Trees In The Database - Advanced data structures

Trees in the Database
Advanced Data Structures

Lorenzo Alberton
lorenzo@ibuildings.com
DPC09, Amsterdam, 13 June 2009

Lorenzo Alberton

MDB2
Calendar
Pager
Translation2
Mail_Queue
DB_QueryTool

2

Tree

Connected, undirected, acyclic graph

A

B C G

D E

F

3

Tree

Connected, undirected, acyclic graph

A

B C

D E

F

3

Adjacency List Model
AKA “parent-child” model

4


CREATE TABLE emp_orgchart (
emp VARCHAR(10) NOT NULL PRIMARY KEY,
boss VARCHAR(10),
salary DECIMAL(6,2) NOT NULL
);

A
emp boss salary
A NULL 1000.00
B C
B A 900.00
C A 900.00
D C 800.00 D E F
E C 700.00
F C 600.00

5


Finding the root node

SELECT *
FROM emp_orgchart
WHERE boss IS NULL;

Finding the leaf nodes

SELECT e1.*
FROM emp_orgchart AS e1
LEFT JOIN emp_orgchart AS e2 ON e1.emp = e2.boss
WHERE e2.emp IS NULL;

6

Adjacency List Model Anomalies

UPDATE anomalies

START TRANSACTION;
emp boss salary
UPDATE emp_orgchart A NULL 1000.00
SET emp = ‘C1’ B A 900.00
WHERE emp = ‘C’; C1 A 900.00
D C 800.00
UPDATE emp_orgchart E C 700.00
SET boss = ‘C1’ F C 600.00
WHERE boss = ‘C’;

COMMIT;

7


UPDATE anomalies

START TRANSACTION;
UPDATE emp_orgchart
SET emp = CASE emp
UPDATE emp_orgchart
WHEN ‘C’ THEN ‘C1’
SET emp = ‘C1’
ELSE emp END,
WHERE emp = ‘C’;
boss = CASE boss
WHEN ‘C’ THEN ‘C1’
UPDATE emp_orgchart
ELSE boss END
SET boss = ‘C1’
WHERE ‘C’ IN (emp, boss);
WHERE boss = ‘C’;

COMMIT;

7


INSERT anomalies

8


INSERT anomalies

INSERT INTO emp_orgchart (emp, boss) VALUES
(‘G’, ‘H’),
(‘H’, ‘G’);

G H

8


INSERT anomalies

INSERT INTO emp_orgchart (emp, boss) VALUES
(‘G’, ‘H’),
(‘H’, ‘G’);

G H

INSERT INTO emp_orgchart VALUES (‘M’, ‘M’);

M

8


DELETE anomalies

DELETE FROM emp_orgchart WHERE emp = ‘C’;

A

B C

D E F

9

Fixing the Adjacency List Model
CREATE TABLE emp (
id INTEGER DEFAULT 0 PRIMARY KEY,
name VARCHAR(10) NOT NULL,
salary DECIMAL (6,2) NOT NULL
CHECK (salary >= 0.00),
...
);

CREATE TABLE orgchart (
emp_id INTEGER NOT NULL DEFAULT 0 -- vacant
REFERENCES emp(id)
ON DELETE SET DEFAULT ON UPDATE CASCADE,
boss_id INTEGER -- NULL means root node
REFERENCES emp(id),
...
);

10


-- cannot be your own boss
CHECK ((boss_id <> emp_id) OR
(boss_id = 0 AND emp_id = 0)),

11



-- prevent longer cycles
UNIQUE (emp_id, boss_id),

11




-- connected graph (edges = nodes - 1)
CHECK ((SELECT COUNT(*) FROM orgchart) - 1
= (SELECT COUNT(boss_id) FROM orgchart)),

11




-- connected graph (edges = nodes - 1)
CHECK ((SELECT COUNT(*) FROM orgchart) - 1
= (SELECT COUNT(boss_id) FROM orgchart)),

-- one root only
CHECK ((SELECT COUNT(*) FROM orgchart WHERE
boss_id IS NULL) = 1),

11

Adjacency List Model - Navigation

Loops / Self-Joins
procedural code
SELECT o1.emp AS e1,
o2.emp AS e2,
CREATE PROCEDURE
o3.emp AS e3
TreeTraversal (IN
FROM emp_orgchart AS o1
current_emp_id INT)
LEFT OUTER JOIN
BEGIN
emp_orgchart AS o2
...
ON o1.emp = o2.boss
LEFT OUTER JOIN
emp_orgchart AS o3
ON o2.emp = o3.boss
WHERE o1.emp = ‘A’;
12

