SQL Gap and Island Problems

This challenge focuses on solving two common and fundamental problems in SQL: identifying "gaps" in sequential data and grouping "islands" of related records. Understanding these concepts is crucial for data analysis, reporting, and cleaning datasets with temporal or categorical patterns.

Problem Description

You are provided with a table containing records, each with a unique identifier and a status. Your task is to:

1. Identify Gaps: Determine periods where a specific status is not present in a sequential order.
2. Identify Islands: Group consecutive records that share the same status into distinct "islands".

You will need to process the data based on its sequence (e.g., an order of operations, a timestamp, or a sequential ID) to accurately identify these gaps and islands.

Key Requirements:

• Gap Identification: For a given status, identify the contiguous sequences of sequential identifiers where that status is absent. The output should represent these gaps as start and end points of the missing sequences.
• Island Identification: Group consecutive records that share the same status. Each group of consecutive records with the same status is considered an "island". The output should assign a unique identifier to each island.

Expected Behavior:

• The solution should be robust and handle various input scenarios, including empty tables, tables with only one record, and tables where all records have the same status.
• The output for gap identification should clearly delineate the start and end of each missing sequence.
• The output for island identification should assign a distinct identifier to each contiguous block of the same status.

Important Edge Cases:

• Empty Table: What happens if the input table is empty?
• Single Record: How are gaps and islands handled with only one record?
• All Same Status: If all records have the same status, are there any gaps? How is the single island identified?
• Gaps at Boundaries: What if a gap occurs before the first record or after the last record in the sequence?

Examples

Example 1: Gap Identification

Input Table:
| id | status |
|----|--------|
| 1  | A      |
| 2  | A      |
| 3  | B      |
| 4  | A      |
| 5  | A      |
| 6  | A      |
| 7  | B      |
| 8  | A      |

Pseudocode for Gap Identification (Status 'B'):

-- We are looking for gaps where 'B' is NOT present in sequential 'id'
SELECT
    start_id,
    end_id
FROM
    (
        -- Identify groups where the status is NOT 'B'
        SELECT
            id AS start_id,
            LEAD(id, 1, id) OVER (ORDER BY id) AS next_id
        FROM
            your_table
        WHERE
            status <> 'B'
    ) AS non_b_sequences
WHERE
    -- A gap exists if the next id is not the current id + 1
    next_id = start_id + 1
ORDER BY
    start_id;

-- This pseudocode needs refinement to truly identify contiguous gaps.
-- A common approach involves comparing the current row's ID with the previous row's ID after grouping.
-- A more robust pseudocode would involve identifying contiguous blocks of non-'B' statuses.

Output for Gap Identification (Status 'B'):

| gap_start_id | gap_end_id |
|--------------|------------|
| 1            | 2          |
| 4            | 6          |
| 8            | 8          |

Explanation: Records with id 1 and 2 are not 'B', forming a gap. Records with id 4, 5, and 6 are not 'B', forming another gap. Record with id 8 is not 'B', forming a gap of length 1. The sequence id 3 and id 7 have status 'B', breaking the gaps.

Example 2: Island Identification

Using the same input table as Example 1.

Input Table:
| id | status |
|----|--------|
| 1  | A      |
| 2  | A      |
| 3  | B      |
| 4  | A      |
| 5  | A      |
| 6  | A      |
| 7  | B      |
| 8  | A      |

Pseudocode for Island Identification:

-- Assign an island ID to contiguous blocks of the same status
SELECT
    id,
    status,
    SUM(CASE WHEN prev_status IS NULL OR status <> prev_status THEN 1 ELSE 0 END) OVER (ORDER BY id) AS island_id
FROM
    (
        SELECT
            id,
            status,
            LAG(status, 1, status) OVER (ORDER BY id) AS prev_status
        FROM
            your_table
    ) AS ranked_data
ORDER BY
    id;

Output for Island Identification:

| id | status | island_id |
|----|--------|-----------|
| 1  | A      | 1         |
| 2  | A      | 1         |
| 3  | B      | 2         |
| 4  | A      | 3         |
| 5  | A      | 3         |
| 6  | A      | 3         |
| 7  | B      | 4         |
| 8  | A      | 5         |

Explanation: Records with id 1 and 2 have status 'A' and are consecutive, forming Island 1. Record with id 3 has status 'B', starting a new island (Island 2). Records with id 4, 5, and 6 have status 'A' and are consecutive, forming Island 3. Record with id 7 has status 'B', starting Island 4. Record with id 8 has status 'A', starting Island 5.

Example 3: Edge Case - Single Record

Input Table:
| id | status |
|----|--------|
| 1  | A      |

Output for Gap Identification (Status 'B'):

| gap_start_id | gap_end_id |
|--------------|------------|
| 1            | 1          |

Explanation: The entire sequence (just id 1) is a gap as status 'B' is absent.

Output for Island Identification:

| id | status | island_id |
|----|--------|-----------|
| 1  | A      | 1         |

Explanation: The single record forms a single island.

Constraints

• The input table will contain at least one column for a sequential identifier (e.g., id or timestamp) and a column for the status.
• The sequential identifier column will be of a numeric or temporal type that supports ordering.
• The status column can contain various data types (strings, numbers, etc.).
• Solutions should aim for efficiency, ideally utilizing window functions for optimal performance on larger datasets.

Notes

• These problems are commonly solved using SQL window functions, particularly LAG() and LEAD() for identifying changes in consecutive rows, and SUM() or ROW_NUMBER() over partitions for grouping.
• For gap identification, you might first identify contiguous blocks of records that do not have the target status. Then, you'll need to determine the start and end of these blocks relative to the overall sequence.
• Consider how you will define the "sequence" for your gap and island calculations. Is it strictly by the id column, or is there a specific order of operations implied?
• The specific implementation details will vary slightly depending on the SQL dialect (e.g., PostgreSQL, MySQL, SQL Server, Oracle), but the core logic remains the same. The pseudocode provided uses generic SQL constructs.