Understanding Time Ranges and Overlap

When working with time-based data, such as scheduling or logging events, it’s essential to understand how different intervals overlap. In this article, we’ll explore a specific problem: summing distinct overlapping time ranges. We’ll delve into the technical details of solving this problem, including gaps-and-islands problems, overlap calculations, and ratio determination.

Background and Context

The given Stack Overflow question revolves around creating a User-Defined Function (UDF) in SQL Server that takes a date range as input and returns the sum of unique overlapping records in a table. The UDF should round start and stop times to the nearest 15-minute interval.

Gaps-and-Islands Problem

The first component of the problem is the gaps-and-islands problem. Imagine a timeline where each shift is represented by an interval with a start time and an end time. The goal is to identify contiguous groups of shifts, also known as islands, that span a specific range. These islands are then combined to calculate the total overlap.

Solution Overview

To solve this problem, we’ll employ two main techniques:

1. Gaps-and-Islands Problem: Identify contiguous intervals (islands) within a larger range using a cumulative sum approach.
2. Overlap Calculation: Calculate the overlapping interval between each island and the target range to determine the unique overlap.

Gaps-and-Islands Solution

The innermost subquery calculates the previous end time for all shifts, which helps identify the start of an island when there are no overlaps. The cumulative sum then identifies all rows on the island.

WITH i AS (
    SELECT min(starttime) as island_start, max(endtime) as island_end
    FROM (
        SELECT s.*,
               SUM(CASE WHEN prev_endtime >= starttime THEN 0 ELSE 1 END) OVER (ORDER BY starttime) as grp
        FROM shifts s
        WHERE endtime > @start OR
              starttime < @end
    ) s
    GROUP BY grp
)
SELECT min(starttime) as island_start, max(endtime) as island_end
FROM i;

Overlap Calculation

To calculate the overlapping interval between each island and the target range, we’ll use a combination of date arithmetic operations.

WITH i AS (
    SELECT min(starttime) as island_start, max(endtime) as island_end
    FROM (
        SELECT s.*,
               SUM(CASE WHEN prev_endtime >= starttime THEN 0 ELSE 1 END) OVER (ORDER BY starttime) as grp
        FROM shifts s
        WHERE endtime > @start OR
              starttime < @end
    ) s
    GROUP BY grp
)
SELECT 
    sum(DATEDIFF(second, INTERVAL_START, INTERVAL_END)) as shift_seconds,
    DATEDIFF(SECOND, DATEDIFF(SECOND, @start, @end), @end) as overall_seconds
FROM (
    SELECT i.island_start, i.island_end,
           (CASE WHEN island_end > @endtime THEN @end ELSE island_end END) as interval_end,
           (CASE WHEN island_start < @start THEN @start ELSE island_start END) as interval_start
    FROM i
) AS subquery;

Ratio Calculation

The final step is to calculate the ratio of the overlapping interval to the overall range.

WITH i AS (
    SELECT min(starttime) as island_start, max(endtime) as island_end
    FROM (
        SELECT s.*,
               SUM(CASE WHEN prev_endtime >= starttime THEN 0 ELSE 1 END) OVER (ORDER BY starttime) as grp
        FROM shifts s
        WHERE endtime > @start OR
              starttime < @end
    ) s
    GROUP BY grp
)
SELECT 
    sum(DATEDIFF(second, INTERVAL_START, INTERVAL_END)) as shift_seconds,
    DATEDIFF(SECOND, DATEDIFF(SECOND, @start, @end), @end) as overall_seconds,
    (sum(DATEDIFF(second, INTERVAL_START, INTERVAL_END)) / 
     DATEDIFF(SECOND, DATEDIFF(SECOND, @start, @end), @end)) * 100 as overlap_percentage
FROM (
    SELECT i.island_start, i.island_end,
           (CASE WHEN island_end > @endtime THEN @end ELSE island_end END) as interval_end,
           (CASE WHEN island_start < @start THEN @start ELSE island_start END) as interval_start
    FROM i
) AS subquery;

Conclusion

In this article, we explored how to sum distinct overlapping time ranges. We used a combination of gaps-and-islands problem and overlap calculations to solve the problem. By understanding the underlying techniques and applying them correctly, you can create efficient and effective solutions for similar problems in your own projects.

Note: The provided code snippets are simplified examples and may need modifications based on specific requirements and database schema changes.

Last modified on 2023-06-23