Consider the following statements:S1 : When in any application the number of insertion are very large but the number of deletion are very less. Then unordered array data structure give better performance than ordered array data structure.S2 : When in any application number of insertion and number of deletion are same then binary search tree data structure give better performance than max heap data structure.Which of the following is correct?a)S1 is true onlyb)S2 is true onlyc)Both S1 and S2 trued)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

The correct answer is option 'A' - S1 is true only. Let's analyze each statement individually to understand why.

S1: When the number of insertions is very large but the number of deletions is very less, an unordered array data structure gives better performance than an ordered array data structure.

- In an unordered array, the elements are stored in an arbitrary order, and the position of an element does not depend on its value.
- When inserting elements into an unordered array, the new element can be placed at any available position in the array.
- Since the number of insertions is very large, the time complexity of inserting an element in an unordered array is O(1) on average.
- On the other hand, for an ordered array, the elements are stored in ascending or descending order, and the position of an element depends on its value.
- When inserting an element into an ordered array, it needs to be placed in the correct position to maintain the order of the array.
- This requires finding the correct position using a linear search or binary search, which takes O(n) or O(log n) time, respectively.
- Therefore, when the number of insertions is very large and the number of deletions is very less, an unordered array data structure gives better performance as it has constant time complexity for insertions.

S2: When the number of insertions and deletions is the same, a binary search tree data structure gives better performance than a max heap data structure.

- In a binary search tree (BST), each node has a key and two child nodes - a left child and a right child.
- The left child has a smaller key, and the right child has a larger key compared to the parent node.
- Inserting an element into a BST requires finding the correct position based on the key, which takes O(log n) time on average.
- Deleting an element from a BST also requires finding the correct position, which takes O(log n) time on average.
- On the other hand, a max heap is a complete binary tree where the value of each node is greater than or equal to the values of its children.
- Inserting an element into a max heap requires finding the correct position and then maintaining the heap property, which takes O(log n) time.
- Deleting an element from a max heap requires replacing the root with the last element and then maintaining the heap property, which also takes O(log n) time.
- Therefore, when the number of insertions and deletions is the same, a binary search tree data structure gives better performance as it has a lower time complexity for both operations compared to a max heap.

In summary, S1 is true because an unordered array gives better performance when the number of insertions is very large and the number of deletions is very less. S2 is false because a binary search tree gives better performance when the number of insertions and deletions is the same, not a max heap.

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