Problem Description

You need to implement a simplified SQL database system that manages multiple tables. Each table has a fixed number of columns and supports basic operations like inserting rows, deleting rows, selecting cells, and exporting data.

The system should work as follows:

Initial Setup:

• You're given two arrays: names (table names) and columns (number of columns for each table)
• The i-th table has name names[i] and contains columns[i] columns

Operations to Implement:

1. Insert (ins): Add a new row to a specified table

   • Each row gets an auto-incremented ID (starting from 1)
   • The ID continues incrementing even if previous rows were deleted
   • Returns true if successful, false if the row length doesn't match the table's column count or if the table doesn't exist

2. Remove (rmv): Delete a row from a table by its ID

   • Does nothing if the table doesn't exist or the row ID doesn't exist
   • Deleting a row doesn't affect the auto-increment counter

3. Select (sel): Retrieve a specific cell value

   • Takes table name, row ID, and column ID (1-indexed)
   • Returns the cell value as a string
   • Returns "<null>" if the table, row, or column doesn't exist

4. Export (exp): Export all rows from a table in CSV format

   • Returns an array of strings, each representing a row
   • Each row string contains the row ID followed by all column values, separated by commas
   • Returns an empty array if the table doesn't exist

Example: If you have a table "users" with 3 columns:

• Insert ["Alice", "25", "NYC"] → gets ID 1
• Insert ["Bob", "30", "LA"] → gets ID 2
• Delete row 1
• Insert ["Charlie", "35", "SF"] → gets ID 3 (not 1, because auto-increment continues)
• Export returns: ["2,Bob,30,LA", "3,Charlie,35,SF"]

The implementation uses a hash table where keys are table names and values are lists of rows. The auto-increment logic needs to track the next available ID for each table separately.

Intuition

When we look at this problem, we need to simulate a basic database system with multiple tables. The key insight is that we need to track two main things for each table: the actual data rows and the auto-increment counter for IDs.

The most straightforward approach is to use a hash table (dictionary) where each table name maps to its data structure. But what should this data structure be?

Initially, we might think of using a simple list to store rows. However, this creates a problem with the delete operation. If we use the list index as the row ID, deleting a row would shift all subsequent rows, changing their IDs. This violates the requirement that row IDs should remain stable.

Instead, we need to separate the concept of row ID from the list index. We can store each row along with its ID. When we delete a row, we can either:

1. Mark it as deleted without removing it from the list
2. Use a dictionary mapping row IDs to row data

The second approach using a nested dictionary structure (tables[name][rowId] = row) is cleaner because:

• Insertion is O(1) - just add with the next ID
• Deletion is O(1) - just delete the key
• Selection is O(1) - direct access by ID
• Export requires iterating through all existing rows

For tracking the auto-increment counter, we need a separate counter for each table that keeps incrementing regardless of deletions. This ensures that even if we delete row 5, the next inserted row gets ID 6, not 5.

The column count validation during insertion is straightforward - we just need to store the expected column count for each table and compare it with len(row).

This leads us to maintain:

• A dictionary of dictionaries for the actual data: tables[table_name][row_id] = row_data
• A dictionary for auto-increment counters: next_id[table_name] = next_available_id
• A dictionary for column counts: column_count[table_name] = expected_columns

Solution Approach

Based on the reference solution approach, we use a hash table to store the mapping between table names and their data rows. Let's walk through the implementation details:

Data Structure:

• Use a defaultdict(list) called tables where each key is a table name and the value is a list storing all rows for that table
• Additionally, we need to track:
  • The expected column count for each table
  • The next auto-increment ID for each table

Implementation of Each Operation:

1. Constructor (__init__):

   def __init__(self, names, columns):
       self.tables = {}  # table_name -> {row_id -> row_data}
       self.next_id = {}  # table_name -> next_available_id
       self.column_count = {}  # table_name -> expected_columns
     
       for i in range(len(names)):
           self.tables[names[i]] = {}
           self.next_id[names[i]] = 1
           self.column_count[names[i]] = columns[i]

