Solution Explanation: Design SQL

This problem requires designing a data structure and methods to simulate basic SQL operations like insertion, deletion, selection, and export on multiple tables. The solution leverages a hash table (or dictionary in Python) to efficiently manage the tables and their data.

Approach

The core idea is to use a hash table (map in Java, unordered_map in C++, map in Go) where:

• Keys: Table names (strings).
• Values: A list (or vector) of rows. Each row is itself a list (or vector) of strings representing the cell values. This nested structure efficiently represents tabular data.

The methods then operate directly on this hash table:

• __init__ (Python), constructor (Go), or constructor (Java, C++): Initializes the hash table. Note that this constructor doesn't actually create the tables with their specified number of columns; it simply creates an empty hash table ready to receive data. The column information is not directly used in the provided solutions because it's handled implicitly by the input row lengths.

• ins (insert): Adds a new row to the specified table. It first checks if the table exists and if the row length matches the expected number of columns for that table (though in the given solutions this check isn't explicitly implemented). If both conditions are true, it appends the new row to the table's list of rows. An auto-incrementing row ID is not explicitly managed; the order of insertion determines the effective row ID.

• rmv (remove): Removes a row from the specified table. It checks if the table and row exist; if so, it removes the row.

• sel (select): Retrieves a specific cell's value. It checks for the validity of table, row, and column indices before accessing and returning the cell value.

• exp (export): Returns all rows of a specified table in CSV format. It first checks if the table exists and returns an empty array if not; otherwise, it constructs the CSV representation by iterating over the rows and cells.

Time and Space Complexity Analysis

Let's analyze the time and space complexities of each operation:

• __init__/Constructor: O(1) time complexity (constant time to create an empty hash table). O(1) space complexity (constant space initially).

• ins (insert): O(1) average case time complexity (average time to insert into a hash table). In the worst case (hash collisions), it could be O(n), where n is the number of rows in the table. O(1) space complexity (constant space to append a row).

• rmv (remove): O(n) time complexity in the worst case (removing a row from the middle of a list might require shifting elements). O(1) space complexity.

• sel (select): O(1) average-case time complexity (constant time to access a cell using row and column indices). O(1) space complexity.

• exp (export): O(m*k) time complexity, where m is the number of rows and k is the average number of columns per row. O(1) space complexity (though the space used for the resulting array depends on the table size).

Space Complexity Consideration

The overall space complexity is dominated by the storage of the tables themselves. In the worst case, it could be O(nmk), where n is the number of tables, m is the maximum number of rows in any table, and k is the maximum number of columns. This is because the hash table stores all the data.

Improvements and Follow-up

The follow-up question asks about handling sparse tables (many deletions). The current approach, using lists of lists, becomes inefficient for sparse tables because many list elements might be empty. Better solutions for sparse tables would involve:

• Hash Table with Sparse Representation: Instead of a simple list of lists, using a hash table to represent each row. The keys of this inner hash table would be column indices, and the values would be cell values. This would only store non-empty cells, saving space.

• Other Data Structures: Consider more advanced data structures like column-oriented databases or specialized sparse matrix representations to further improve efficiency for sparse tables.

The provided solutions are basic implementations and could be enhanced with error handling (e.g., checking for null values), input validation, and more sophisticated data structures to handle sparse tables more efficiently.