the few frequently used terminologies for Tree data structure.
  • Node — A node is a structure which may contain a value or condition, or represent a separate data structure.
  • Root — The top node in a tree, the prime ancestor.
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Child — A node directly connected to another node when moving away from the root, an immediate descendant. Parent — The converse notion of a child, an immediate ancestor. Leaf — A node with no children. Internal node — A node with at least one child. Edge — The connection between one node and another.

Depth — The distance between a node and the root. Level — the number of edges between a node and the root + 1 Height — The number of edges on the longest path between a node and a descendant leaf. Breadth — The number of leaves. Sub Tree — A tree T is a tree consisting of a node in T and all of its descendants in T,

Binary Tree — is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. Binary Search Tree — is a special type of binary tree which has the following properties.

  • The left subtree of a node contains only nodes with keys lesser than the node’s key.
  • The right subtree of a node contains only nodes with keys greater than the node’s key.
  • The left and right subtree each must also be a binary search tree.

Note: For the sake of simplicity, we will use Binary Tree as an example to understand Tree Traversal Algorithms. But those algorithms can be generalised to other types of tree, as well. “In computer science, tree traversal (also known as tree search ) is a form of graph traversal and refers to the process of visiting (checking and/or updating) each node in a tree data structure, exactly once.

Such traversals are classified by the order in which the nodes are visited.” — Wikipedia The definition of Wikipedia is self-explanatory to understand what Tree Traversal mean. But I want to elaborate more about the last line of the definition, which will help us to understand the types of Tree Traversal and how they are different.

Tree Traversal Algorithms can be classified broadly in the following two categories by the order in which the nodes are visited:

  • Depth-First Search (DFS) Algorithm: It starts with the root node and first visits all nodes of one branch as deep as possible of the chosen Node and before backtracking, it visits all other branches in a similar fashion. There are three sub-types under this, which we will cover in this article.
  • Breadth-First Search (BFS) Algorithm: It also starts from the root node and visits all nodes of current depth before moving to the next depth in the tree. We will cover one algorithm of BFS type in the upcoming section.

It’s time to understand the concept in a practical way. I will use Java Programming Language to explain the code. But these algorithms can be coded in your preferred programming language the same way we will do in Java. Below is the blueprint of our Node class which will act as the atomic member of the Tree Data Structure.

We will call it TreeNode, which is holding data as an integer value, left and right children of the same type(TreeNode). You can use any other data structure to keep as data under the TreeNode. Inorder Traversal is the one the most used variant of DFS(Depth First Search) Traversal of the tree. As DFS suggests, we will first focus on the depth of the chosen Node and then go to the breadth at that level.

Therefore, we will start from the root node of the tree and go deeper-and-deeper into the left subtree with recursive manner. When we will reach to the left-most node with the above steps, then we will visit that current node and go to the left-most node of its right subtree(if exists).

  1. Go to left-subtree
  2. Visit Node
  3. Go to right-subtree

Inorder Traversal || Designed by Anand K Parmar Important Fact: Inorder Traversal of Binary Search Tree will always give you Nodes in sorted manner. Preorder Traversal is another variant of DFS. Where atomic operations in a recursive function, are as same as Inorder traversal but with a different order.

  1. Visit Node
  2. Go to left-subtree
  3. Go to right-subtree

Preorder Traversal || Designed by Anand K Parmar Similar goes with Postorder Traversal. Where we visit the left subtree and the right subtree before visiting the current node in recursion. So, the sequence of the steps will be

  1. Go to left-subtree
  2. Go to right-subtree
  3. Visit Node

Postorder Traversal || Designed by Anand K Parmar This is a different traversal than what we have covered above. Level order traversal follows BFS(Breadth-First Search) to visit/modify every node of the tree. As BFS suggests, the breadth of the tree takes priority first and then move to depth. Level Order Traversal || Designed by Anand K Parmar Implementation is slightly challenging here than the above three traversals. We will use a Queue(FIFO) data structure to implement Level order traversal, where after visiting a Node, we simply put its left and right children to queue sequentially.

  • Depth-First Search (DFS) Algorithms
  • Breadth-First Search (BFS) Algorithms

Depth-First Search (DFS) Algorithms have three variants:

  1. Preorder Traversal (current-left-right)— Visit the current node before visiting any nodes inside left or right subtrees.
  2. Inorder Traversal (left-current-right)— Visit the current node after visiting all nodes inside left subtree but before visiting any node within the right subtree.
  3. Postorder Traversal (left-right-current) — Visit the current node after visiting all the nodes of left and right subtrees.

Breadth-First Search (BFS) Algorithm has one variant:

Level Order Traversal — Visit nodes level-by-level and left-to-right fashion at the same level.

Check out my Github Repository for detailed code. Important Fact: There are other tree traversal algorithms that classify as neither Depth-First Search nor Breadth-First Search. One such algorithm is the Monte Carlo tree search, which concentrates on the analysis of the most promising moves, expanding the search tree based on a random sampling of the search space.

