✔ PASS Graph & Hierarchy task_116_graph_cycle_visited_protection Scaled: 1M+ Records Ordered: Yes

Directed Dependency Graph Cycle Protection via Visited Array Path

Candidate Latency (1M Rows)

1.04 ms

(1.2x slower than golden)

Golden Latency (1M Rows)

0.86 ms

DuckDB in-memory engine

Underlying Data Volume

5 rows

200 B across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 4.9s

✔ Correctness Verified on 1M+ Records

Candidate SQL output matches ground truth golden query across all multiset rows and numeric tolerances (tol=1e-3). Zero data skew or anti-patterns detected on full dataset scale.

1. Analytical Significance & What It Means

Scenario & Frontier Trap

Business Scenario & Problem

Traverses downstream dependencies in a directed acyclic graph that contains an intentional cyclic loop (A -> B -> C -> A), requiring visited path arrays to prevent infinite recursion OOM.

⚡ The Frontier Trap (Why LLMs Fail)

Standard recursive CTEs without cycle tracking (omitting visited array state) enter an infinite recursion loop on cyclic graphs, causing DuckDB or any relational database to fail with a max-recursion limit error or crash with an Out-of-Memory exception.

Prompt / User Request Given to Model

Traverse all reachable downstream tasks starting from 'BUILD_CORE'.
CRITICAL: The graph contains a cyclic dependency ('COMPILE_LIB' -> 'TEST_SUITE' -> 'BUILD_CORE'). The query MUST detect already-visited nodes and terminate traversal to prevent infinite recursion.

Required output columns:
- task_id (VARCHAR)
- min_depth (INT)

Order by min_depth ASC, task_id ASC.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (5 rows • 200 B)

Production-scale fixtures loaded into the isolated DuckDB sandbox with at least 1,000,000 records per table:

📊 task_edges 5 rows 200 B Data Volume

parent_task (VARCHAR) child_task (VARCHAR)

Data Preview (showing sample rows from 5 total rows):

#	parent_task	child_task
1	START	BUILD_CORE
2	BUILD_CORE	COMPILE_LIB
3	COMPILE_LIB	TEST_SUITE
4	TEST_SUITE	BUILD_CORE
5	TEST_SUITE	PACKAGE_APP

3. Graphical Query Execution Plan & Cost Bottlenecks

Physical Operator Tree (DuckDB 2.0 Profiler)

Visual flowchart of the physical execution pipeline. Operators with high relative costs (≥ 20% of query runtime or heavy latency) are visually highlighted:

Pipeline Latency Distribution (Total Plan Time: 1.04 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders

⏳ ORDER_BY 17.7%

Latency: 0.18 ms

Rows In/Out: 3

Data Vol: 60 B

📊 HASH_GROUP_BY 21.7%

Latency: 0.23 ms

Rows In/Out: 3

Data Vol: 60 B

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 60 B

📁 Projections: ['task_id', 'depth'...

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 60 B

📁 Projections: ['#0', '#1']

🔄 RECURSIVE_CTE 47.1%

Latency: 0.49 ms

Rows In/Out: 3

Data Vol: 252 B

📐 PROJECTION 0.4%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 68 B

📁 Projections: ['task_id', 'depth'...

🔍 TABLE_SCAN 1.7%

Latency: 0.02 ms

Rows In/Out: 1

Data Vol: 16 B

📁 memory.main.task_edges

📐 PROJECTION 1.7%

Latency: 0.02 ms

Rows In/Out: 2

Data Vol: 184 B

📁 Projections: ['task_id', 'depth'...

⚡ HASH_JOIN 8.6%

Latency: 0.09 ms

Rows In/Out: 2

Data Vol: 152 B

🔍 RECURSIVE_CTE_SCAN 0.5%

Latency: 0.01 ms

Rows In/Out: 3

Data Vol: 252 B

🔍 TABLE_SCAN 0.5%

Latency: 0.01 ms

Rows In/Out: 5

Data Vol: 160 B

📁 memory.main.task_edges

Operator	Cost %	Latency	Processed Rows	Details / Table	Status
RECURSIVE_CTE	47.1%	0.49 ms	3	-	Normal
HASH_GROUP_BY	21.7%	0.23 ms	3	-	Normal
ORDER_BY	17.7%	0.18 ms	3	-	Normal
HASH_JOIN	8.6%	0.09 ms	2	-	Normal
TABLE_SCAN	1.7%	0.02 ms	1	memory.main.task_edges	Normal
PROJECTION	1.7%	0.02 ms	2	Projections: ['task_id', 'depth', 'visited_path'	Normal
TABLE_SCAN	0.5%	0.01 ms	5	memory.main.task_edges	Normal
RECURSIVE_CTE_SCAN	0.5%	0.01 ms	3	-	Normal
PROJECTION	0.4%	0.00 ms	1	Projections: ['task_id', 'depth', 'visited_path'	Normal
PROJECTION	0.1%	0.00 ms	3	Projections: ['#0', '#1']	Normal
PROJECTION	0.0%	0.00 ms	3	Projections: ['task_id', 'depth']	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH RECURSIVE downstream_tasks AS
  (SELECT child_task AS task_id,
          1 AS depth,
          ['build_core', child_task] AS visited_path
   FROM task_edges
   WHERE parent_task = 'BUILD_CORE'
   UNION ALL SELECT e.child_task AS task_id,
                    d.depth + 1 AS depth,
                    list_append(d.visited_path, e.child_task) AS visited_path
   FROM downstream_tasks d
   JOIN task_edges e ON d.task_id = e.parent_task
   WHERE NOT list_contains(d.visited_path, e.child_task))
SELECT task_id,
       min(depth) AS min_depth
FROM downstream_tasks
GROUP BY task_id
ORDER BY min_depth ASC,
         task_id ASC;

WITH RECURSIVE downstream_graph AS
  (SELECT child_task AS task_id,
          1 AS depth,
          ['build_core', child_task] AS path_nodes
   FROM task_edges
   WHERE parent_task = 'BUILD_CORE'
   UNION ALL SELECT e.child_task,
                    g.depth + 1,
                    list_append(g.path_nodes, e.child_task)
   FROM downstream_graph g
   JOIN task_edges e ON g.task_id = e.parent_task
   WHERE NOT list_contains(g.path_nodes, e.child_task)
     AND g.depth < 10)
SELECT task_id,
       min(depth) AS min_depth
FROM downstream_graph
GROUP BY task_id
ORDER BY min_depth ASC,
         task_id ASC;

CREATE TABLE task_edges (parent_task VARCHAR, child_task VARCHAR);


INSERT INTO task_edges
VALUES ('START', 'BUILD_CORE'),
       ('BUILD_CORE', 'COMPILE_LIB'),
       ('COMPILE_LIB', 'TEST_SUITE'),
       ('TEST_SUITE', 'BUILD_CORE'),
       -- Circular loop!
 ('TEST_SUITE', 'PACKAGE_APP');

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (3 rows × 2 cols)

#	task_id	min_depth
1	COMPILE_LIB	1
2	TEST_SUITE	2
3	PACKAGE_APP	3

Expected Golden Output (3 rows × 2 cols)

#	task_id	min_depth
1	COMPILE_LIB	1
2	TEST_SUITE	2
3	PACKAGE_APP	3

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