Hashrocket.com / blog

Large blackboard

Understanding Common Table Expressions with FizzBuzz

posted on and written by in

Image 100x100 josh branchaud

For a long time, I avoided trying to understand what common table expressions were or how they worked. The name alone was intimidating. I figured I could just get by with the database features supported by my ORM. Better that way; I won't have to get my hands dirty with all that raw SQL.

It turns out that I was missing out on some solid database features by avoiding all that raw SQL goodness. Common table expressions (CTEs) are a potent feature of PostgreSQL and most other modern relational databases. By avoiding features like CTEs, I was treating Postgres like a dumb data store instead of the powerful computation engine that it is. CTEs are one Postgres feature that epitomize this power.

The PostgreSQL documentation gives the following description of common table expressions:

[CTEs] can be thought of as defining temporary tables that exist just for one query.

That sounds nice, but it undersells what we can do with CTEs once we understand how they work. Let's interact with some concrete examples. You'll want to pop open a psql session for this. Use \e in psql to edit the SQL in your default editor.

For a first example, how about something straightforward like a CTE that counts to 100:

with numbers as (
  select generate_series(1,100)
)
select * from numbers;

This results in:

 generate_series
-----------------
               1
               2
               3
             ...

all the way up to 100.

Sure, that example isn't all that exciting. We could easily achieve the same with a simpler looking query that involves a sub-select. Nevertheless, we can see how the temporary table constructed by the CTE is visually set apart from the rest of the query and its namespace (numbers) made explicit. This temporary table numbers now has the set of integers from 1 to 100 from which we make our selection -- all of them.

We depart from what can be achieved with mere sub-selects when we employ the recursive option. By making a CTE recursive, it essentially becomes a dynamically-built temporary table. With a recursive CTE, we can achieve the same as above, but doing so on the fly and without the generate_series function:

with recursive numbers (x) as (
  select 1
  union
  select x + 1
  from numbers
  where x < 100
)
select * from numbers;

That is a funky looking query, so let's break it down.

I've added in the recursive keyword to declare that this will be a recursive CTE. I've also named the single column of the CTE as x. If there were more columns, I could include them with separating commas. This makes it so that I can reference the individual columns within the CTE.

The end of the query looks the same, so it's just the internals of the CTE that we have left to dissect. So let's take a look at that starting from the top.

The select 1 means we start with a single column, single row table that contains 1. This provides a base on which the recursive part of the CTE can build.

This base table is then unioned with a dynamically-built table where each row is recursively computed as 1 added to the row before it (select x + 1). This process happens until some terminating condition is met. In this case, that terminating condition is when the value of the latest x reaches 100 (where x < 100).

The end result is a temporary table, numbers, with the values from 1 to 100. We can select from this dynamically generated temporary table like we do any other table. If we only want the rows where x is greater than 50, we just query this table like we do any other table -- select * from numbers where x > 50. In our case, we want to grab everything -- all 100 rows -- which we can do with select * from numbers. We wanted a selection that included the values from 1 to 100 and now we've got it.

Let that soak in for a moment. We just dynamically built a temporary table of values where each value was an individual computation based on previously computed values. And we can do a lot more than just add 1 to x. We can fill the CTE with all kinds of formulas and logic in order to build a temporary table full of interesting and useful data. That's powerful. This means that with a little SQL we can do a lot of fancy stuff right in the database. Better yet, we can avoid expensive and complicated trips between the database and some script or process that we would otherwise rely on to build that intermediate set of data.

Let's see what it means to add some logic and formulas to our CTE by taking our existing query a step further. How about solving the FizzBuzz programming challenge? We've already got the set of numbers from 1 to 100; they just need to be transformed into Fizz, Buzz, and FizzBuzz.

So let's start with Fizz. The rule is that any value that is evenly divisible by 3 should be represented by Fizz (we'll ignore the FizzBuzz rule for the moment). We can know that the given value is divisible by 3 if we take the modulo of 3 and the result is 0. A list of values and whether or not they are divisible by 3 is a good starting point.

with recursive fizzbuzz (num,val) as (
  select 0, false
  union
  select (num + 1),
    (num + 1) % 3 = 0
  from fizzbuzz
  where num < 100
)
select num, val from fizzbuzz where num > 0;

The result with just the first 10 rows:

 num | val
-----+-----
   1 | f
   2 | f
   3 | t
   4 | f
   5 | f
   6 | t
   7 | f
   8 | f
   9 | t
  10 | f
...

Great. Now we want to display Fizz whenever there is a true, otherwise leave the value as is. We can use a case (switch) statement to populate the second row accordingly.

with recursive fizzbuzz (num,val) as (
  select 0, '0'
  union
  select (num + 1),
    case
      when (num + 1) % 3 = 0 then 'Fizz'
      else (num + 1)::text
    end
  from fizzbuzz
  where num < 100
)
select num, val from fizzbuzz where num > 0;

The result with just the first 10 rows:

 num | val
-----+------
   1 | 1
   2 | 2
   3 | Fizz
   4 | 4
   5 | 5
   6 | Fizz
   7 | 7
   8 | 8
   9 | Fizz
  10 | 10
...

This is really close to what we want. By incorprating the rules for Buzz and FizzBuzz, we should have what we are looking for. That can be achieved by extending the case statement a bit further for values of 5 and 15.

with recursive fizzbuzz (num,val) as (
  select 0, '0'
  union
  select (num + 1),
    case
      when (num + 1) % 15 = 0 then 'FizzBuzz'
      when (num + 1) % 5  = 0 then 'Buzz'
      when (num + 1) % 3  = 0 then 'Fizz'
      else (num + 1)::text
    end
  from fizzbuzz
  where num < 100
)
select val from fizzbuzz where num > 0;

The result out to 20 rows:

 num |   val
-----+----------
   1 | 1
   2 | 2
   3 | Fizz
   4 | 4
   5 | Buzz
   6 | Fizz
   7 | 7
   8 | 8
   9 | Fizz
  10 | Buzz
  11 | 11
  12 | Fizz
  13 | 13
  14 | 14
  15 | FizzBuzz
  16 | 16
  17 | 17
  18 | Fizz
  19 | 19
  20 | Buzz
...

And there you have it, FizzBuzz solved with PostgreSQL. Try that out at your next programming job interview.

CTEs are great for a lot more than solving FizzBuzz. Non-recursive CTEs alone can be used to simplify and dry up complicated queries that would otherwise involve many nested sub-selects1. Recursive CTEs allow you to do things in-database that simply aren't possible with other SQL constructs (e.g. sub-selects). The possibilities include but are not limited to generating reports from data aggregated from many tables and transforming data when migrating from one schema to another. This makes them a valuable addition to your SQL repertoire. CTEs are even more powerful than I've illustrated. To see some other cool capabilities of CTEs, check out this post on Writeable Common Table Expressions.


  1. It is my understanding that the Postgres query planning engine optimizes sub-selects differently than with queries, which may have performance implications. That is, sub-selects may be more aggressively optimized. That being said, CTEs generally reduce round-trips to the database and simplify SQL code, so unless you have hard performance numbers saying otherwise, CTEs are likely still a win. 

Posted in PostgreSQL and tagged with PostgreSQL