SQL Server：显示一个基于其他行进行计算的新列

Question

I'm using SQL Server, I have a table which I have simplified as the follow:

item ----- order-----Active
-------------------------------    
a-------------1---------true
b-------------2---------false
c-------------3---------true
d-------------4---------true
e-------------5---------false
f-------------6---------true

I want to query that return the three columns and an extra column call new-order, which for each item it subtract one for every inactive(Active being false) items that has a order number lower than itself. So the above table will become

item ----- ordering-----Active----------NewOrder
-------------------------------------------------    
a-------------1---------true----------1
b-------------2---------false----------2
c-------------3---------true----------2
d-------------4---------true----------3
e-------------5---------false----------4
f-------------6---------true----------4

My attempt:

Select 
    g.item, g.ordering, g.active,  
    g.ordering - (Select Count(x.ordering)
                  from grocery As x
                  where x.ordering < g.ordering 
                    and x.active = false
                  group by x.ordering) As NewOrder
 From 
     grocery as g

which doesn't work because the subquery contain more than one row. But I honestly don't have any idea how to approach this. Is this even possible using just subquery?

Appreciate any advice or help

Edit:

In the database there are more than 6 rows, and not in the correct order. Basically an item's new order is its own ordering# subtract the number of inactive items whose ordering# is lower than the item's ordering#. Again inactive items is items whose active = false.

Answer 1

I think following query will give you the result you want, you can omit NULL values. You basically want the NEWORDER when active is true so you can omit NULL values for false

select
a.*,
b.NEWORDER
from
(
select
*
from
test1
)
as a
left join
(
    select [order] as NO,ROW_NUMBER() over(order by [order]) as NEWORDER from test1 where active='true'
)
as b
on a.[order]=b.no

OUTPUT

 item   order   active  NEWORDER
-------------------------------------
a       1       true    1
b       2       false   NULL
c       3       true    2
d       4       true    3
e       5       false   NULL
f       6       true    4

Answer 2

Here is one way

SELECT item,
       [order],
       active,
       NewOrder = Sum(t)OVER(ORDER BY [order]) 
FROM   (SELECT *,
               CASE WHEN Lag(Active)OVER(ORDER BY [order]) = 'false' THEN 0 ELSE 1 END AS t
        FROM   (VALUES ('a',1,'true' ),
                       ('b',2,'false' ),
                       ('c',3,'true' ),
                       ('d',4,'true' ),
                       ('e',5,'false' ),
                       ('f',6,'true' )) tc (item, [order], Active)) a 

Result :

+------+-------+--------+----------+
| item | order | active | NewOrder |
+------+-------+--------+----------+
| a    |     1 | true   |        1 |
| b    |     2 | false  |        2 |
| c    |     3 | true   |        2 |
| d    |     4 | true   |        3 |
| e    |     5 | false  |        4 |
| f    |     6 | true   |        4 |
+------+-------+--------+----------+