Max Recursion Exhausted before Statement Completion - sql-server

Question

I know this has been asked and answered a few times here, but I can't seem to find the answer to my specific problem. Here's the recursive query:
CTE as (
SELECT
ZipCode
,Age
,[Population]
,Deaths
,DeathRate
,Death_Proportion
,DeathProbablity
,SurvivalProbablity
,PersonsAlive
FROM ProbabilityTable
WHERE Age = 0
UNION ALL
SELECT
p.ZipCode
,p.Age
,p.[Population]
,p.Deaths
,p.DeathRate
,p.Death_Proportion
,p.DeathProbablity
,p.SurvivalProbablity
,LAG(c.PersonsAlive,1) OVER(PARTITION BY p.ZipCode ORDER BY p.Age) * p.SurvivalProbablity
FROM ProbabilityTable p
INNER JOIN CTE c
ON p.ZipCode = c.ZipCode
and p.Age = c.Age
WHERE p.Age < 86
)
In the ProbabilityTable PersonsAlive is set to 100,000 when Age = 0. What I'm looking to do with the recursive CTE is multiple the previous value of PersonsAlive by the current SurvivalProbability to calculate the PersonsAlive of that Age. Age goes up to 85 so that's why I have my termination clause set at 86.
I've tried tweaking the recursive part of the query a number of times (and also setting PersonsAlive to 100,000 in the anchor part) but I can't figure it out. This is my first attempt at a recursive query and even with some course work it's not clicking for me.
EDIT
Here is the updated code that actually runs:
CTE as (
SELECT
ZipCode
,Age
,[Population]
,Deaths
,DeathRate
,Death_Proportion
,DeathProbablity
,SurvivalProbablity
,PersonsAlive
FROM ProbabilityTable
WHERE Age = 0
UNION ALL
SELECT
p.ZipCode
,p.Age
,p.[Population]
,p.Deaths
,p.DeathRate
,p.Death_Proportion
,p.DeathProbablity
,p.SurvivalProbablity
,LAG(c.PersonsAlive,1) OVER(PARTITION BY p.ZipCode ORDER BY p.Age) * p.SurvivalProbablity
FROM ProbabilityTable p
INNER JOIN CTE c
ON p.ZipCode = c.ZipCode
and p.Age = c.Age + 1
WHERE p.Age < 6
)
And here is the results it returns:
What I want the results to be for PersonsAlive is as follows:
So with each iteration of the CTE, it needs to reference the previous row of PersonsAlive and the current row of SurvivalProbability to calculate PersonsAlive

Answer 1

It's hard to test this without your raw data but I think your issue is you're lagging over the previous row, causing your frame of reference to be 2 rows back.
When you're using a recursive CTE, you already have access to the previous row, via CTE c. When you do LAG(c.PersonsAlive,1) you're actually telling it to look at PersonsAlive from 2 rows back from the current row (lagging 1 row back from the previous row).
Since on the first recursive pass, there is only 1 row back, the LAG() function will return NULL by default since there is no 2 rows back at that point. This is why every row in your results has NULL for the PersonsAlive column, except for the first row (anchor row from the first half of your UNION ALL clause). So if you remove the LAG() function from it and instead just do c.PersonsAlive * p.SurvivalProbablity, you should get all of the expected PersonsAlive values.
That being said, a recursive CTE seems like overkill here and you probably can just use the LAG() window function in a static call on your ProbabilityTable like so:
SELECT
ZipCode,
Age,
[Population],
Deaths,
DeathRate,
Death_Proportion,
DeathProbablity,
SurvivalProbablity,
ISNULL(LAG(PersonsAlive,1) OVER (PARTITION BY ZipCode ORDER BY Age), PersonsAlive) AS PersonsAlive
FROM ProbabilityTable
As I mentioned, I can't really test this, so please let me know if you run into any issues, and I'll help you accordingly.
Recursive CTEs are good for tree-like problems, e.g. when you need to compare multiple child rows to their parent, or interact with multiple levels of the tree simultaneously. Window functions like LAG() allow you to interact with any single row at a time relative to the current row. Your problem seems to be the latter kind.