Adjacency List Model - Deletion

13


A

B C

D E F

13


A

B C

D
x
E F

13


A A

B C B C

D
x
E F D E F

13


A A

A
B C B C

D
x
E F
B D
D
E
E
F
F

13


A A A

A
B C B C B C

D
x
E F
B D
D
E
E
F
F D E F

13


A A A

A
B C B C B D
C

D
x
E F
B D
D
E
E
F
F D E F

13


A A A

A
B C B C B D
C

D
x
E F
B D
D
E
E
F
F D E F

Requires traversal (deferred constraints)

13

Path Enumeration Model
aka Materialized Path

14


emp_id CHAR(1) NOT NULL PRIMARY KEY
-- if using a separator, don’t use it in the ID
CHECK (REPLACE(emp_id, ‘/’, ‘’) = emp_id),
emp_name VARCHAR(10) NOT NULL,
path_string VARCHAR(512) NOT NULL
);

emp_id emp_name path_string A
A Anthony A
B Beryl AB
B C
C Charles AC
D Denise ACD
E Ellen ACE D E F
F Frank ACF
15


-- prevent cycles (nodes appearing twice: ‘ABCA’)
CHECK (NOT EXISTS(
SELECT *
FROM emp_orgchart AS D1,
emp_orgchart AS P1
WHERE LENGTH(REPLACE(P1.path_string, D1.emp_id,
‘’)) <
LENGTH(P1.path_string) - LENGTH(D1.emp_id))
))

-- No path can be longer than the number of nodes
CHECK((SELECT MAX(LENGTH(path_string))
FROM emp_orgchart AS E1) <=
(SELECT COUNT(emp_id) * LENGTH(emp_id)
FROM emp_orgchart AS E2))

16


17


Depth of the node

17


Depth of the node
• LENGTH(path_string) / LENGTH(emp_id)

17


Depth of the node
• LENGTH(path_string) -
LENGTH(REPLACE(path_string, ‘/’, ‘’)) + 1

17


Depth of the node

Searching for subordinates

17


Depth of the node

• SELECT * FROM emp_orgchart
WHERE path_string LIKE ‘%’ || :parent_emp_id ||
‘%’;

17


Depth of the node

WHERE path_string LIKE ‘%’ || :parent_emp_id ||
‘%’;
WHERE path_string LIKE
(SELECT path_string FROM emp_orgchart
WHERE emp_id = :parent_emp_id) || ‘%’;

17


Searching for superiors

SELECT SUBSTRING(P1.path_string
FROM seq * LENGTH(P1.emp_id)
FOR LENGTH(P1.emp_id)) AS emp_id
FROM emp_orgchart AS P1,
sequence AS S1
WHERE P1.emp_id = :search_emp_id
AND S1.seq <= LENGTH(path_string)/
LENGTH(emp_id);

18


Deleting a subtree:

DELETE FROM emp_orgchart
WHERE path_string LIKE (
SELECT path_string
FROM emp_orgchart
WHERE emp_id = :deleted_node) || ‘%’;

Deleting a single node:
START TRANSACTION;
DELETE FROM emp_orgchart
WHERE emp_id = :deleted_node;
UPDATE emp_orgchart SET path_string =
REPLACE(path_string, :deleted_node, ‘’);
COMMIT;
19


Insertion of a new node
INSERT INTO emp_orgchart VALUES (
:new_emp_id, -- ‘M’
:new_name, -- ‘Maggie’
(SELECT path_string
FROM emp_orgchart
WHERE emp_id = :boss_of_new_emp) -- ‘D’
|| :new_emp_id -- ‘M’
);

emp_id emp_name path_string

D Denise ACD

M Maggie ACDM

20


Splitting the path string into nodes
SELECT CASE
WHEN SUBSTRING(‘/’ || P1.path_string || ‘/’
FROM S1.seq FOR 1) = ‘/’
THEN SUBSTRING(‘/’ || P1.path_string || ‘/’
FROM (S1.seq + 1)
FOR CharIndex(‘/’ ,
‘/’ || P1.path_string || ‘/’,
S1.seq + 1) - S1.seq - 1
ELSE NULL END AS emp_id
FROM sequence AS S1,
emp_orgchart AS P1
WHERE S1.seq BETWEEN 1
AND LENGTH(P1.path_string) + 1
AND SUBSTRING(‘/’ || P1.path_string || ‘/’
FROM S1.seq FOR 1) = ‘/’
21


emp_name edge_path Edge
Anthony 1.
Beryl 1.1.
Enumeration
Charles 1.2. Model
Denise 1.2.1.
Ellen 1.2.2.
Frank 1.2.3.
Anthony

