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

Sorting Algorithms in Data Structures

A sorting algorithm is used to organize the elements of an array or list. Sorting an array, for example.

Unsorted array

572941

Sorted array

124579

We're sorting the array in ascending order right now.

This procedure may be completed using a variety of sorting algorithms. And, depending on the situation, we may apply any algorithm.

Various Sorting Algorithms

  • Bubble Sort
  • Selection Sort
  • Insertion Sort
  • Merge Sort
  • Quick Sort
  • Counting Sort
  • Radix Sort
  • Bucket Sort
  • Heap Sort
  • Shell Sort
  • Comb Sort

Sorting Algorithms' Complexity

The time complexity and space difficulty of any sorting algorithm influence the method's efficiency.

  1. Time Complexity: The time it takes an algorithm to finish its execution in relation to the amount of the input is referred to as time complexity. It can be expressed in a variety of ways:
    • Big-O notation (O)
    • Omega notation (Ω)
    • Theta notation (θ)
  2. Space Complexity: The entire amount of memory utilised by the method for

    A sorting algorithm is used to organize the elements of an array or list. Sorting an array, for example.

    Unsorted array

    572941

    Sorted array

    124579

    We're sorting the array in ascending order right now.

    This procedure may be completed using a variety of sorting algorithms. And, depending on the situation, we may apply any algorithm.

    Various Sorting Algorithms

    • Bubble Sort
    • Selection Sort
    • Insertion Sort
    • Merge Sort
    • Quick Sort
    • Counting Sort
    • Radix Sort
    • Bucket Sort
    • Heap Sort
    • Shell Sort
    • Comb Sort

    Sorting Algorithms' Complexity

    The time complexity and space difficulty of any sorting algorithm influence the method's efficiency.

    1. Time Complexity: The time it takes an algorithm to finish its execution in relation to the amount of the input is referred to as time complexity. It can be expressed in a variety of ways:
      • Big-O notation (O)
      • Omega notation (Ω)
      • Theta notation (θ)
    2. Space Complexity: The entire amount of memory utilised by the method for a complete execution is referred to as space complexity. Both the extra memory and the input are included.

    Auxiliary memory is the space used up by the method in addition to the input data. When determining the space complexity of an algorithm, auxiliary memory is usually taken into account.

    Let's look at the complexity of several sorting methods.

    Sorting AlgorithmsTime Complexity BestTime Complexity AverageTime Complexity WorstSpace complexity
         
    Bubble Sortnn2n21
    Selection Sortn2n2n21
    Insertion Sortnn2n21
    Merge Sortn log nn log nn log nN
    Quick Sortn log nn2nlog nlog n
    Counting Sortn + kn + kn + kmax
    Radix Sortn + kn + kn + kmax
    Bucket Sortn + kn2nmax
    Heap Sortn log nn log nn log n1
    Shell Sortn log nn2n log nN
    Comb Sortn log nn2/2pn21

    Sorting Algorithm Stability

    When two or more items with the same value keep the same relative positions after sorting, the sorting method is deemed stable.

    In the figure below, for example, there are two objects with the identical value of 3. The two places of 3 may or may not be maintained depending on the stability of the sorting algorithm.

    Unsorted array

    572942

    After unstable sorting there are 2 possibilities

    224579
    224579

    However, there is always one alternative following a stable sorting algorithm in which the locations are preserved as in the original array.

    Unsorted array

    572942

    Sorted array

    224579

    This table displays the consistency of several sorting algorithms.

    Sorting AlgorithmsStability
      
    Bubble SortYes
    Selection SortNo
    Insertion SortYes
    Merge SortYes
    Quick SortNo
    Counting SortYes
    Radix SortYes
    Bucket SortYes
    Heap SortNo
    Shell SortNo
    Comb SortNo
    a complete execution is referred to as space complexity. Both the extra memory and the input are included.

Auxiliary memory is the space used up by the method in addition to the input data. When determining the space complexity of an algorithm, auxiliary memory is usually taken into account.

Let's look at the complexity of several sorting methods.

Sorting AlgorithmsTime Complexity BestTime Complexity AverageTime Complexity WorstSpace complexity
     
Bubble Sortnn2n21
Selection Sortn2n2n21
Insertion Sortnn2n21
Merge Sortn log nn log nn log nN
Quick Sortn log nn2nlog nlog n
Counting Sortn + kn + kn + kmax
Radix Sortn + kn + kn + kmax
Bucket Sortn + kn2nmax
Heap Sortn log nn log nn log n1
Shell Sortn log nn2n log nN
Comb Sortn log nn2/2pn21

Sorting Algorithm Stability

When two or more items with the same value keep the same relative positions after sorting, the sorting method is deemed stable.

In the figure below, for example, there are two objects with the identical value of 3. The two places of 3 may or may not be maintained depending on the stability of the sorting algorithm.

Unsorted array

572942

After unstable sorting there are 2 possibilities

224579
224579

However, there is always one alternative following a stable sorting algorithm in which the locations are preserved as in the original array.

Unsorted array

572942

Sorted array

224579

This table displays the consistency of several sorting algorithms.

Sorting AlgorithmsStability
  
Bubble SortYes
Selection SortNo
Insertion SortYes
Merge SortYes
Quick SortNo
Counting SortYes
Radix SortYes
Bucket SortYes
Heap SortNo
Shell SortNo
Comb SortNo



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