Get access to my personal Java Collection Cheatsheet as a FREE Welcome Gift after joining my tribe. Get it now! Anand K Parmar is a Software Engineer, who loves designing and building Mobile Apps. He is a writer, publishing articles on Computer Science, Programming and Personal Finance. Connect with him on LinkedIn or Twitter,

Check out his latest articles underneath.

What is the most efficient type of algorithm?

Quicksort – Quicksort is one of the most efficient sorting algorithms, and this makes of it one of the most used as well. The first thing to do is to select a pivot number, this number will separate the data, on its left are the numbers smaller than it and the greater numbers on the right.

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With this, we got the whole sequence partitioned. After the data is partitioned, we can assure that the partitions are oriented, we know that we have bigger values on the right and smaller values on the left. The quicksort uses this divide and conquer algorithm with recursion. So, now that we have the data divided we use recursion to call the same method and pass the left half of the data, and after the right half to keep separating and ordinating the data.

At the end of the execution, we will have the data all sorted. Main characteristics:

From the family of Exchange Sort Algorithms Divide and conquer paradigm Worst case complexity O(n²)

Python implementation: #!/usr/bin/env python3 # -*- coding: utf-8 -*- “”” Created on Sun Mar 10 18:09:35 2019 @note: Exchanging sort – Bubble Sort algorithm @source: http://interactivepython.org/courselib/static/pythonds/SortSearch/TheQuickSort.html “”” def quickSort(alist): quickSortHelper(alist,0,len(alist)-1) def quickSortHelper(alist,first,last): if first = pivotvalue and rightmark >= leftmark: rightmark = rightmark -1 if rightmark < leftmark: done = True else: temp = alist alist = alist alist = temp temp = alist alist = alist alist = temp return rightmark

Which algorithm is more efficient linear or binary?

Differences between Linear search and Binary search – For Tree Construction Which Is The Most Efficient Data Structure The following are the differences between linear search and binary search: Description Linear search is a search that finds an element in the list by searching the element sequentially until the element is found in the list. On the other hand, a binary search is a search that finds the middle element in the list recursively until the middle element is matched with a searched element.

  • Working of both the searches The linear search starts searching from the first element and scans one element at a time without jumping to the next element.
  • On the other hand, binary search divides the array into half by calculating an array’s middle element.
  • Implementation The linear search can be implemented on any linear data structure such as vector, singly linked list, double linked list.

In contrast, the binary search can be implemented on those data structures with two-way traversal, i.e., forward and backward traversal.

  1. Complexity
  2. The linear search is easy to use, or we can say that it is less complex as the elements for a linear search can be arranged in any order, whereas in a binary search, the elements must be arranged in a particular order.
  3. Sorted elements

The elements for a linear search can be arranged in random order. It is not mandatory in linear search that the elements are arranged in a sorted order. On the other hand, in a binary search, the elements must be arranged in sorted order. It can be arranged either in an increasing or in decreasing order, and accordingly, the algorithm will be changed.

As binary search uses a sorted array, it is necessary to insert the element at the proper place. In contrast, the linear search does not need a sorted array, so that the new element can be easily inserted at the end of the array. Approach The linear search uses an iterative approach to find the element, so it is also known as a sequential approach.

In contrast, the binary search calculates the middle element of the array, so it uses the divide and conquer approach. Data set Linear search is not suitable for the large data set. If we want to search the element, which is the last element of the array, a linear search will start searching from the first element and goes on till the last element, so the time taken to search the element would be large.

  • Dimensions
  • Linear search can be used on both single and multidimensional array, whereas the binary search can be implemented only on the one-dimensional array.
  • Efficiency

Linear search is less efficient when we consider the large data sets. Binary search is more efficient than the linear search in the case of large data sets. Let’s look at the differences in a tabular form.

Basis of comparison Linear search Binary search
Definition The linear search starts searching from the first element and compares each element with a searched element till the element is not found. It finds the position of the searched element by finding the middle element of the array.
Sorted data In a linear search, the elements don’t need to be arranged in sorted order. The pre-condition for the binary search is that the elements must be arranged in a sorted order.
Implementation The linear search can be implemented on any linear data structure such as an array, linked list, etc. The implementation of binary search is limited as it can be implemented only on those data structures that have two-way traversal.
Approach It is based on the sequential approach. It is based on the divide and conquer approach.
Size It is preferrable for the small-sized data sets. It is preferrable for the large-size data sets.
Efficiency It is less efficient in the case of large-size data sets. It is more efficient in the case of large-size data sets.
Worst-case scenario In a linear search, the worst- case scenario for finding the element is O(n). In a binary search, the worst-case scenario for finding the element is O(log 2 n).
Best-case scenario In a linear search, the best-case scenario for finding the first element in the list is O(1). In a binary search, the best-case scenario for finding the first element in the list is O(1).
Dimensional array It can be implemented on both a single and multidimensional array. It can be implemented only on a multidimensional array.

Next Topic : Linear Search vs Binary Search

Which is the best data structure and why?

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)

Which is better BST or AVL tree?

