How to recursively compute ratio of remaining amounts based on rounded values from preceding rows?

问题

I need to split 1 amount into 2 fields. I know the total sums of the resulting fields = the ratio to split the first row, but i need to round the resulting sums and only then compute the ratio for next row (so the total sum of the rounded values will be correct).

How can i write this algorithm in Oracle 10g PL/SQL? I need to test some migrated data. Here is what i came up with (so far):

with temp as (
  select 1 id, 200 amount, 642 total_a from dual union all
  select 2, 200, 642 from dual union all
  select 3, 200, 642 from dual union all
  select 4, 200, 642 from dual union all
  select 5, 200, 642 from dual
)
select
  temp2.*,
  remaining_a / remaining_amount ratio,
  round(amount * remaining_a / remaining_amount, 0) rounded_a,
  round(amount - amount * remaining_a / remaining_amount, 0) rounded_b
from (
  select
    temp.id,  
    temp.amount,
    sum(amount) over (
      order by id
      range between current row and unbounded following
    ) remaining_amount,
    case when id=1 then total_a /* else ??? */ end remaining_a
  from temp
) temp2

Update: If you can't see the image above, expected rounded_A values are:

1 128
2 129
3 128
4 129
5 128

回答1:

Here is my suggestion. It is not getting exactly what you want . . . by my calculation the 129 doesn't come until the 3rd row.

The idea is to add more columns. For each row, calculate the estimated split. Then, keep track of the accumulative fraction. When the cum remainder exceeds an integer, then bump up the A amount by 1. Once you have the A amount, you can calculate the rest:

WITH temp AS (
     SELECT 1 id, 200 amount, 642 total_a FROM dual UNION ALL
     SELECT 2, 200, 642 FROM dual UNION ALL
     SELECT 3, 200, 642 FROM dual UNION ALL
     SELECT 4, 200, 642 FROM dual UNION ALL
     SELECT 5, 200, 642 FROM dual
)
select temp3.*,
       sum(estArem) over (order by id) as cumrem,
       trunc(estA) + (case when trunc(sum(estArem) over (order by id)) > trunc(- estArem + sum(estArem) over (order by id))
                          then 1 else 0 end)
from (SELECT temp2.*,
             trunc(Aratio*amount) as estA,
             Aratio*amount - trunc(ARatio*amount) as estArem
      FROM (SELECT temp.id, temp.amount,
                   sum(amount) over (ORDER BY id range BETWEEN CURRENT ROW AND unbounded following
                              ) remaining_amount,
                   sum(amount) over (partition by null) as total_amount,      
                   max(total_a) over (partition by null)as maxA, 
                   (max(total_a) over (partition by null) /
                    sum(amount) over (partition by null)
                   )  as ARatio
            FROM temp
           ) temp2
      ) temp3

This isn't exactly a partitioning problem. This is an integer approximation problem.

If you are rounding the values rather than truncating them, then you need a slight tweak to the logic.

       trunc(estA) + (case when trunc(sum(0.5+estArem) over (order by id)) > trunc(0.5 - estArem + sum(estArem) over (order by id))

This statement was originally just looking for the cumulative remainder passing over the integer threshhold. This should do rounding instead of truncation.

来源：https://stackoverflow.com/questions/11454201/how-to-recursively-compute-ratio-of-remaining-amounts-based-on-rounded-values-fr