How to create a cumulative count distinct with partition by in SQL?

Question

I have a table with user data and want to create a cumulative count distinct but this type of window function does not exist. This is my table

date       | user-id | purchase-id
2020-01-01 | 1       | 244         
2020-01-03 | 1       | 244         
2020-02-01 | 1       | 524         
2020-03-01 | 2       | 443         

Now, I want a cum count distinct for purchase id like this:

date       | user-id | purchase-id | cum_purchase
2020-01-01 | 1       | 244         | 1
2020-01-03 | 1       | 244         | 1
2020-02-01 | 1       | 524         | 2
2020-03-01 | 2       | 443         | 1

I tried

Select 
dt, 
user_id, 
count(distinct purchase_id) over (partition by user_id ORDER BY date ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) as cum_ct
from table

I get an error that I cannot use count distinct with an order by statement. What to do?

Answer 1

Something like this

Select 
  dt as [date], 
  user_id, 
  purchase_id
  SUM(CASE WHEN rn = 1 THEN 1 ELSE 0 END) over (partition by user_id ORDER BY dt ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) as cum_ct
from (
  SELECT 
    dt,
    user_id,
    purchase_id,
    ROW_NUMBER() OVER (PARTITION BY user_id, purchase_id ORDER BY dt) as RN
  FROM sometable  
) sub