Data Structures Tutorial

Data Structures Tutorial Asymptotic Notation Structure and Union Array Data Structure Linked list Data Structure Type of Linked list Advantages and Disadvantages of linked list Queue Data Structure Implementation of Queue Stack Data Structure Implementation of Stack Sorting Insertion sort Quick sort Selection sort Heap sort Merge sort Bucket sort Count sort Radix sort Shell sort Tree Traversal of the binary tree Binary search tree Graph Spanning tree Linear Search Binary Search Hashing Collision Resolution Techniques

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Priority Queue in Data Structure Deque in Data Structure Difference Between Linear And Non Linear Data Structures Queue Operations In Data Structure About Data Structures Data Structures Algorithms Types of Data Structures Big O Notations Introduction to Arrays Introduction to 1D-Arrays Operations on 1D-Arrays Introduction to 2D-Arrays Operations on 2D-Arrays Strings in Data Structures String Operations Application of 2D array Bubble Sort Insertion Sort Sorting Algorithms What is DFS Algorithm What Is Graph Data Structure What is the difference between Tree and Graph What is the difference between DFS and BFS Bucket Sort Dijkstra’s vs Bellman-Ford Algorithm Linear Queue Data Structure in C Stack Using Array Stack Using Linked List Recursion in Fibonacci Stack vs Array What is Skewed Binary Tree Primitive Data Structure in C Dynamic memory allocation of structure in C Application of Stack in Data Structures Binary Tree in Data Structures Heap Data Structure Recursion - Factorial and Fibonacci What is B tree what is B+ tree Huffman tree in Data Structures Insertion Sort vs Bubble Sort Adding one to the number represented an array of digits Bitwise Operators and their Important Tricks Blowfish algorithm Bubble Sort vs Selection Sort Hashing and its Applications Heap Sort vs Merge Sort Insertion Sort vs Selection Sort Merge Conflicts and ways to handle them Difference between Stack and Queue AVL tree in data structure c++ Bubble sort algorithm using Javascript Buffer overflow attack with examples Find out the area between two concentric circles Lowest common ancestor in a binary search tree Number of visible boxes putting one inside another Program to calculate the area of the circumcircle of an equilateral triangle Red-black Tree in Data Structures Strictly binary tree in Data Structures 2-3 Trees and Basic Operations on them Asynchronous advantage actor-critic (A3C) Algorithm Bubble Sort vs Heap Sort Digital Search Tree in Data Structures Minimum Spanning Tree Permutation Sort or Bogo Sort Quick Sort vs Merge Sort Boruvkas algorithm Bubble Sort vs Quick Sort Common Operations on various Data Structures Detect and Remove Loop in a Linked List How to Start Learning DSA Print kth least significant bit number Why is Binary Heap Preferred over BST for Priority Queue Bin Packing Problem Binary Tree Inorder Traversal Burning binary tree Equal Sum What is a Threaded Binary Tree? 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Bubble Sort vs Merge Sort B+ Tree Program in Q language Deletion Operation from A B Tree Deletion Operation of the binary search tree in C++ language Does Overloading Work with Inheritance Balanced Binary Tree Binary tree deletion Binary tree insertion Cocktail Sort Comb Sort FIFO approach Operations of B Tree in C++ Language Recaman’s Sequence Tim Sort Understanding Data Processing Applications of trees in data structures Binary Tree Implementation Using Arrays Convert a Binary Tree into a Binary Search Tree Create a binary search tree Horizontal and Vertical Scaling Invert binary tree LCA of binary tree Linked List Representation of Binary Tree Optimal binary search tree in DSA Serialize and Deserialize a Binary Tree Tree terminology in Data structures Vertical Order Traversal of Binary Tree What is a Height-Balanced Tree in Data Structure Convert binary tree to a doubly linked list Fundamental of Algorithms Introduction and Implementation of Bloom Filter Optimal binary search tree using dynamic programming Right side view of binary tree Symmetric binary tree Trim a binary search tree What is a Sparse Matrix in Data Structure What is a Tree in Terms of a Graph What is the Use of Segment Trees in Data Structure What Should We Learn First Trees or Graphs in Data Structures All About Minimum Cost Spanning Trees in Data Structure Convert Binary Tree into a Threaded Binary Tree Difference between Structured and Object-Oriented Analysis FLEX (Fast Lexical Analyzer Generator) Object-Oriented Analysis and Design Sum of Nodes in a Binary Tree What are the types of Trees in Data Structure What is a 2-3 Tree in Data Structure What is a Spanning Tree in Data Structure What is an AVL Tree in Data Structure Given a Binary Tree, Check if it's balanced B Tree in Data Structure Convert Sorted List to Binary Search Tree Flattening a Linked List Given a Perfect Binary Tree, Reverse Alternate Levels Left View of Binary Tree What are Forest Trees in Data Structure Compare Balanced Binary Tree and Complete Binary Tree Diameter of a Binary Tree Given a Binary Tree Check the Zig Zag Traversal Given a Binary Tree Print the Shortest Path Given a Binary Tree Return All Root To Leaf Paths Given a Binary Tree Swap Nodes at K Height Given a Binary Tree Find Its Minimum Depth Given a Binary Tree Print the Pre Order Traversal in Recursive Given a Generate all Structurally Unique Binary Search Trees Perfect Binary Tree Threaded Binary Trees Function to Create a Copy of Binary Search Tree Function to Delete a Leaf Node from a Binary Tree Function to Insert a Node in a Binary Search Tree Given Two Binary Trees, Check if it is Symmetric A Full Binary Tree with n Nodes Applications of Different Linked Lists in Data Structure B+ Tree in Data Structure Construction of B tree in Data Structure Difference between B-tree and Binary Tree Finding Rank in a Binary Search Tree Finding the Maximum Element in a Binary Tree Finding the Minimum and Maximum Value of a Binary Tree Finding the Sum of All Paths in a Binary Tree Time Complexity of Selection Sort in Data Structure How to get Better in Data Structures and Algorithms Binary Tree Leaf Nodes Classification of Data Structure Difference between Static and Dynamic Data Structure Find the Union and Intersection of the Binary Search Tree Find the Vertical Next in a Binary Tree Finding a Deadlock in a Binary Search Tree Finding all Node of k Distance in a Binary Tree Finding Diagonal Sum in a Binary Tree Finding Diagonal Traversal of The Binary Tree Finding In-Order Successor Binary Tree Finding the gcd of Each Sibling of the Binary Tree Greedy Algorithm in Data Structure How to Calculate Space Complexity in Data Structure How to find missing numbers in an Array Kth Ancestor Node of Binary Tree Minimum Depth Binary Tree Mirror Binary Tree in Data Structure Red-Black Tree Insertion Binary Tree to Mirror Image in Data Structure Calculating the Height of a Binary Search Tree in Data Structure Characteristics of Binary Tree 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Asymptotic Notation

