Explain various algorithms used in data structure and the operations associated with them.

Data structures are organized ways of storing and accessing data in a computer. They provide efficient ways of managing large amounts of data and performing various operations on it. Algorithms are step-by-step procedures used to manipulate data in data structures. Here are some common algorithms used in data structures and their associated operations:

1. Linear Data Structures:

- Array:

• Operations:
  • Insertion: Adding an element at a specific index.
  • Deletion: Removing an element from a specific index.
  • Search: Finding an element based on its value.
  • Update: Modifying the value of an element at a specific index.

- Linked List:

• Operations:
  • Insertion: Adding an element at the beginning, end, or any specified position.
  • Deletion: Removing an element from the beginning, end, or any specified position.
  • Search: Traversing the list to find an element with a specific value.
  • Update: Modifying the value of an element at a specific position.

2. Non-Linear Data Structures:

- Tree:

• Operations:
  • Insertion: Adding a node as a child of another node.
  • Deletion: Removing a node and its descendants from the tree.
  • Search: Traversing the tree to find a node with a specific value.
  • Update: Modifying the value of a node or its descendants.

- Graph:

• Operations:
  • Insertion: Adding a node or an edge to the graph.
  • Deletion: Removing a node or an edge from the graph.
  • Search: Traversing the graph to find a path between two nodes.
  • Update: Modifying the weight or label of an edge or the value of a node.

3. Sorting Algorithms:

- Merge Sort:

• Algorithm:
  • Divide the array into smaller subarrays.
  • Sort each subarray recursively.
  • Merge the sorted subarrays