## Telling if entries in table are increasing

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I've a table temp(person text, year int,count int). It stores

```person, year, count
("a",2009,1),
("a",2010,2),
("a",2011,3),
("a",2012,4),
("b",2010,1),
("b",2011,2),
("b",2012,3),
("c",2011,1),
("d",2009,4),
("d",2010,4),
("d",2011,4),
("d",2012,4),
("e",2009,1),
("e",2010,2),
("e",2012,4)
```

I'm supposed to tell that for which person(s) count is strictly increasing from 2009 to 2012 , count is always a positive integer. For the given table, the output will be "a" and "b". Note that "b" also has strictly increasing since it's count was 0 in 2009 (I know it's a little wierd that above it's written that count has to be positive and now I'm saying that it is 0 for 2009, but it's just given like that in the question).

Expected Output:- In the given table, a has strictly increasing from 2009-2012. That's cool. For b, it is missing 2009, but we take that as zero (to be precise, names are the names of authors and count is the number of papers published by them- we have to find those authors who publish more papers in 2010 than 2009, in 2011 than 2010 and 2012 than 2011, so taking count=0 does makes sense). So for b, 2009 is 0. And so, the sequence is 0, 2, 3, 4 - strictly increasing. c shouldn't be printed since count in both 2009 and 10 is zero. Similar, d shouldn't be printed since its count is constant. e shouldn't be printed because after taking 0, its sequence becomes 1, 2, 0, 4. So, a and b should be the only output.

My try:- I tried using lag function, but there's problem in that since it won't be able to distinguish if 2009 is present or not. I can use count in that too, but then I won't be able to differentiate between which one is absent. What would be the most optimal solution for this? Thanks!

Edit:

Based on the new data & more detailed logic this should work (based on Tim's query):

```WITH cte AS
(
SELECT person, count_, year_
,Lag(Count_, 1, 0) Over (PARTITION BY person ORDER BY YEAR_) AS prev_count
,Lag(year_, 1,year_-1) Over (PARTITION BY person ORDER BY YEAR_) AS prev_year
FROM vt
)
SELECT person
FROM cte
GROUP BY person
HAVING Min(year) <= 2010                  -- only one of the first two years might be missing
AND Max(CASE WHEN prev_count < count   -- count increased
AND prev_year  = YEAR -1 -- no missing year
THEN 0
ELSE 1
END) = 0
```

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Use `generate_series()` left-joined with the table to get data with complete `counts`:

```select year, person, coalesce(count, 0) as count
from generate_series(2009, 2012) as year
cross join (
select distinct person
from temp
) p
left join temp using(year, person)
order by 2, 1

year | person | count
------+--------+-------
2009 | a      |     1
2010 | a      |     2
2011 | a      |     3
2012 | a      |     4
2009 | b      |     0
2010 | b      |     1
2011 | b      |     2
2012 | b      |     3
2009 | c      |     0
2010 | c      |     0
2011 | c      |     1
2012 | c      |     0
2009 | d      |     4
2010 | d      |     4
2011 | d      |     4
2012 | d      |     4
2009 | e      |     1
2010 | e      |     2
2011 | e      |     0
2012 | e      |     4
(20 rows)
```

Use `array_agg()` on the result to find `persons` which fulfill the conditions:

```select person, array_agg(count order by year) as counts
from (
select person, year, coalesce(count, 0) as count
from generate_series(2009, 2012) as year
cross join (
select distinct person
from temp
) p
left join temp using(year, person)
) s
group by person
having  array_agg(distinct count order by count) = array_agg(count order by year)

person |  counts
--------+-----------
a      | {1,2,3,4}
b      | {0,1,2,3}
(2 rows)
```

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I like klin's solution but you don't need `generate_series()` and `cross join`:

```select person
from temp t
where year between 2009 and 2012
group by person
having (count(*) = 4 and count(distinct count) = 4 or
count(*) = 3 and min(year) = 2010 and count(distinct count) = 3
) and
array_agg(count order by count) = array_agg(count order by year) ;
```

Note that this version also handled strictly increasing meaning that equal counts are not included as valid.

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