2. Insert Operation (insertRow):

   • Check if the table exists and if the row length matches the expected column count
   • If valid, assign the current auto-increment ID to the row
   • Store the row with its ID as the key
   • Increment the next available ID for that table

   def insertRow(self, name, row):
       if name not in self.tables or len(row) != self.column_count[name]:
           return False
     
       row_id = self.next_id[name]
       self.tables[name][row_id] = row
       self.next_id[name] += 1
       return True

3. Delete Operation (deleteRow):

   • Simply remove the row from the dictionary if it exists
   • No need to adjust other row IDs or the auto-increment counter

   def deleteRow(self, name, rowId):
       if name in self.tables and rowId in self.tables[name]:
           del self.tables[name][rowId]

4. Select Operation (selectCell):

   • Check if the table exists, row exists, and column index is valid
   • Return the cell value (using 1-indexed column ID)
   • Return "<null>" for any invalid access

   def selectCell(self, name, rowId, columnId):
       if (name not in self.tables or 
           rowId not in self.tables[name] or 
           columnId < 1 or 
           columnId > len(self.tables[name][rowId])):
           return "<null>"
     
       return self.tables[name][rowId][columnId - 1]

5. Export Operation (exp):

   • Iterate through all existing rows in the table
   • Format each row as CSV: "id,value1,value2,..."
   • Sort by row ID to maintain order

   def exp(self, name):
       if name not in self.tables:
           return []
     
       result = []
       for row_id in sorted(self.tables[name].keys()):
           row_str = str(row_id) + "," + ",".join(self.tables[name][row_id])
           result.append(row_str)
     
       return result

Time Complexity:

• Insert: O(1)
• Delete: O(1)
• Select: O(1)
• Export: O(n log n) where n is the number of rows (due to sorting)

Space Complexity:

• O(m × n × c) where m is the number of tables, n is the average number of rows per table, and c is the average number of columns per row

Example Walkthrough

Let's walk through a small example to illustrate how the solution works:

Initial Setup:

names = ["users", "products"]
columns = [3, 2]

This creates two tables:

• "users" with 3 columns
• "products" with 2 columns

Our data structures after initialization:

tables = {"users": {}, "products": {}}
next_id = {"users": 1, "products": 1}
column_count = {"users": 3, "products": 2}

Step 1: Insert into "users" table

insertRow("users", ["Alice", "25", "NYC"])

• Check: "users" exists ✓, len(["Alice", "25", "NYC"]) = 3 = column_count["users"] ✓
• Assign row_id = next_id["users"] = 1
• Store: tables["users"][1] = ["Alice", "25", "NYC"]
• Increment: next_id["users"] = 2
• Return: true

State after insertion:

tables["users"] = {1: ["Alice", "25", "NYC"]}
next_id["users"] = 2

Step 2: Insert another row

insertRow("users", ["Bob", "30", "LA"])

• Row gets ID 2
• tables["users"][2] = ["Bob", "30", "LA"]
• next_id["users"] = 3

Step 3: Delete row 1

deleteRow("users", 1)

• Remove key 1 from tables["users"]
• Note: next_id["users"] remains 3 (unchanged)

State after deletion:

tables["users"] = {2: ["Bob", "30", "LA"]}
next_id["users"] = 3  # Still 3!

Step 4: Insert after deletion

insertRow("users", ["Charlie", "35", "SF"])

• Gets row_id = 3 (not 1, because auto-increment continues)
• tables["users"][3] = ["Charlie", "35", "SF"]
• next_id["users"] = 4

Step 5: Select a cell

selectCell("users", 2, 2)

• Check: "users" exists ✓, row 2 exists ✓, column 2 ≤ 3 ✓
• Return tables["users"][2][2-1] = tables["users"][2][1] = "30"

Step 6: Export the table

exp("users")

• Iterate through sorted keys: [2, 3]
• For row_id=2: "2,Bob,30,LA"
• For row_id=3: "3,Charlie,35,SF"
• Return: ["2,Bob,30,LA", "3,Charlie,35,SF"]

Step 7: Invalid operations

insertRow("users", ["Dan", "40"])  # Returns false (2 values, needs 3)
selectCell("users", 1, 1)          # Returns "<null>" (row 1 was deleted)
selectCell("inventory", 1, 1)      # Returns "<null>" (table doesn't exist)

This example demonstrates:

1. Auto-increment IDs persist through deletions (row 3 comes after row 2, even though row 1 was deleted)
2. Direct access to rows by ID using dictionary structure
3. Validation of column counts during insertion
4. Handling of invalid access attempts

Solution Implementation

Time and Space Complexity

Time Complexity:

• __init__: O(1) - Simply initializes an empty defaultdict
• insertRow: O(1) - Appends a row to the list, which is a constant time operation
• deleteRow: O(1) - Currently empty implementation, but would be O(1) if implemented as marking deletion without actual removal
• selectCell: O(1) - Direct access to a list element by index

Overall, each operation has O(1) time complexity.