Asymptotic notation is expressions that are used to represent the complexity of algorithms. The complexity of the algorithm is analyzed from two perspectives: 

  1. Time complexity
  2. Space complexity

Time complexity

The time complexity of an algorithm is the amount of time the algorithm takes to complete its process. Time complexity is calculated by calculating the number of steps performed by the algorithm to complete the execution.

Space complexity

The space complexity of an algorithm is the amount of memory used by the algorithm. Space complexity includes two spaces: Auxiliary space and Input space. The auxiliary space is the temporary space or extra space used during execution by the algorithm. The space complexity of an algorithm is expressed by Big O (O(n)) notation. Many algorithms have inputs that vary in memory size. In this case, the space complexity that is there depends on the size of the input.

Different types of asymptotic notations are used to describe the algorithm complexity.

  • O? Big Oh
  • ?? Big omega
  • ?? Big theta
  • o? Little Oh
  • ?? Little omega

O- Big Oh: Asymptotic Notation (Upper Bound)

"O- Big Oh" is the most commonly used notation. Big Oh describes the worst-case scenario. It represents the upper bound of the algorithm.

Function, f(n) = O (g(n)), if and only if positive constant C is present and thus:

                              0 <= f(n) <= C(g(n))              for all n >= n0

Therefore, function g(n) is an upper bound for function f(n) because it grows faster than function f(n).

The value of f(n) function always lies below the C(g(n)) function, as shown in the graph.

Asymptotic Notation

?-Big omega: Asymptotic Notation (Lower Bound)

The Big Omega (?) notation describes the best-case scenario. It represents the lower bound of the algorithm.

Function, f(n) = ? (g(n)), if and only if positive constant C is present and thus:

                              0 <= C(g(n)) <= f(n)               for all n >= n0

The value of f(n) function always lies above the C(g(n)) function, as shown in the graph.

Asymptotic Notation

?-Big theta: Asymptotic Notation (Tight Bound)

The Big Theta (?) notation describes both the upper bound and the lower bound of the algorithm. So, you can say that it defines precise asymptotic behavior. It represents the tight bound of the algorithm.

Function, f(n) = ? (g(n)), if and only if positive constant C1, C2 and n0 is present and thus:

                           0 <= C1(g(n)) <= f(n) <= C2(g(n))                 for all n >= n0

Asymptotic Notation

o-Little Oh: Asymptotic Notation

The Little Oh (o) notation is used to represent an upper-bound that is not asymptotically-tight.

Function, f(n) = o (g(n)), if and only if positive constant C is present and thus:

                           0 <= f(n) < C(g(n))              for all n >=n0

The relation, f(n) = o(g(n)) implies that limn-? [ f(n) / g(n)] = 0.

??Little omega: Asymptotic Notation

The Little omega (?) notation is used to represent a lower-bound that is not asymptotically-tight. Function, f(n) = ?(g(n)), if and only if positive constant C is present and thus:

                           0 <= C(g(n)) < f(n)                for all n >=n0

The relation, f(n) = ?(g(n)) implies that limn-? [ f(n) / g(n)] = ?.