Which of the below given statements are correct about Trees?

All three statements are correct. Statement I is true: in-order traversal of a BST produces sorted output. Statement II is true: trees can be represented in arrays using index-based parent-child relationships (parent at i, children at 2i and 2i+1). Statement III is true: trees are commonly implemented using linked lists with node pointers. Therefore, the correct answer is D.

Step-by-step Derivation:
Evaluate each statement:

Statement I: Binary search tree can be used to sort elements

• TRUE. In-order traversal (Left → Root → Right) of a BST yields elements in sorted order.
• Example: BST with values [5, 3, 7, 1, 4, 6, 8] → in-order gives [1, 3, 4, 5, 6, 7, 8]

Statement II: Trees can be implemented using array

• TRUE. Array-based representation uses index mapping:
  • Node at index i has left child at 2i+1, right child at 2i+2 (0-indexed)
  • Or left child at 2i, right child at 2i+1 (1-indexed)
• Commonly used for heap data structures and complete binary trees

Statement III: Trees can be implemented using linked list

• TRUE. Each node contains data and pointers to child nodes.
• Most flexible and common approach: struct Node { data; left_ptr; right_ptr; }
• Supports any tree structure without space overhead from unused array slots

Conclusion: All three statements I, II, and III are correct → Answer is D.