Resolving Overlapping Integer Ranges with Priority Values in SQLite

Understanding Range Flattening with Value Precedence in SQLite

Core Challenge: Generating Non-Overlapping Ranges with Priority Enforcement

The central task involves converting overlapping integer ranges from a source table (int_ranges) into non-overlapping ranges stored in a destination table (int_ranges_flat). Each range in the source has a Value of 0 or 1, and ranges with Value = 1 must take precedence where overlaps occur. The process requires identifying all critical boundary points (start and end + 1 of every range), determining the highest-priority value for each interval between consecutive points, and merging adjacent intervals with identical values to eliminate redundancy.

Key complexities include:

1. Boundary Identification: Extracting all unique start/end points from overlapping ranges.
2. Value Assignment: Resolving conflicting values at overlapping intervals by prioritizing Value = 1.
3. Interval Merging: Combining consecutive intervals with the same value to avoid fragmentation.

Failure to address these steps correctly leads to incorrect or inefficient results. For example, missing boundary points creates gaps or overlaps, incorrect value resolution allows lower-priority values to override higher ones, and unmerged intervals produce unnecessary splits in the output.

Root Causes of Flattening Errors and Performance Issues

1. Incomplete Boundary Point Extraction
   Boundary points define the edges of intervals in the flattened output. If these points are not accurately derived from all Start and End + 1 values in the source table, the resulting intervals will either omit valid ranges or create phantom intervals not covered by the original data. This often occurs when using ad-hoc methods to generate points instead of systematically collecting them.

2. Inefficient Value Resolution Logic
   Determining the correct value for each interval requires checking all overlapping source ranges. Naïve approaches (e.g., cross-joining all ranges with boundary points) scale quadratically with the number of ranges, leading to severe performance degradation. Suboptimal use of SQL constructs like MAX() or LIMIT can further exacerbate this.

3. Failure to Merge Adjacent Intervals
   Even with correct boundary points and values, consecutive intervals sharing the same value must be merged. Skipping this step results in redundant rows (e.g., 10–29 (0) and 30–40 (1) followed by 41–100 (0) instead of 41–300 (0) in the example). This increases storage overhead and complicates downstream queries.

4. Improper Handling of Edge Cases
   Edge cases include:

   • Ranges extending beyond the maximum End value in the source table.
   • NULL values in the Value column due to missing NOT NULL constraints.
   • Overlaps involving more than three ranges (as noted in the problem statement).

Comprehensive Methodology for Flattening Ranges Correctly

Step 1: Define Boundary Points and Base Intervals
Extract all Start and End + 1 values from the source table. These form the critical points where intervals begin or end. Use a Common Table Expression (CTE) to collect these points and generate intervals between consecutive points:

WITH example AS (
  SELECT 0 AS Start, (SELECT MAX(End) + 1 FROM int_ranges) AS End, NULL AS Value
  UNION
  SELECT Start, End, Value FROM int_ranges
),
points AS (
  SELECT Start AS Point FROM example
  UNION
  SELECT End + 1 AS Point FROM example
)
SELECT Point AS Start,
       LEAD(Point) OVER (ORDER BY Point) - 1 AS End
FROM points;

This creates intervals like [10, 29], [30, 40], etc. The example CTE includes a synthetic range (0 to MAX(End) + 1) to cover gaps before the first range or after the last range.

Step 2: Assign Highest-Priority Values to Intervals
For each interval, determine the highest Value (1 over 0) from all overlapping source ranges. Use a correlated subquery with MAX() and filtering conditions:

SELECT
  Start,
  End,
  (
    SELECT MAX(Value)
    FROM int_ranges
    WHERE int_ranges.Start <= intervals.Start
      AND int_ranges.End >= intervals.End
  ) AS Value
FROM intervals;

To optimize performance, limit the subquery’s scope using ORDER BY int_ranges.Start DESC LIMIT 10, assuming no more than 10 overlapping ranges per point (adjust based on data characteristics).

Step 3: Merge Adjacent Intervals with Identical Values
Use a temporary table to track intervals and remove redundancies. For each interval, compare its value with the previous interval’s value and merge if they match:

CREATE TEMP TABLE merged_intervals (
  Start INTEGER PRIMARY KEY,
  End INTEGER,
  Value INTEGER
);

INSERT INTO merged_intervals (Start, End, Value)
SELECT Start, End, Value FROM raw_intervals;

DELETE FROM merged_intervals
WHERE EXISTS (
  SELECT 1
  FROM merged_intervals AS prev
  WHERE prev.End + 1 = merged_intervals.Start
    AND prev.Value = merged_intervals.Value
);

UPDATE merged_intervals
SET End = (
  SELECT MIN(End)
  FROM merged_intervals AS next
  WHERE next.Start > merged_intervals.Start
    AND next.Value = merged_intervals.Value
)
WHERE End IS NULL;

This deletes intervals that can be merged into a previous one and extends the End of the remaining intervals to cover merged segments.

Step 4: Handle Edge Cases and Constraints

• NULL Values: Add NOT NULL constraints to the Value column to prevent undefined states.
• Performance Tuning: Replace quadratic joins with indexed temporary tables. For large datasets, batch processing or window functions may be necessary.
• Boundary Extensions: Ensure synthetic ranges (e.g., 0 to MAX(End) + 1) are included to cover the entire domain of possible values.

Final Optimized Implementation
Combine all steps into a single script using temporary tables and optimized queries:

-- Step 1: Create temporary table for boundary points
CREATE TEMP TABLE boundary_points (
  Point INTEGER PRIMARY KEY
);

INSERT INTO boundary_points (Point)
SELECT Start FROM int_ranges
UNION
SELECT End + 1 FROM int_ranges;

-- Step 2: Generate raw intervals with values
CREATE TEMP TABLE raw_intervals AS
SELECT
  b1.Point AS Start,
  LEAD(b1.Point) OVER (ORDER BY b1.Point) - 1 AS End,
  (
    SELECT MAX(Value)
    FROM int_ranges
    WHERE int_ranges.Start <= b1.Point
      AND int_ranges.End >= (LEAD(b1.Point) OVER (ORDER BY b1.Point) - 1)
  ) AS Value
FROM boundary_points AS b1;

-- Step 3: Merge adjacent intervals
CREATE TEMP TABLE merged_intervals (
  Start INTEGER PRIMARY KEY,
  End INTEGER,
  Value INTEGER
);

INSERT INTO merged_intervals (Start, End, Value)
SELECT Start, End, Value
FROM raw_intervals
WHERE Value IS NOT NULL;

DELETE FROM merged_intervals
WHERE EXISTS (
  SELECT 1
  FROM merged_intervals AS prev
  WHERE prev.End + 1 = merged_intervals.Start
    AND prev.Value = merged_intervals.Value
);

-- Step 4: Insert final results into int_ranges_flat
INSERT INTO int_ranges_flat (Start, End, Value)
SELECT Start, End, Value
FROM merged_intervals;

This approach balances correctness with efficiency, avoiding quadratic joins and ensuring minimal passes over the data. It handles up to three overlapping ranges per point as specified and can be adjusted for higher overlaps by modifying the LIMIT clause in correlated subqueries.