✔ PASS Graph & Hierarchy task_079_Q79_graph_cycle_detection_visited_array Scaled: 1M+ Records Ordered: No

Cycle Detection in Directed Dependency Graphs with Visited Array

Candidate Latency (1M Rows)

0.66 ms

(1.2x slower than golden)

Golden Latency (1M Rows)

0.56 ms

DuckDB in-memory engine

Underlying Data Volume

3 rows

120 B across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 13.8s

✔ 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

In build systems (e.g. Webpack, Bazel) or task scheduling, circular dependencies (Task A -> Task B -> Task A) cause deadlocks. The engine must detect cycles and abort gracefully.

⚡ The Frontier Trap (Why LLMs Fail)

Standard recursive CTEs without cycle tracking loop infinitely until the database crashes with out-of-memory errors.

Prompt / User Request Given to Model

In build systems (e.g. Webpack, Bazel) or task scheduling, circular dependencies (Task A -> Task B -> Task A) cause deadlocks. The engine must detect cycles and abort gracefully.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: task_id, depends_on, visited_path, has_cycle.
Row order does not matter.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (3 rows • 120 B)

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

📊 task_dependencies 3 rows 120 B Data Volume

task_id (VARCHAR) depends_on (VARCHAR)

Data Preview (showing sample rows from 3 total rows):

#	task_id	depends_on
1	compile	codegen
2	codegen	lint
3	lint	compile

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: 0.66 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders

✂️ STREAMING_LIMIT 0.4%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 193 B

🎯 FILTER 2.9%

Latency: 0.02 ms

Rows In/Out: 3

Data Vol: 291 B

🔄 RECURSIVE_CTE 🔥 77.7% Cost

Latency: 0.51 ms

Rows In/Out: 9

Data Vol: 729 B

📐 PROJECTION 0.5%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 195 B

📁 Projections: ['task_id', 'depend...

🔍 TABLE_SCAN 1.1%

Latency: 0.01 ms

Rows In/Out: 3

Data Vol: 96 B

📁 memory.main.task_dependencies

📐 PROJECTION 2.2%

Latency: 0.01 ms

Rows In/Out: 6

Data Vol: 534 B

📁 Projections: ['task_id', 'depend...

⚡ HASH_JOIN 11.7%

Latency: 0.08 ms

Rows In/Out: 6

Data Vol: 528 B

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 6

Data Vol: 432 B

📁 Projections: ['#0', '#1', '#2']

🎯 FILTER 2.0%

Latency: 0.01 ms

Rows In/Out: 6

Data Vol: 438 B

🔍 RECURSIVE_CTE_SCAN 0.7%

Latency: 0.00 ms

Rows In/Out: 6

Data Vol: 438 B

🔍 TABLE_SCAN 0.6%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 96 B

📁 memory.main.task_dependencies

Operator	Cost %	Latency	Processed Rows	Details / Table	Status
RECURSIVE_CTE	77.7%	0.51 ms	9	-	🔥 BOTTLENECK
HASH_JOIN	11.7%	0.08 ms	6	-	Normal
FILTER	2.9%	0.02 ms	3	-	Normal
PROJECTION	2.2%	0.01 ms	6	Projections: ['task_id', 'depends_on', 'list_con	Normal
FILTER	2.0%	0.01 ms	6	-	Normal
TABLE_SCAN	1.1%	0.01 ms	3	memory.main.task_dependencies	Normal
RECURSIVE_CTE_SCAN	0.7%	0.00 ms	6	-	Normal
TABLE_SCAN	0.6%	0.00 ms	3	memory.main.task_dependencies	Normal
PROJECTION	0.5%	0.00 ms	3	Projections: ['task_id', 'depends_on', 'visited_	Normal
STREAMING_LIMIT	0.4%	0.00 ms	1	-	Normal
PROJECTION	0.1%	0.00 ms	6	Projections: ['#0', '#1', '#2']	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH RECURSIVE path_finder AS
  (SELECT task_id,
          depends_on,
          [task_id] AS visited_path,
          FALSE AS has_cycle
   FROM task_dependencies
   UNION ALL SELECT p.task_id,
                    d.depends_on,
                    list_append(p.visited_path, d.task_id),
                    list_contains(p.visited_path, d.depends_on) AS has_cycle
   FROM path_finder p
   JOIN task_dependencies d ON p.depends_on = d.task_id
   WHERE NOT p.has_cycle
     AND array_length(p.visited_path) < 10)
SELECT task_id,
       depends_on,
       visited_path,
       has_cycle
FROM path_finder
WHERE has_cycle = TRUE
LIMIT 1;

-- Detect circular loops using array path tracking
 WITH RECURSIVE path_finder AS
  (SELECT task_id,
          depends_on,
          [task_id] AS visited_path,
          FALSE AS has_cycle
   FROM task_dependencies
   UNION ALL SELECT p.task_id,
                    d.depends_on,
                    list_append(p.visited_path, d.task_id),
                    list_contains(p.visited_path, d.depends_on) AS has_cycle
   FROM path_finder p
   JOIN task_dependencies d ON p.depends_on = d.task_id
   WHERE NOT p.has_cycle
     AND array_length(p.visited_path) < 10)
SELECT task_id,
       depends_on,
       visited_path,
       has_cycle
FROM path_finder
WHERE has_cycle = TRUE
LIMIT 1;

CREATE TABLE task_dependencies (task_id VARCHAR, depends_on VARCHAR);


INSERT INTO task_dependencies
VALUES ('compile', 'codegen'),
       ('codegen', 'lint'),
       ('lint', 'compile'); -- Circular cycle!

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (1 rows × 4 cols)

#	task_id	depends_on	visited_path	has_cycle
1	compile	compile	['compile' 'codegen' 'lint']	1

Expected Golden Output (1 rows × 4 cols)

#	task_id	depends_on	visited_path	has_cycle
1	compile	compile	['compile' 'codegen' 'lint']	1

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