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Perché Oracle ignora l'indice con ORDER BY?

molto probabilmente la tua colonna FIRST_NAME è nullable.

SQL> create table customer (first_name varchar2(20), last_name varchar2(20));

Table created.

SQL> insert into customer select dbms_random.string('U', 20), dbms_random.string('U', 20) from dual connect by level <= 100000;

100000 rows created.

SQL> create index c on customer(first_name);

Index created.

SQL> explain plan for select * from (
  2    select /*+ FIRST_ROWS(20) */ FIRST_NAME, ROW_NUMBER() over (order by FIRST_NAME) RN
  3    from CUSTOMER C
  4  )
  5  where RN between 1 and 20
  6  order by RN;

Explained.

SQL> @explain ""

Plan hash value: 1474094583

----------------------------------------------------------------------------------------------
| Id  | Operation                 | Name     | Rows  | Bytes |TempSpc| Cost (%CPU)| Time     |
----------------------------------------------------------------------------------------------
|   0 | SELECT STATEMENT          |          |   117K|  2856K|       |  1592   (1)| 00:00:20 |
|   1 |  SORT ORDER BY            |          |   117K|  2856K|  4152K|  1592   (1)| 00:00:20 |
|*  2 |   VIEW                    |          |   117K|  2856K|       |   744   (2)| 00:00:09 |
|*  3 |    WINDOW SORT PUSHED RANK|          |   117K|  1371K|  2304K|   744   (2)| 00:00:09 |
|   4 |     TABLE ACCESS FULL     | CUSTOMER |   117K|  1371K|       |   205   (1)| 00:00:03 |
----------------------------------------------------------------------------------------------

Predicate Information (identified by operation id):
---------------------------------------------------

   2 - filter("RN">=1 AND "RN"<=20)
   3 - filter(ROW_NUMBER() OVER ( ORDER BY "FIRST_NAME")<=20)

Note
-----
   - dynamic sampling used for this statement (level=2)

21 rows selected.

SQL> alter table customer modify first_name not null;

Table altered.

SQL> explain plan for select * from (
  2    select /*+ FIRST_ROWS(20) */ FIRST_NAME, ROW_NUMBER() over (order by FIRST_NAME) RN
  3    from CUSTOMER C
  4  )
  5  where RN between 1 and 20
  6  order by RN;

Explained.

SQL> @explain ""

Plan hash value: 1725028138

----------------------------------------------------------------------------------------
| Id  | Operation               | Name | Rows  | Bytes |TempSpc| Cost (%CPU)| Time     |
----------------------------------------------------------------------------------------
|   0 | SELECT STATEMENT        |      |   117K|  2856K|       |   850   (1)| 00:00:11 |
|   1 |  SORT ORDER BY          |      |   117K|  2856K|  4152K|   850   (1)| 00:00:11 |
|*  2 |   VIEW                  |      |   117K|  2856K|       |     2   (0)| 00:00:01 |
|*  3 |    WINDOW NOSORT STOPKEY|      |   117K|  1371K|       |     2   (0)| 00:00:01 |
|   4 |     INDEX FULL SCAN     | C    |   117K|  1371K|       |     2   (0)| 00:00:01 |
----------------------------------------------------------------------------------------

Predicate Information (identified by operation id):
---------------------------------------------------

   2 - filter("RN">=1 AND "RN"<=20)
   3 - filter(ROW_NUMBER() OVER ( ORDER BY "FIRST_NAME")<=20)

Note
-----
   - dynamic sampling used for this statement (level=2)

21 rows selected.

SQL>

aggiungi un NOT NULL per risolverlo.

SQL> explain plan for select * from (
  2    select /*+ FIRST_ROWS(20) */ FIRST_NAME, ROW_NUMBER() over (order by FIRST_NAME) RN
  3    from CUSTOMER C
  4    where first_name is not null
  5  )
  6  where RN between 1 and 20
  7  order by RN;

Explained.

SQL> @explain ""

Plan hash value: 1725028138

----------------------------------------------------------------------------------------
| Id  | Operation               | Name | Rows  | Bytes |TempSpc| Cost (%CPU)| Time     |
----------------------------------------------------------------------------------------
|   0 | SELECT STATEMENT        |      |   117K|  2856K|       |   850   (1)| 00:00:11 |
|   1 |  SORT ORDER BY          |      |   117K|  2856K|  4152K|   850   (1)| 00:00:11 |
|*  2 |   VIEW                  |      |   117K|  2856K|       |     2   (0)| 00:00:01 |
|*  3 |    WINDOW NOSORT STOPKEY|      |   117K|  1371K|       |     2   (0)| 00:00:01 |
|*  4 |     INDEX FULL SCAN     | C    |   117K|  1371K|       |     2   (0)| 00:00:01 |
----------------------------------------------------------------------------------------

Predicate Information (identified by operation id):
---------------------------------------------------

   2 - filter("RN">=1 AND "RN"<=20)
   3 - filter(ROW_NUMBER() OVER ( ORDER BY "FIRST_NAME")<=20)
   4 - filter("FIRST_NAME" IS NOT NULL)

Note
-----
   - dynamic sampling used for this statement (level=2)

22 rows selected.

SQL>