AVL tree is also a BST but it can rebalance itself. This behavior makes it faster in worst cases. It keeps rebalancing itself so in worst case it will consume O(log n ) time when the plain BST will take O(n). So, the answer to your question: It is always better to implement AVL tree than just plain BST.

What is the strongest tree type?

1. Australian Buloke – 5,060 IBF – For Tree Construction Which Is The Most Efficient Data Structure An ironwood tree that is native to Australia, this wood comes from a species of tree occurring across most of Eastern and Southern Australia. Known as the hardest wood in the world, this particular type has a Janka hardness of 5,060 lbf.

Which is the best decision tree algorithm?

The ID3 algorithm builds decision trees using a top-down greedy search approach through the space of possible branches with no backtracking.

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Which of the following tree structure which is efficient considering space and time complexities?

Answer: B) Complete Binary Tree Explanation: Full binary tree loses its nature when operations of insertions and deletions are done. For incomplete binary trees, extra storage is required and overhead of NULL node checking takes place. So complete binary tree is the better one since the property of complete binary tree is maintained even after operations like additions and deletions are done on it.

Which of the following is efficient memory data structure?

Concept – A Bloom filter is a space-efficient approximate data structure. It can be used if not even a well-loaded hash table fits in memory and we need constant read access. Due to its approximate nature, however, one must be aware that false positives are possible, i.e.

  • A membership request might return true although the element was never inserted into the set.
  • The idea behind a Bloom filter is similar to a hash table.
  • The first difference is that instead of reserving space for an array of integers, we allocate an array of m bits.
  • Secondly, we utilize not one but k independent hash functions.

Each hash function takes a (potential) element of the set and produces a position in the bit array. Initially all bits are set to 0. In order to insert a new value into the set, we compute its hash value using each of the k hash functions. We then set all bits at the corresponding positions to 1. A membership query also computes all hash values and checks the bits at every position.

If all bits are set to 1, we return true with a certain probability of being correct. If we see at least one 0, we can be sure that the element is not a member of the set. The probability of false positives depends on the number of hash functions k, the size of the bit array m, and the number of elements n already inserted into the Bloom filter.

Assuming that all bits are set independently, the false positive rate FP can be approximated by For a Bloom filter with 1 million bits, 5 hash functions, and 100k elements already inserted, we get FP ≈ 1%, If you want to play around with the variables yourself, check out this awesome Bloom filter calculator by Thomas Hurst. A big disadvantage besides the fact that there can be false positives is that deletions are not supported.

We cannot simply set all positions of the element to be deleted to 0, as we do not know if there have been hash collisions while inserting other elements. Well, we cannot even be sure if the element we are trying to delete is inside the Bloom filter because it might be a false positive. So what are Bloom filters used for in practice? One use case is in web crawling.

In order to avoid duplicate work a crawler needs to determine whether he already visited a site before following a link. Bloom filters are perfect as storing all visited websites in memory is not really possible. Also if we get a false positive it means that we are not visiting a website although it has not been visited before.

  • If the output of the crawler is used as an input to a search engine we do not really mind as highly ranked websites will most likely not have only one incoming link and thus we have a chance of seeing it again.
  • Another use case is in databases.
  • Bloom filters are used in combination with LSM trees which we know already from the previous blog post,

When performing a read operation we potentially have to inspect every level of the log. We can use a Bloom filter to efficiently check if the key we are looking for is present in each of the blocks. If the Bloom filter tells us that the key is not present we can be sure and do not have to touch that block, which is very useful for higher levels which are commonly stored on disk.

Which is more efficient DFS or BFS?

DFS is faster than BFS. Time Complexity of BFS = O(V+E) where V is vertices and E is edges. Time Complexity of DFS is also O(V+E) where V is vertices and E is edges.

Which is more space efficient DFS or BFS?

Applications –

BFS is used to find the shortest path between two nodes.It’s used to find neighbouring locations in GPS systems.It’s also used in finding all the neighbouring nodes in a peer-to-peer network like BitTorrent.

The time complexity of both algorithms is the same. But in the case of space complexity, if the maximum height is less than the maximum number of nodes in a single level, then DFS will be more space optimised than BFS or vice versa. So if the problem involves finding the nearest neighbour or the shortest path, BFS performs better — as in the case of DFS, leaf nodes are visited first.

What is the most efficient way to traverse a binary tree?

Try in order traversing of Binary Search tree. The complexity of search is nlogn and traverse is n, which is considered to be the best.

Which data structure is likely to be used by a TreeMap?

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 used for expression tree?

How to construct an expression tree? – To construct an Expression Tree for the given expression, we generally use Stack Data Structure. Initially we Iterate over the given postfix expression and follow the steps as given below –

If we get an operand in the given expression, then push it in the stack. It will become the root of the expression Tree.If an operator gets two values in the expression, then add in the expression tree as its child, and push them in the current node.Repeat Step-1 and Step-2 until we do not complete over the given expression.Now check if every root node contains nothing but operands and every child node contains only values.

Updated on 23-Feb-2021 18:11:51

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