Beryl Charles

Denise Ellen Frank

22

Nested Set Model
aka Modified Preorder Tree Traversal (MPTT)

23

Nested Set Model

A
C
B D E F

24

Nested Set Model

A
C
B D E F

A
1 12
B C
2 3 4 11
D E F
5 6 7 8 9 10

24

Nested Set Model

lft INTEGER NOT NULL,
rgt INTEGER NOT NULL
); A
1 12
B C
2 3 4 11
D E F
5 6 7 8 9 10

25

Nested Set Model

lft INTEGER NOT NULL,
rgt INTEGER NOT NULL
); A
1 12
B C
1 A 12 2 3 4 11
D E F
5 6 7 8 9 10

2 B 3 4 C 11

D E F
5 6 7 8 9 10

25

Nested Set Model
Finding root node

1 A 12

2 B 3 4 C 11

D E F
5 6 7 8 9 10

26

Nested Set Model
Finding root node
SELECT *
FROM orgchart
WHERE lft = 1; 1 A 12

2 B 3 4 C 11

D E F
5 6 7 8 9 10

26

Nested Set Model
Finding root node
SELECT *
FROM orgchart

Finding leaf nodes
2 B 3 4 C 11

D E F
5 6 7 8 9 10

26

Nested Set Model
Finding root node
SELECT *
FROM orgchart

Finding leaf nodes
SELECT *
2 B 3 4 C 11

FROM orgchart
WHERE lft = (rgt - 1);
D E F
5 6 7 8 9 10

26

Nested Set Model
Finding root node
SELECT *
FROM orgchart

Finding leaf nodes
SELECT *
2 B 3 4 C 11

FROM orgchart
D E F
Finding subtrees 5 6 7 8 9 10

26

Nested Set Model
Finding root node
SELECT *
FROM orgchart

Finding leaf nodes
SELECT *
2 B 3 4 C 11

FROM orgchart
D E F

SELECT Mgrs.emp AS boss
Workers.emp AS worker
FROM orgchart AS Mgrs,
orgchart AS Workers
WHERE Workers.lft > Mgrs.lft
AND Workers.lft < Mgrs.rgt
26

Nested Set Model
Finding root node
SELECT *
FROM orgchart

Finding leaf nodes
SELECT *
2 B 3 4 C 11

FROM orgchart
D E F

SELECT Mgrs.emp AS boss
Workers.emp AS worker
FROM orgchart AS Mgrs,
orgchart AS Workers
WHERE Workers.lft > Mgrs.lft
BETWEEN Mgrs.lft AND Mgrs.rgt
AND Workers.lft < Mgrs.rgt
26

Nested Set Model
Finding the level of a node

27

Nested Set Model
SELECT o2.emp,
COUNT(o1.emp) AS lvl
FROM orgchart AS o1,
orgchart AS o2
WHERE o2.lft BETWEEN o1.lft AND o1.rgt
GROUP BY o2.emp;

27

Nested Set Model
SELECT o2.emp,
orgchart AS o2
GROUP BY o2.emp;

Finding the height of the tree

27

Nested Set Model
SELECT o2.emp,
orgchart AS o2
GROUP BY o2.emp;

Finding the height of the tree
SELECT MAX(lvl) AS height FROM (
SELECT o2.emp,
COUNT(o1.emp) - 1
orgchart AS o2
GROUP BY o2.emp) AS L1(emp, lvl);

27

Nested Set Model
Finding relative position
SELECT CASE
WHEN :emp1 = :emp2
THEN :emp1 || ‘ is ’ || :emp2

WHEN o1.lft BETWEEN o2.lft AND o2.rgt
THEN :emp1 || ‘ subordinate to ’ || :emp2

WHEN o2.lft BETWEEN o1.lft AND o1.rgt
THEN :emp2 || ‘ subordinate to ’ || :emp1

ELSE :emp1 || ‘ no relation to ’ || :emp2
END
orgchart AS o2
WHERE o1.emp = :emp1 AND o2.emp = :emp2;
28

