What are time complexities of sorted array operations?

The time complexities of various operations on a sorted array can be summarized as follows:

Search Operation

• Binary Search: The time complexity for searching an element in a sorted array using binary search is $$O(\log n)$$ in the worst case. This is because binary search repeatedly divides the search interval in half[1][2][15].

Insert Operation

• Insertion: Inserting an element into a sorted array requires finding the correct position for the new element and then shifting all subsequent elements one position to the right. This results in a time complexity of $$O(n)$$ in the worst case[1][2][15].

Delete Operation

• Deletion: Deleting an element from a sorted array involves shifting all subsequent elements one position to the left to fill the gap left by the deleted element. This operation also has a time complexity of $$O(n)$$ in the worst case[2][15].

Summary Table

Operation	Time Complexity
Search	$$O(\log n)$$
Insert	$$O(n)$$
Delete	$$O(n)$$

Additional Notes

• Accessing an Element: Accessing an element by its index in a sorted array is $$O(1)$$ because arrays allow direct access to any element using its index[4][20].
• Space Complexity: The space complexity for these operations is $$O(1)$$ as no additional space is required beyond the input array itself[15].

These complexities highlight the trade-offs involved in using sorted arrays, particularly the efficiency of search operations versus the cost of insertions and deletions.

Citations:
[1] http...