How to create a flag that increments by 1 based on conditions - postgresql

Question

How can I create a flag by looking at values of consecutive variables?
For example, in the table(image) below,
For row#1, flag takes the value 1;
For row#2 onwards it checks:
If variable1 =lag(variable2)
and variable2=lag(variable1) then flag = lag(flag) else flag increments by 1.
In this case, the condition doesn’t match therefore the flag takes value 2.
For row#3:
Since it matches the above condition flag is same as 2
For row#4: Even though it matches the above condition, the flag changes to 3 as the previous 2 rows(row#2 &row#3) have already been matched
And so on..
The final flag will look like:

Answer 1

Bear in mind that you better have your input data sorted to implement a "moving flag" with 2-row-based aggregation. For this answer's sake I've added a row_number() function to generate the order in which your sample data is given.
Test data
create table flagtest( var1 text, var2 text);
insert into flagtest(var1,var2) values
('T','Z'),('B','A'),('A','B'),('B','A'),('A','B'),('A','B'),
('A','B'),('B','A'),('C','D'),('E','F'),('F','E'),('M','N');
Code
-- fourth part
select var1, var2, sum(change_flag_2_based) over (order by ordcol) as flag
from( -- third part
select *,
case when
lag(change_flag) over (order by ordcol) = 0
and lag(change_flag, 2) over (order by ordcol) = 1
then 1 else change_flag
end as change_flag_2_based
from ( -- second part
select
var1, var2, ordcol,
case when
var1 = lag(var2) over (order by ordcol) and
var2 = lag(var1) over (order by ordcol)
then 0 else 1
end as change_flag
from ( -- first part
select var1, var2, row_number() over () as ordcol
from flagtest
) ordered_data
) prep_aggr_all
) prep_aggr_two_rows_based;
How does it work?
First part is all about providing a column to order the input data later in window functions. This will be any other column that you currently have in your table. In the example it introduces row_number() window function to generate such numerical order.
Second part is where we are marking rows, with assumed strategy of cross-equals between two variables comparing current with previous row, with indicators 1 and 0 whether the flag should change in this particular row. This is not a 2-based pair aggregation (yet).
Third part introduces comparing current row change flag indicator with indicators from two previous rows and if 1 row behind doesn't change the flag and 2 rows behind does change it it means that we should mark current row as flag-changing (2-row-based flag).
Fourth part is just for moving sum which makes final flags by summing those groups.
Output
var1 | var2 | flag
------+------+------
T | Z | 1
B | A | 2
A | B | 2
B | A | 3
A | B | 3
A | B | 4
A | B | 5
B | A | 5
C | D | 6
E | F | 7
F | E | 7
M | N | 8