Finding missing data in a sequence in MySQL - mysql

Question

Is there an efficient way to find missing data not just in one sequence, but many sequences?
This is probably unavoidably O(N**2), so efficient here is defined as relatively few queries using MySQL
Let's say I have a table of temporary employees and their starting and ending months.
employees | start_month | end_month
------------------------------------
Jane 2017-05 2017-07
Bob 2017-10 2017-12
And there is a related table of monthly payments to those employees
employee | paid_month
---------------------
Jane 2017-05
Jane 2017-07
Bob 2017-11
Bob 2017-12
Now, it's clear that we're missing a month for Jane (2017-06) and one for Bob too (2017-10).
Is there a way to somehow find the gaps in their payment record, without lots of trips back and forth?
In the case where there's just one sequence to check, some people generate a temporary table of valid values, and then LEFT JOIN to find the gaps. But here we have different sequences for each employee.
One possibility is that we could do an aggregate query to find the COUNT() of paid_months for each employee, and then check it versus the expected delta of months. Unfortunately the data here is a bit dirty so we actually have payment dates that could be before or after that employee start or end date. But we're verifying that the official sequence definitely has payments.

Answer 1

Form a Cartesian product of employees and months, then left join the actual data to that, then the missing data is revealed when there is no matched payment to the Cartesian product.
You need a list of every months. This might come from a "calendar table" you already have, OR, it MIGHT be possible using a subquery if every month is represented in the source data)
e.g.
select
m.paid_month, e.employee
from (select distinct paid_month from payments) m
cross join (select employee from employees) e
left join payments p on m.paid_month = p.paid_month and e.employee = p.employee
where p.employee is null
The subquery m can be substituted by the calendar table or some other technique for generating a series of months. e.g.
select
DATE_FORMAT(m1, '%Y-%m')
from (
select
'2017-01-01'+ INTERVAL m MONTH as m1
from (
select #rownum:=#rownum+1 as m
from (select 1 union select 2 union select 3 union select 4) t1
cross join (select 1 union select 2 union select 3 union select 4) t2
## cross join (select 1 union select 2 union select 3 union select 4) t3
## cross join (select 1 union select 2 union select 3 union select 4) t4
cross join(select #rownum:=-1) t0
) d1
) d2
where m1 < '2018-01-01'
order by m1
The subquery e could contain other logic (e.g. to determine which employees are still currently employed, or that are "temporary employees")

Answer 2

First we need to get all the months between start date and end_date in a temporary table then need do a left outer join with the payments table on paid month filtering all non matching months ( payment employee name is null )
select e.employee, e.yearmonth as missing_paid_month from (
with t as (
select e.employee, to_date(e.start_date, 'YYYY-MM') as start_date, to_date(e.end_date, 'YYYY-MM') as end_date from employees e
)
select distinct t.employee,
to_char(add_months(trunc(start_date,'MM'),level - 1),'YYYY-MM') yearmonth
from t
connect by trunc(end_date,'mm') >= add_months(trunc(start_date,'mm'),level - 1)
order by t.employee, yearmonth
) e
left outer join payments p
on p.paid_month = e.yearmonth
where p.employee is null
output
EMPLOYEE MISSING_PAID_MONTH
Bob 2017-10
Jane 2017-06
SQL Fiddle http://sqlfiddle.com/#!4/2b2857/35