Space Complexity:

• The space complexity is O(n) where n is the total number of elements stored across all tables
• Each row inserted adds to the space usage proportionally
• The defaultdict stores lists of rows, with total space proportional to the number of rows multiplied by the number of columns per row

Note: The deleteRow method is not implemented in the given code. If it were to be implemented using actual deletion from the list, it would have O(m) time complexity where m is the number of rows in the table due to list shifting. However, the reference answer suggests O(1), which implies a logical deletion approach (like marking as deleted) rather than physical removal.

Learn more about how to find time and space complexity quickly.

Common Pitfalls

1. Incorrect Auto-Increment Implementation

The provided code doesn't properly implement the auto-increment ID feature. It simply appends rows to a list, making row IDs position-based rather than persistent. When a row is deleted, all subsequent rows shift position, changing their IDs.

Problem Example:

sql = SQL(["users"], [3])
sql.insertRow("users", ["Alice", "25", "NYC"])  # Should be ID 1
sql.insertRow("users", ["Bob", "30", "LA"])     # Should be ID 2
sql.deleteRow("users", 1)                       # Delete Alice
sql.insertRow("users", ["Charlie", "35", "SF"]) # Should be ID 3, not 2
# Current code would make Charlie ID 2 (position-based)

2. Missing Validation in Insert Operation

The current insertRow method doesn't validate:

• Whether the table exists
• Whether the row has the correct number of columns
• It should return True/False based on success

3. Missing Error Handling in Select Operation

The selectCell method doesn't handle invalid cases properly:

• Non-existent table
• Invalid row ID
• Invalid column ID Should return "<null>" for any invalid access.

4. Missing Export Functionality

The code completely lacks the exp method required by the problem specification.

Corrected Solution

class SQL:
    def __init__(self, names: List[str], columns: List[int]):
        # Use dictionaries to store table data with persistent IDs
        self.tables = {}  # table_name -> {row_id -> row_data}
        self.next_id = {}  # table_name -> next_available_id
        self.column_count = {}  # table_name -> expected_columns
      
        for i in range(len(names)):
            self.tables[names[i]] = {}
            self.next_id[names[i]] = 1
            self.column_count[names[i]] = columns[i]
  
    def insertRow(self, name: str, row: List[str]) -> bool:
        # Validate table exists and column count matches
        if name not in self.tables or len(row) != self.column_count[name]:
            return False
      
        # Assign auto-incremented ID and store row
        row_id = self.next_id[name]
        self.tables[name][row_id] = row
        self.next_id[name] += 1
        return True
  
    def deleteRow(self, name: str, rowId: int) -> None:
        # Only delete if table and row exist
        if name in self.tables and rowId in self.tables[name]:
            del self.tables[name][rowId]
  
    def selectCell(self, name: str, rowId: int, columnId: int) -> str:
        # Comprehensive validation
        if (name not in self.tables or 
            rowId not in self.tables[name] or 
            columnId < 1 or 
            columnId > len(self.tables[name][rowId])):
            return "<null>"
      
        return self.tables[name][rowId][columnId - 1]
  
    def exp(self, name: str) -> List[str]:
        # Export table in CSV format
        if name not in self.tables:
            return []
      
        result = []
        # Sort by row ID to maintain order
        for row_id in sorted(self.tables[name].keys()):
            row_str = str(row_id) + "," + ",".join(self.tables[name][row_id])
            result.append(row_str)
      
        return result

Key Improvements:

1. Uses dictionary to store rows with persistent IDs instead of position-based list
2. Properly implements auto-increment that continues even after deletions
3. Validates all inputs and returns appropriate values/errors
4. Includes the missing exp method with proper CSV formatting
5. Maintains row order by ID when exporting