The WITH clause allows you to specify common table expressions (CTEs). Regular (non-recursive) common-table-expressions are essentially views that are limited in scope to a particular query. CTEs can reference each-other and can be nested.
Basic CTE examples
-- create a CTE called "cte" and use it in the main query
WITH cte AS (SELECT 42)
SELECT * FROM cte;
┌────┐
│ 42 │
├────┤
│ 42 │
└────┘
-- create two CTEs, where the second CTE references the first CTE
WITH cte AS (SELECT 42 AS i),
cte2 AS (SELECT i*100 FROM cte)
SELECT * FROM cte2;
┌─────────┐
│ i * 100 │
├─────────┤
│ 4200 │
└─────────┘
Recursive CTE examples
Tree traversal
WITH RECURSIVE can be used to traverse trees. For example, take a hiearchy of tags:
CREATE TABLE tag(id int, name varchar, subclassof int);
INSERT INTO tag VALUES
(1, 'U2', 5),
(2, 'Blur', 5),
(3, 'Oasis', 5),
(4, '2Pac', 6),
(5, 'Rock', 7),
(6, 'Rap', 7),
(7, 'Music', 9),
(8, 'Movies', 9),
(9, 'Art', NULL);
The following query returns the path from the node Oasis to the root of the tree (Art).
WITH RECURSIVE tag_hierarchy(id, source, path) AS (
SELECT id, name, [name] AS path
FROM tag
WHERE subclassof IS NULL
UNION ALL
SELECT tag.id, tag.name, list_prepend(tag.name, tag_hierarchy.path)
FROM tag, tag_hierarchy
WHERE tag.subclassof = tag_hierarchy.id
)
SELECT path
FROM tag_hierarchy
WHERE source = 'Oasis';
┌───────────────────────────┐
│ path │
├───────────────────────────┤
│ [Oasis, Rock, Music, Art] │
└───────────────────────────┘
Graph traversal
The WITH RECURSIVE clause can be used to express graph traversal on arbitrary graphs. However, if the graph has cycles, the query must perform cycle detection to prevent infinite loops.
Take the following undirected social graph:
CREATE TABLE knows(person1id int, person2id int);
INSERT INTO knows VALUES (1, 2), (1, 4), (2, 3), (2, 4), (3, 4), (5, 6);
INSERT INTO knows SELECT person2id, person1id FROM knows;
Note that there is a cycle e.g. between nodes 1, 2, and 4. To detect cycles, the query stores the path in a list and, before adding a new edge, checks whether its endpoint has been visited before.
The following query returns all paths from person 1:
WITH RECURSIVE paths(startPerson, endPerson, path) AS (
SELECT -- define the path as the first edge of the traversal
person1id AS startPerson,
person2id AS endPerson,
[person1id, person2id]::bigint[] AS path
FROM knows
UNION ALL
SELECT -- concatenate new edge to the path
paths.startPerson AS startPerson,
person2id AS endPerson,
array_append(path, person2id) AS path
FROM paths
JOIN knows ON paths.endPerson = knows.person1id
WHERE knows.person2id != ALL(paths.path) -- detect cycles
)
SELECT startPerson, endPerson, path
FROM paths
WHERE startPerson = 1;
┌─────────────┬───────────┬──────────────┐
│ startPerson │ endPerson │ path │
├─────────────┼───────────┼──────────────┤
│ 1 │ 2 │ [1, 2] │
│ 1 │ 4 │ [1, 4] │
│ 1 │ 3 │ [1, 4, 3] │
│ 1 │ 4 │ [1, 2, 4] │
│ 1 │ 2 │ [1, 4, 2] │
│ 1 │ 3 │ [1, 2, 3] │
│ 1 │ 2 │ [1, 4, 3, 2] │
│ 1 │ 3 │ [1, 2, 4, 3] │
│ 1 │ 4 │ [1, 2, 3, 4] │
│ 1 │ 3 │ [1, 4, 2, 3] │
└─────────────┴───────────┴──────────────┘
WITH RECURSIVE can be used to find all unweighted shortest paths between two nodes. The following query returns all unweighted shortest paths between person 1 and person 3:
WITH RECURSIVE paths(startPerson, endPerson, path, endReached) AS (
SELECT person1id AS startPerson,
person2id AS endPerson,
[person1id, person2id]::bigint[] AS path,
max(CASE WHEN person2id = 3 THEN true ELSE false END)
OVER (ROWS BETWEEN UNBOUNDED PRECEDING
AND UNBOUNDED FOLLOWING) AS endReached
FROM knows
WHERE person1id = 1
UNION ALL
SELECT paths.startPerson AS startPerson,
person2id AS endPerson,
array_append(path, person2id) AS path,
max(CASE WHEN person2id = 3 THEN true ELSE false END)
OVER (ROWS BETWEEN UNBOUNDED PRECEDING
AND UNBOUNDED FOLLOWING) AS endReached
FROM paths
JOIN knows
ON person1id = paths.endPerson
WHERE person2id != ALL(paths.path)
AND NOT paths.endReached
)
SELECT startPerson, endPerson, path
FROM paths
WHERE endPerson = 3;
┌─────────────┬───────────┬───────────┐
│ startPerson │ endPerson │ path │
├─────────────┼───────────┼───────────┤
│ 1 │ 3 │ [1, 4, 3] │
│ 1 │ 3 │ [1, 2, 3] │
└─────────────┴───────────┴───────────┘