Nested Set Model
Deleting subtrees
DELETE FROM orgchart
WHERE lft BETWEEN (SELECT lft
FROM orgchart
WHERE emp = :start_node)
AND (SELECT rgt
FROM orgchart
Filling gaps WHERE emp = :start_node);
CREATE VIEW LftRgt (seq) AS
SELECT lft FROM orgchart
UNION ALL
SELECT rgt FROM orgchart;

UPDATE orgchart SET
lft = (SELECT COUNT(*) FROM LftRgt WHERE seq <= lft),
rgt = (SELECT COUNT(*) FROM LftRgt WHERE seq <= rgt)

29

Nested Set Model
Deleting a single node


A
C
B D E F

30

Nested Set Model


A

B D E F

30

Nested Set Model
CREATE PROCEDURE downsize(IN removed VARCHAR(10))
LANGUAGE SQL DETERMINISTIC
UPDATE orgchart SET emp = CASE
WHEN orgchart.emp = removed
AND orgchart.lft + 1 = orgchart.rgt --leaf
THEN ‘{vacant}’
WHEN orgchart.emp = removed
AND orgchart.lft + 1 <> orgchart.rgt
-- promote subordinate and vacate
THEN (SELECT o1.emp
FROM orgchart AS o1
WHERE orgchart.lft + 1 = o1.lft)
WHEN orgchart.emp = (SELECT o1.emp
FROM orgchart AS o1
WHERE orgchart.lft + 1 = o1.lft)
THEN ‘{vacant}’ ELSE emp END;
31

Nested Set to Adjacency List
SELECT B.id AS boss,
P.emp, P.lft, P.rgt
FROM orgchart as P
LEFT OUTER JOIN emp AS B ON B.lft =
(SELECT MAX(S.lft)
FROM orgchart AS S
WHERE P.lft > S.lft
AND P.lft < S.rgt);

boss emp lft rgt
NULL Anthony 1 12
Anthony Beryl 2 3
Anthony Charles 4 11
Charles Denise 5 6
Charles Ellen 7 8
Charles Frank 9 10

32

Frequent Insertion Trees

Avoid overhead (locking + updating) with larger spreads
and bigger gaps

emp lft rgt
Anthony 100 1200
Beryl 200 300
Charles 400 1100
Denise 500 600
Ellen 700 800
Frank 900 1000

33

Frequent Insertion Trees

Avoid overhead (locking + updating) with larger spreads
and bigger gaps

emp lft rgt
Anthony 100 1200
Beryl 200 300
Charles 400 1100
Denise 500 600
Ellen 700 800
Frank 900 1000

Datatype of (lft, rgt)?
- INTEGER (full range)
- FLOAT / REAL / DOUBLE
- NUMERIC(p,s) / DECIMAL(p,s)
33

Hybrid Models

Adjacency List with Nested Sets (node, parent, lft, rgt)
Nested Sets with depth
Adjacency List with depth
...

Denormalisation to save
subselects or joins

34

Nested Intervals
Rational Number Encodings

35

Nested Intervals Model

Rational numbers (a/b, with a and b integers)

((p.lft <= c.lft) AND (c.rgt <= p.rgt))

0/5 A 5/5

1/5 B 2/5 3/5 C 4/5

36


a b

37


a b

a+(b-a)/3 a+2(b-a)/3

37


Finding GCD (greatest common divisor)

CREATE FUNCTION gcd(IN x INTEGER, IN y INTEGER)
RETURNS INTEGER
BEGIN

WHILE x <> y DO
IF x > y THEN SET x = x - y; END IF;
IF y > x THEN SET y = y - x; END IF;
END WHILE;
RETURN x;

END;

38


Binary Node (x, y)
Fractions

39


Binary Node (x, y)
Fractions

First node (1, 1/2)

39


Binary Node (x, y)
Fractions

First node (1, 1/2)

depth-ﬁrst
convergence point

39


Binary Node (x, y)
Fractions
First child of ﬁrst node (1, 3/4)

First node (1, 1/2)

depth-ﬁrst
convergence point

39


Binary Node (x, y)
Fractions
First child of first node (1, 3/4)

First node (1, 1/2)

depth-first
convergence point

breadth-first
convergence point
39


40

CREATE FUNCTION x_numer(
IN numer INT, IN denom INT
) RETURNS INTEGER
BEGIN

DECLARE ret_num INTEGER;
DECLARE ret_den INTEGER;
SET ret_num = numer + 1;
SET ret_den = 2 * denom;
WHILE FLOOR(ret_num/2)
= ret_num/2
DO SET ret_num = ret_num/2;
SET red_den = ret_den/2;
END WHILE;
RETURN ret_num; -- ret_den
-- for x_denom()
END;
40

