问题

注意：我指的是数学序列，而不是PostgreSQL的序列机制。

我有一张表，代表整数序列。定义是：

CREATE TABLE sequences
(
  id serial NOT NULL,
  title character varying(255) NOT NULL,
  date date NOT NULL,
  sequence integer[] NOT NULL,
  CONSTRAINT "PRIM_KEY_SEQUENCES" PRIMARY KEY (id)
);

我的目标是使用给定的子序列查找行。也就是说，其中sequence字段是包含给定子序列的序列的行（在我的情况下，该序列是有序的）。

例

假设该表包含以下数据：

+----+-------+------------+-------------------------------+
| id | title |    date    |           sequence            |
+----+-------+------------+-------------------------------+
|  1 | BG703 | 2004-12-24 | {1,3,17,25,377,424,242,1234}  |
|  2 | BG256 | 2005-05-11 | {5,7,12,742,225,547,2142,223} |
|  3 | BD404 | 2004-10-13 | {3,4,12,5698,526}             |
|  4 | BK956 | 2004-08-17 | {12,4,3,17,25,377,456,25}     |
+----+-------+------------+-------------------------------+

因此，如果给定的子序列是{12, 742, 225, 547}，我想找到第二行。

同样，如果给定的子序列是{3, 17, 25, 377}，我想找到第1行和第4行。

最后，如果给定的子序列为{12, 4, 3, 25, 377}，则不会返回任何行。

调查

首先，我不能完全确定用数组数据类型表示序列是明智的。尽管这似乎适合这种情况；我担心这会使处理更加复杂。也许最好使用与另一个表的关系模型来不同地表示序列。

同样，我考虑使用unnest数组函数扩展序列，然后添加搜索条件。但是，序列中的术语数是可变的，我看不出该怎么做。

我知道也可以使用intarray模块的subarray功能在子序列中剪切序列，但是我看不出它对我的搜索有何好处。

约束条件

即使目前仍在开发我的模型，该表也打算由许多序列组成，这些序列介于50,000至300,000行之间。所以我有很强的性能约束。

在我的示例中，我使用了相对较小的整数。实际上，这些整数有可能变得更大，直到溢出为止bigint。在这种情况下，我认为最好的方法是将数字存储为字符串（因为没有必要执行这些数学运算序列）。但是，选择此解决方案将导致无法使用上述intarray模块。

如果要为dnoeth的答案寻求显着的性能改进，请考虑使用本机C函数并创建适当的运算符。

这是int4数组的示例。（通用数组变体和相应的SQL脚本）。

Datum
_int_sequence_contained(PG_FUNCTION_ARGS)
{
    return DirectFunctionCall2(_int_contains_sequence,
                               PG_GETARG_DATUM(1),
                               PG_GETARG_DATUM(0));
}

Datum
_int_contains_sequence(PG_FUNCTION_ARGS)
{
    ArrayType  *a = PG_GETARG_ARRAYTYPE_P(0);
    ArrayType  *b = PG_GETARG_ARRAYTYPE_P(1);
    int         na, nb;
    int32      *pa, *pb;
    int         i, j;

    na = ArrayGetNItems(ARR_NDIM(a), ARR_DIMS(a));
    nb = ArrayGetNItems(ARR_NDIM(b), ARR_DIMS(b));
    pa = (int32 *) ARR_DATA_PTR(a);
    pb = (int32 *) ARR_DATA_PTR(b);

    /* The naive searching algorithm. Replace it with a better one if your arrays are quite large. */
    for (i = 0; i <= na - nb; ++i)
    {
        for (j = 0; j < nb; ++j)
            if (pa[i + j] != pb[j])
                break;

        if (j == nb)
            PG_RETURN_BOOL(true);
    }

    PG_RETURN_BOOL(false);
}

CREATE FUNCTION _int_contains_sequence(_int4, _int4)
RETURNS bool
AS 'MODULE_PATHNAME'
LANGUAGE C STRICT IMMUTABLE;

CREATE FUNCTION _int_sequence_contained(_int4, _int4)
RETURNS bool
AS 'MODULE_PATHNAME'
LANGUAGE C STRICT IMMUTABLE;

CREATE OPERATOR @@> (
  LEFTARG = _int4,
  RIGHTARG = _int4,
  PROCEDURE = _int_contains_sequence,
  COMMUTATOR = '<@@',
  RESTRICT = contsel,
  JOIN = contjoinsel
);

CREATE OPERATOR <@@ (
  LEFTARG = _int4,
  RIGHTARG = _int4,
  PROCEDURE = _int_sequence_contained,
  COMMUTATOR = '@@>',
  RESTRICT = contsel,
  JOIN = contjoinsel
);

现在，您可以像这样过滤行。

SELECT * FROM sequences WHERE sequence @@> '{12, 742, 225, 547}'

我进行了一个小实验，以找出此解决方案的速度。

CREATE TEMPORARY TABLE sequences AS
SELECT array_agg((random() * 10)::int4) AS sequence, g1 AS id
FROM generate_series(1, 100000) g1
  CROSS JOIN generate_series(1, 30) g2
GROUP BY g1;

