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Atualizar o total com base na linha anterior de saldo


Aqui vem uma solução com a ajuda de uma variável de usuário.

O resultado é verificado com a demonstração completa anexada.

SQL:
-- data preparation for demo
create table tbl(Name char(100), id int, Col1 int, Col2 int, Col3 char(20), Col4 char(20), Total int, Balance int);
insert into tbl values
('Row1',1,6,1,'A','Z',0,0),
('Row2',2,2,3,'B','Z',0,0),
('Row3',3,9,5,'B','Y',0,0),
('Row4',4,12,8,'C','Y',0,0);
SELECT * FROM tbl;

-- Query needed
SET @bal = 0;
UPDATE tbl
SET
    Total = CASE    WHEN Col3 = 'A' and Col4 <> 'Z'
                        THEN Col1+Col2
                    WHEN Col3 = 'B' and Col4 <> 'Z'
                        THEN Col1-Col2
                    WHEN Col3 = 'C' and Col4 <> 'Z'
                        THEN Col1*Col2
                    ELSE 0 END,
    Balance = (@bal:[email protected] + Total);
SELECT * FROM tbl;

Saída (como esperado):
mysql> SELECT * FROM tbl;
+------+------+------+------+------+------+-------+---------+
| Name | id   | Col1 | Col2 | Col3 | Col4 | Total | Balance |
+------+------+------+------+------+------+-------+---------+
| Row1 |    1 |    6 |    1 | A    | Z    |     0 |       0 |
| Row2 |    2 |    2 |    3 | B    | Z    |     0 |       0 |
| Row3 |    3 |    9 |    5 | B    | Y    |     0 |       0 |
| Row4 |    4 |   12 |    8 | C    | Y    |     0 |       0 |
+------+------+------+------+------+------+-------+---------+
4 rows in set (0.00 sec)

mysql> -- Query needed
mysql> SET @bal = 0;
Query OK, 0 rows affected (0.00 sec)

mysql> UPDATE tbl
    -> SET
    ->     Total = CASE    WHEN Col3 = 'A' and Col4 <> 'Z'
    ->                         THEN Col1+Col2
    ->                     WHEN Col3 = 'B' and Col4 <> 'Z'
    ->                         THEN Col1-Col2
    ->                     WHEN Col3 = 'C' and Col4 <> 'Z'
    ->                         THEN Col1*Col2
    ->                     ELSE 0 END,
    ->     Balance = (@bal:[email protected] + Total);
Query OK, 2 rows affected (0.00 sec)
Rows matched: 4  Changed: 2  Warnings: 0

mysql>
mysql> SELECT * FROM tbl;
+------+------+------+------+------+------+-------+---------+
| Name | id   | Col1 | Col2 | Col3 | Col4 | Total | Balance |
+------+------+------+------+------+------+-------+---------+
| Row1 |    1 |    6 |    1 | A    | Z    |     0 |       0 |
| Row2 |    2 |    2 |    3 | B    | Z    |     0 |       0 |
| Row3 |    3 |    9 |    5 | B    | Y    |     4 |       4 |
| Row4 |    4 |   12 |    8 | C    | Y    |    96 |     100 |
+------+------+------+------+------+------+-------+---------+
4 rows in set (0.00 sec)