CREATE FUNCTION parent_numer(IN numer INTEGER,
IN denom INTEGER) RETURNS INTEGER
BEGIN
DECLARE ret_num INTEGER;
DECLARE ret_den INTEGER;
IF numer = 3
THEN RETURN CAST(NULL AS INTEGER)
END IF;
SET ret_num = (numer - 1)/2;
SET ret_den = denom/2;
WHILE FLOOR((ret_num - 1)/4) = (ret_num - 1)/4
DO SET ret_num = (ret_num + 1)/2;
SET red_den = ret_den/2;
END WHILE;
RETURN ret_num; -- ret_den for parent_denom()
END;
41


Similar functions for:
sibling_numer(), sibling_denom()
child_numer(), child_denom()
enumerated_path(), distance()
path_numer(), path_denom()

42


Similar functions for:
sibling_numer(), sibling_denom()
child_numer(), child_denom()
enumerated_path(), distance()
path_numer(), path_denom()

INSERT INTO orgchart (name, numer, denom) VALUES
(‘Anthony’, path_numer(‘1’), path_denom(‘1’)),
(‘Beryl’, path_numer(‘1.1’), path_denom(‘1.1’)),
(‘Charles’, path_numer(‘1.2’), path_denom(‘1.2’)),
(‘Denise’, path_numer(‘1.2.1’), path_denom(‘1.2.1’));

42

Nested Intervals Encodings

Interval Halving

average:
(lft + rgt) / 2

43


Interval Halving

average:
(lft + rgt) / 2

Farey Fractions
a/b and c/d neighbours
=> bc -ad = 1

mediant:
(lft_num + rgt_num)
(lft_den + rgt_den)

43


Continued Fractions

1.1.2.1

Reverse (or additive) Continued Fractions

44

Proprietary Solutions
Oracle

45

Oracle: CONNECT BY PRIOR

Traversing the tree
SELECT emp, boss
FROM emp_orgchart
START WITH boss IS NULL
CONNECT BY [NOCYCLE] PRIOR emp = boss;

emp boss
A NULL
B A
G B
C A
D C
E C
F C

46


Traversing the tree
SELECT emp, boss
FROM emp_orgchart
START WITH boss = ‘C’
IS NULL
CONNECT BY [NOCYCLE] PRIOR emp = boss;

emp boss
D C
E C
F C

46

Traversing the tree
SELECT emp, boss, salary, LEVEL AS lvl,
LPAD(' ', 2*(LEVEL-1)) || emp AS tree,
CONNECT_BY_IS_LEAF AS is_leaf
FROM emp_orgchart
CONNECT BY PRIOR emp = boss
ORDER SIBLINGS BY salary DESC;
emp boss salary lvl tree is_leaf
A NULL 1000.00 1 A 0
B A 900.00 2 B 0
G B 800.00 3 G 1
C A 900.00 2 C 0
D C 800.00 3 D 1
E C 700.00 3 E 1
F C 600.00 3 F 1
47


Determining the relationship between two nodes

SELECT COUNT(*) AS ‘is_subordinate’
FROM emp_orgchart
WHERE emp = :subordinate
AND LEVEL > 1
START WITH emp = :superior
CONNECT BY PRIOR emp = boss;

48


Determining the relationship between two nodes

SELECT COUNT(*) AS ‘is_subordinate’
FROM emp_orgchart
WHERE emp = :subordinate
AND LEVEL > 1
START WITH emp = :superior
CONNECT BY PRIOR emp = boss;

A subordinate of C? 0
F subordinate of A? 1

48

Oracle: CONNECT_BY_ROOT

Determining the ancestor of a node

SELECT emp_id,
CONNECT_BY_ROOT emp_id AS root
FROM orgchart
START WITH boss = ‘A’
CONNECT BY PRIOR emp_id = boss;

emp_id root
B B
G B
C C
D C
E C
F C

49

Oracle: SYS_CONNECT_BY_PATH

Materialized Path View
SELECT emp_id,
SYS_CONNECT_BY_PATH (emp_id,'.')
AS path_string
FROM orgchart
CONNECT BY PRIOR emp_id = boss
ORDER BY 2;
emp_id path_string
A .A
B .A.B
C .A.C
D .A.C.D
E .A.C.E
F .A.C.F

50

Common Table Expressions
SQL-99 Standard

51

emp VARCHAR(10) PRIMARY KEY,
boss VARCHAR(10) REFERENCES emp_orgchart(emp_id),
salary TEXT
);