EXPLAIN ANALYZE SELECT * FROM sequences
WHERE        translate(cast(sequence as text), '{}',',,')
 LIKE '%' || translate(cast('{1,2,3,4}'as text), '{}',',,') || '%'

"Seq Scan on sequences  (cost=0.00..7869.42 rows=28 width=36) (actual time=2.487..334.318 rows=251 loops=1)"
"  Filter: (translate((sequence)::text, '{}'::text, ',,'::text) ~~ '%,1,2,3,4,%'::text)"
"  Rows Removed by Filter: 99749"
"Planning time: 0.104 ms"
"Execution time: 334.365 ms"

EXPLAIN ANALYZE SELECT * FROM sequences WHERE sequence @@> '{1,2,3,4}'

"Seq Scan on sequences  (cost=0.00..5752.01 rows=282 width=36) (actual time=0.178..20.792 rows=251 loops=1)"
"  Filter: (sequence @@> '{1,2,3,4}'::integer[])"
"  Rows Removed by Filter: 99749"
"Planning time: 0.091 ms"
"Execution time: 20.859 ms"

因此，它快了大约16倍。如果这还不够，您可以添加对GIN或GiST索引的支持，但这将是更加困难的任务。

将数组转换为字符串并将大括号替换为逗号后，可以轻松找到子序列：

translate(cast(sequence as varchar(10000)), '{}',',,')

{1,3,17,25,377,424,242,1234} -> ',1,3,17,25,377,424,242,1234,'

对要搜索的数组执行相同的操作，并添加前导和尾随%：

'%' || translate(cast(searchedarray as varchar(10000)), '{}',',,') || '%'

{3, 17, 25, 377} -> '%,3,17,25,377,%'

现在，您可以使用进行比较LIKE：

WHERE        translate(cast(sequence      as varchar(10000)), '{}',',,')
 LIKE '%' || translate(cast(searchedarray as varchar(10000)), '{}',',,') || '%'

编辑：

小提琴又在工作。

如果将数组标准化为每个值一行，则可以应用基于集合的逻辑：

CREATE TABLE sequences
( id int NOT NULL,
  n int not null,
  val numeric not null
);

insert into sequences values(  1, 1,1     );
insert into sequences values(  1, 2,3     );
insert into sequences values(  1, 3,17    );
insert into sequences values(  1, 4,25    );
insert into sequences values(  1, 5,377   );
insert into sequences values(  1, 6,424   );
insert into sequences values(  1, 7,242   );
insert into sequences values(  1, 8,1234  );
insert into sequences values(  2, 1,5     );
insert into sequences values(  2, 2,7     );
insert into sequences values(  2, 3,12    );
insert into sequences values(  2, 4,742   );
insert into sequences values(  2, 5,225   );
insert into sequences values(  2, 6,547   );
insert into sequences values(  2, 7,2142  );
insert into sequences values(  2, 8,223   );
insert into sequences values(  3, 1,3     );
insert into sequences values(  3, 2,4     );
insert into sequences values(  3, 3,12    );
insert into sequences values(  3, 4,5698  );
insert into sequences values(  3, 5,526   );          
insert into sequences values(  4, 1,12    );
insert into sequences values(  4, 2,4     );
insert into sequences values(  4, 3,3     );
insert into sequences values(  4, 4,17    );
insert into sequences values(  4, 5,25    );
insert into sequences values(  4, 6,377   );
insert into sequences values(  4, 7,456   );
insert into sequences values(  4, 8,25    );
insert into sequences values(  5, 1,12    );
insert into sequences values(  5, 2,4     );
insert into sequences values(  5, 3,3     );
insert into sequences values(  5, 4,17    );
insert into sequences values(  5, 5,17    );
insert into sequences values(  5, 6,25    );
insert into sequences values(  5, 7,377   );
insert into sequences values(  5, 8,456   );
insert into sequences values(  5, 9,25    );

n必须是连续的，没有重复，没有空隙。现在加入共同值并利用序列是顺序的事实:-)

with searched (n,val) as (
  VALUES
   ( 1,3  ),
   ( 2,17 ),
   ( 3,25 ),
   ( 4,377)
)
select seq.id, 
   -- this will return the same result if the values from both tables are in the same order
   -- it's a meaningless dummy, but the same meaningless value for sequential rows 
   seq.n - s.n as dummy,
   seq.val,
   seq.n,
   s.n 
from sequences as seq join searched as s
on seq.val = s.val
order by seq.id, dummy, seq.n;

最后计算具有相同虚拟对象的行数，并检查其是否正确：

with searched (n,val) as (
  VALUES
   ( 1,3  ),
   ( 2,17 ),
   ( 3,25 ),
   ( 4,377)
)
select distinct seq.id
from sequences as seq join searched as s
on seq.val = s.val
group by 
   seq.id,
   seq.n - s.n
having count(*) = (select count(*) from searched)
;

尝试对sequence（val，id，n）进行索引。