✔ PASS Graph & Hierarchy task_077_Q77_org_hierarchy_span_of_control Scaled: 1M+ Records Ordered: Yes

Organizational Reporting Depth & Management Span of Control

Candidate Latency (1M Rows)

0.89 ms

(1.0x faster than golden)

Golden Latency (1M Rows)

0.91 ms

DuckDB in-memory engine

Underlying Data Volume

5 rows

140 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

HR analytics measures how deep the management chain is from the CEO to individual contributors and calculates direct vs indirect headcounts for each manager.

⚡ The Frontier Trap (Why LLMs Fail)

Unbounded recursive queries crash if there is an accidental circular reporting loop (e.g. A reports to B, B reports to A).

Prompt / User Request Given to Model

HR analytics measures how deep the management chain is from the CEO to individual contributors and calculates direct vs indirect headcounts for each manager.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: emp_id, emp_name, hierarchy_level, reporting_path.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (5 rows • 140 B)

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

📊 employees 5 rows 140 B Data Volume

emp_id (INTEGER) emp_name (VARCHAR) manager_id (INTEGER)

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

#	emp_id	emp_name	manager_id
1	1	Alice (CEO)	NULL
2	2	Bob (VP Eng)	1
3	3	Charlie (VP Sales)	1
4	4	David (Staff Eng)	2
5	5	Eve (Senior Eng)	4

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

⏳ ORDER_BY 13.3%

Latency: 0.12 ms

Rows In/Out: 5

Data Vol: 200 B

🔄 RECURSIVE_CTE 🔥 64.8% Cost

Latency: 0.58 ms

Rows In/Out: 5

Data Vol: 200 B

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 40 B

📁 Projections: ['emp_id', 'emp_nam...

🔍 TABLE_SCAN 2.0%

Latency: 0.02 ms

Rows In/Out: 1

Data Vol: 20 B

📁 memory.main.employees

📐 PROJECTION 2.1%

Latency: 0.02 ms

Rows In/Out: 4

Data Vol: 0.02 MB

📁 Projections: ['emp_id', 'emp_nam...

⚡ HASH_JOIN 15.5%

Latency: 0.14 ms

Rows In/Out: 4

Data Vol: 0.02 MB

🔍 RECURSIVE_CTE_SCAN 1.6%

Latency: 0.01 ms

Rows In/Out: 5

Data Vol: 200 B

🔍 TABLE_SCAN 0.6%

Latency: 0.01 ms

Rows In/Out: 5

Data Vol: 376 B

📁 memory.main.employees

Operator	Cost %	Latency	Processed Rows	Data Volume	Details / Table	Status
RECURSIVE_CTE	64.8%	0.58 ms	5	0.00 MB	-	🔥 BOTTLENECK
HASH_JOIN	15.5%	0.14 ms	4	0.02 MB	-	Normal
ORDER_BY	13.3%	0.12 ms	5	0.00 MB	-	Normal
PROJECTION	2.1%	0.02 ms	4	0.02 MB	Projections: ['emp_id', 'emp_name', 'hierarchy_l	Normal
TABLE_SCAN	2.0%	0.02 ms	1	0.00 MB	memory.main.employees	Normal
RECURSIVE_CTE_SCAN	1.6%	0.01 ms	5	0.00 MB	-	Normal
TABLE_SCAN	0.6%	0.01 ms	5	0.00 MB	memory.main.employees	Normal
PROJECTION	0.1%	0.00 ms	1	0.00 MB	Projections: ['emp_id', 'emp_name', 'hierarchy_l	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH RECURSIVE employee_hierarchy AS
  (-- Anchor member: Start with top-level employees (CEO / no manager)
 SELECT emp_id,
        emp_name,
        1 AS hierarchy_level,
        cast(emp_name AS VARCHAR) AS reporting_path
   FROM employees
   WHERE manager_id IS NULL
   UNION ALL -- Recursive member: Traverse down reporting chains
 SELECT e.emp_id,
        e.emp_name,
        eh.hierarchy_level + 1 AS hierarchy_level,
        eh.reporting_path || ' -> ' || e.emp_name AS reporting_path
   FROM employees e
   JOIN employee_hierarchy eh ON e.manager_id = eh.emp_id)
SELECT emp_id,
       emp_name,
       hierarchy_level,
       reporting_path
FROM employee_hierarchy
ORDER BY hierarchy_level,
         emp_id;

-- Traverse management tree from CEO downward, tracking reporting depth
 WITH RECURSIVE org_hierarchy AS
  (SELECT emp_id,
          emp_name,
          manager_id,
          1 AS hierarchy_level,
          emp_name AS reporting_path
   FROM employees
   WHERE manager_id IS NULL
   UNION ALL SELECT e.emp_id,
                    e.emp_name,
                    e.manager_id,
                    h.hierarchy_level + 1,
                    h.reporting_path || ' -> ' || e.emp_name
   FROM employees e
   JOIN org_hierarchy h ON e.manager_id = h.emp_id)
SELECT emp_id,
       emp_name,
       hierarchy_level,
       reporting_path
FROM org_hierarchy
ORDER BY hierarchy_level,
         emp_id;

CREATE TABLE employees (emp_id INT, emp_name VARCHAR, manager_id INT);


INSERT INTO employees
VALUES (1, 'Alice (CEO)', NULL),
       (2, 'Bob (VP Eng)', 1),
       (3, 'Charlie (VP Sales)', 1),
       (4, 'David (Staff Eng)', 2),
       (5, 'Eve (Senior Eng)', 4);

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (5 rows × 4 cols)

#	emp_id	emp_name	hierarchy_level	reporting_path
1	1	Alice (CEO)	1	Alice (CEO)
2	2	Bob (VP Eng)	2	Alice (CEO) -> Bob (VP Eng)
3	3	Charlie (VP Sales)	2	Alice (CEO) -> Charlie (VP Sales)
4	4	David (Staff Eng)	3	Alice (CEO) -> Bob (VP Eng) -> David (Staff Eng)
5	5	Eve (Senior Eng)	4	Alice (CEO) -> Bob (VP Eng) -> David (Staff Eng) -> Eve (Senior Eng)

Expected Golden Output (5 rows × 4 cols)

#	emp_id	emp_name	hierarchy_level	reporting_path
1	1	Alice (CEO)	1	Alice (CEO)
2	2	Bob (VP Eng)	2	Alice (CEO) -> Bob (VP Eng)
3	3	Charlie (VP Sales)	2	Alice (CEO) -> Charlie (VP Sales)
4	4	David (Staff Eng)	3	Alice (CEO) -> Bob (VP Eng) -> David (Staff Eng)
5	5	Eve (Senior Eng)	4	Alice (CEO) -> Bob (VP Eng) -> David (Staff Eng) -> Eve (Senior Eng)

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