INSERT INTO emp_orgchart (emp, boss, salary) VALUES
(‘A’, NULL, 1000.00),
(‘B’, ‘A’, 900.00),
(‘C’, ‘A’, 900.00), A
(‘D’, ‘C’, 800.00),
(‘E’, ‘C’, 700.00),
(‘F’, ‘C’, 600.00), B C
(‘G’, ‘B’, 800.00);

G D E F

52


WITH RECURSIVE hierarchy AS (
-- non recursive term
SELECT *
FROM emp_orgchart
WHERE boss IS NULL
UNION ALL
-- recursive term
SELECT E1.*
FROM emp_orgchart AS E1
JOIN hierarchy AS E2
ON E1.boss = E2.emp
)
SELECT *
FROM hierarchy
ORDER BY emp;

53


-- non recursive term
SELECT *
FROM emp_orgchart
WHERE boss IS NULL emp boss salary
UNION ALL A NULL 1000.00
-- recursive term B A 900.00
SELECT E1.* C A 900.00
FROM emp_orgchart AS E1 D C 800.00
E C 700.00
ON E1.boss = E2.emp
F C 600.00
)
SELECT * G B 800.00
FROM hierarchy
ORDER BY emp;

53

SELECT *,
1 AS lvl,
CAST(emp AS TEXT) AS tree,
emp || ‘.’ AS path
FROM emp_orgchart
WHERE boss IS NULL
UNION ALL
SELECT E1.*,
E2.lvl + 1 AS lvl,
LPAD(E1.emp, lvl * 2, ‘ ’) AS tree,
E2.path || E1.emp || ‘.’ AS path
FROM emp_orgchart
ON E1.boss = E2.emp
)
SELECT *
FROM hierarchy
ORDER BY path;
54

SELECT *,
1 AS lvl,
emp CAST(emp salary
boss AS TEXT) AS tree, tree
lvl path
emp || ‘.’ AS path
A NULL 1000.00 1 A A.
FROM emp_orgchart
WHERE boss IS NULL
B A 900.00 2 B A.B.
UNION ALL
SELECT E1.*,
G B 800.00 3 G A.B.G.
E2.lvl + 1 AS lvl,
C LPAD(E1.emp, lvl * 2, ‘ ’)CAS tree,
A 900.00 2 A.C.
E2.path || E1.emp || ‘.’ AS path
D C 800.00
FROM emp_orgchart 3 D A.C.D.
E C 700.00 3 E A.C.E.
ON E1.boss = E2.emp
) F C 600.00 3 F A.C.F.
SELECT *
FROM hierarchy
ORDER BY path;
54


SELECT *,
1 AS lvl,
CAST(emp AS TEXT) AS tree
FROM emp_orgchart
WHERE boss = ‘A’
UNION ALL
SELECT E1.*,
E2.lvl + 1 AS lvl,
LPAD(E1.emp, depth * 2, ‘ ’) AS tree
FROM emp_orgchart
JOIN hierarchy AS E2 ON E1.boss = E2.emp
WHERE E2.lvl < 3 -- termination condition
)
SELECT *
FROM hierarchy
ORDER BY path;

55

SELECT *,
1 AS lvl,
CAST(emp AS TEXT) AS tree
FROM emp_orgchart
WHERE boss = ‘A’
UNION ALL
SELECT E1.*,
E2.lvl + 1 AS lvl,
LPAD(E1.emp, depth * 2, ‘ ’) AS tree
FROM emp_orgchart
JOIN hierarchy AS E2 ON E1.boss = E2.emp
)
SELECT *,
COALESCE((SELECT 0 FROM emp_orgchart E3
WHERE hierarchy.emp = E3.boss
FETCH FIRST ROW ONLY), 1) AS is_leaf
FROM hierarchy;

56

And the winner is...

57

Resources
Joe Celko, “Trees and Hierarchies in SQL for
Smarties”, Morgan Kaufmann:
http://www.amazon.com/dp/1558609202/

Vadim Tropashko, various articles and papers:

http://www.dbazine.com/top-auth/top-auth-trop/
http://www.sigmod.org/sigmod/record/issues/
0506/p47-article-tropashko.pdf
http://arxiv.org/pdf/cs/0402051

59

Thank you!
Contact details:

Lorenzo Alberton
lorenzo@ibuildings.com
http://www.alberton.info
http://joind.in/talk/view/585

Trees In The Database - Advanced data structures

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