ClickHouse supports Common Table Expressions ([CTE](https://en.wikipedia.org/wiki/Hierarchical_and_recursive_queries_in_SQL)) and substitutes the code defined in the `WITH` clause in all places of use for the rest of `SELECT` query. Named subqueries can be included to the current and child query context in places where table objects are allowed. Recursion is prevented by hiding the current level CTEs from the WITH expression.
However, due to the fact that we are referring `cte_numbers` twice, random numbers are generated each time and, accordingly, we see different random results, `280501, 392454, 261636, 196227` and so on...
The optional RECURSIVE modifier allows for a WITH query to refer to its own output. Example:
**Example:** Sum integers from 1 throught 100
```sql
WITH RECURSIVE test_table AS (
SELECT 1 AS number
UNION ALL
SELECT number + 1 FROM test_table WHERE number <100
)
SELECT sum(number) FROM test_table;
```
``` text
┌─sum(number)─┐
│ 5050 │
└─────────────┘
```
The general form of a recursive `WITH` query is always a non-recursive term, then `UNION ALL`, then a recursive term, where only the recursive term can contain a reference to the query's own output. Recursive CTE query is executed as follows:
1. Evaluate the non-recursive term. Place result of non-recursive term query in a temporary working table.
2. As long as the working table is not empty, repeat these steps:
1. Evaluate the recursive term, substituting the current contents of the working table for the recursive self-reference. Place result of recursive term query in a temporary intermediate table.
2. Replace the contents of the working table with the contents of the intermediate table, then empty the intermediate table.
Recursive queries are typically used to work with hierarchical or tree-structured data. For example, we can write a query that performs tree traversal:
**Example:** Tree traversal
First let's create tree table:
```sql
DROP TABLE IF EXISTS tree;
CREATE TABLE tree
(
id UInt64,
parent_id Nullable(UInt64),
data String
) ENGINE = MergeTree ORDER BY id;
INSERT INTO tree VALUES (0, NULL, 'ROOT'), (1, 0, 'Child_1'), (2, 0, 'Child_2'), (3, 1, 'Child_1_1');
```
We can traverse those tree with such query:
**Example:** Tree traversal
```sql
WITH RECURSIVE search_tree AS (
SELECT id, parent_id, data
FROM tree t
WHERE t.id = 0
UNION ALL
SELECT t.id, t.parent_id, t.data
FROM tree t, search_tree st
WHERE t.parent_id = st.id
)
SELECT * FROM search_tree;
```
```text
┌─id─┬─parent_id─┬─data──────┐
│ 0 │ ᴺᵁᴸᴸ │ ROOT │
│ 1 │ 0 │ Child_1 │
│ 2 │ 0 │ Child_2 │
│ 3 │ 1 │ Child_1_1 │
└────┴───────────┴───────────┘
```
## Search order
To create a depth-first order, we compute for each result row an array of rows that we have already visited:
**Example:** Graph traversal without cycle detection
```sql
WITH RECURSIVE search_graph AS (
SELECT from, to, label FROM graph g
UNION ALL
SELECT g.from, g.to, g.label
FROM graph g, search_graph sg
WHERE g.from = sg.to
)
SELECT DISTINCT * FROM search_graph ORDER BY from;
```
```text
┌─from─┬─to─┬─label──┐
│ 1 │ 4 │ 1 -> 4 │
│ 1 │ 2 │ 1 -> 2 │
│ 1 │ 3 │ 1 -> 3 │
│ 2 │ 3 │ 2 -> 3 │
│ 4 │ 5 │ 4 -> 5 │
└──────┴────┴────────┘
```
But if we add cycle in that graph, previous query will fail with `Maximum recursive CTE evaluation depth` error:
```sql
INSERT INTO graph VALUES (5, 1, '5 -> 1');
WITH RECURSIVE search_graph AS (
SELECT from, to, label FROM graph g
UNION ALL
SELECT g.from, g.to, g.label
FROM graph g, search_graph sg
WHERE g.from = sg.to
)
SELECT DISTINCT * FROM search_graph ORDER BY from;
```
```text
Code: 306. DB::Exception: Received from localhost:9000. DB::Exception: Maximum recursive CTE evaluation depth (1000) exceeded, during evaluation of search_graph AS (SELECT from, to, label FROM graph AS g UNION ALL SELECT g.from, g.to, g.label FROM graph AS g, search_graph AS sg WHERE g.from = sg.to). Consider raising max_recursive_cte_evaluation_depth setting.: While executing RecursiveCTESource. (TOO_DEEP_RECURSION)
```
The standard method for handling cycles is to compute an array of the already visited nodes:
**Example:** Graph traversal with cycle detection
```sql
WITH RECURSIVE search_graph AS (
SELECT from, to, label, false AS is_cycle, [tuple(g.from, g.to)] AS path FROM graph g
