Subquery in select statement from a join table - postgresql

Question

I have an accounts table, units table and reports table. An account has many units (foreign key of units is account_id), and a unit has many reports (foreign key of reports is unit_id). I want to select account name, total number of units for that account, and the last report time:
SELECT accounts.name AS account_name,
COUNT(units.id) AS unit_count,
(SELECT reports.time FROM reports INNER JOIN units ON units.id = reports.unit_id ORDER BY time desc LIMIT 1) AS last_reported_time
FROM accounts
INNER JOIN units ON accounts.id = units.account_id
INNER JOIN reports ON units.id = reports.unit_id
GROUP BY account_name, last_reported_time
ORDER BY unit_count desc;
This query has been running forever, and I am not sure it's doing what I expect.
An account has many units and a unit has many reports. I want to display the time of the newest report from all the units associated for each given account. Is this query correct? If not, how can I accomplish my task (if possible without using a scripting language)?
The result of EXPLAIN:
Sort (cost=21466114.58..21466547.03 rows=172980 width=38)
Sort Key: (count(public.units.id))
InitPlan 1 (returns $0)
-> Limit (cost=0.00..12.02 rows=1 width=8)
-> Nested Loop (cost=0.00..928988485.04 rows=77309416 width=8)
-> Index Scan Backward using index_reports_on_time on reports (cost=0.00..296291138.34 rows=77309416 width=12)
-> Index Scan using units_pkey on units (cost=0.00..8.17 rows=1 width=4)
Index Cond: (public.units.id = public.reports.unit_id)
-> GroupAggregate (cost=20807359.99..21446321.09 rows=172980 width=38)
-> Sort (cost=20807359.99..20966559.70 rows=63679885 width=38)
Sort Key: accounts.name, public.units.last_reported_time
-> Hash Join (cost=975.50..3846816.82 rows=63679885 width=38)
Hash Cond: (public.reports.unit_id = public.units.id)
-> Seq Scan on reports (cost=0.00..2919132.16 rows=77309416 width=4)
-> Hash (cost=961.43..961.43 rows=1126 width=38)
-> Hash Join (cost=16.37..961.43 rows=1126 width=38)
Hash Cond: (public.units.account_id = accounts.id)
-> Seq Scan on units (cost=0.00..928.67 rows=1367 width=28)
-> Hash (cost=11.72..11.72 rows=372 width=18)
-> Seq Scan on accounts (cost=0.00..11.72 rows=372 width=18)

Answer 1

About 95% of the cost of the query is here:
-> Sort (cost=20807359.99..20966559.70 rows=63679885 width=38)
Sort Key: accounts.name, public.units.last_reported_time
-> Hash Join (cost=975.50..3846816.82 rows=63679885 width=38)
Hash Cond: (public.reports.unit_id = public.units.id)
-> Seq Scan on reports (cost=0.00..2919132.16 rows=77309416 width=4)
Do you have an index on reports.unit_id? If not, you should definitely add one.
Other than that, the output column unit_count appears to be giving the number of units per account, but calculating it after all the joins and then ordering by it is very wasteful. The sub-query in the select list is something of mystery to me; I presume you want the most recent reporting time for each unit but it will give you only the last time of reporting over all units combined. Try this instead:
SELECT a.account_name, u.unit_count, r.last_reported_time
FROM account a
JOIN (
SELECT account_id, COUNT(*) AS unit_count
FROM units
GROUP BY 1) u ON u.account_id = a.id
LEFT JOIN ( -- allow for units that have not yet submitted a report
SELECT u.account_id, max(r.time) AS last_reported_time
FROM reports r
JOIN units u ON u.id = r.unit_id
GROUP BY 1) r ON r.account_id = a.id
ORDER BY 2 DESC;