Compute unique duration by merging intervals

## Problem You have an autonomous-driving clip dataset where each row represents a time interval from a driving run. ### Table: `clips` | column | type | description | |---|---|---| | `set_id` | INT | Session/clip set identifier (e.g., 1–6) | | `run_id` | STRING | Driving run identifier, formatted like `YYYYMMDD_HHMMSS` | | `start_time` | INT | Clip start time offset (e.g., seconds) | | `end_time` | INT | Clip end time offset (e.g., seconds) | | `set_number` | INT | Dataset/source identifier | Assume each interval is **half-open**: `[start_time, end_time)` so duration is `end_time - start_time`. Intervals for the same `run_id` may: - overlap (partially or fully), - be duplicated/redundant, - have gaps (non-contiguous). ## Task Compute, for **each `run_id`**, the **cumulative deduplicated time**: the total duration covered by the **union** of all intervals for that `run_id` (i.e., after merging overlaps). ## Example input For run `20250101_122334`: - set 1: `[58, 70)` - set 2: `[57, 69)` - set 3: `[55, 72)` - set 4: `[56, 71)` - set 5: `[80, 100)` For run `20250102_101010`: - set 6: `[43, 62)` ## Expected output Return a result with: - `run_id` - `cumulative_unique_time` (same unit as the time offsets) Using the example above, results would be: - `20250101_122334` → `39` - `20250102_101010` → `19` ## Requirements 1. Write a **SQL** solution to compute `cumulative_unique_time` per `run_id`. 2. Write a **Python** solution to compute the same metric (given a list/dataframe of intervals).