A Curious Case of Optimisation

Jan 9, 2020 by Abhishek Kumar

Consider the following problem often encountered in web applications:

There are two models Student and User. The students table has an attribute user_id which references the id on the users table. You want to print out the username of students in section A.

You implement the following code, which translates to the pseudocode - Fetch all students in section A from the database. For each student, fetch the user from the database.

students = Student.where(section: 'A')

students.each do |student|
  puts User.find(student.user_id).username

Someone reviews your code and correctly points out that you are running N + 1 queries which slows the page. You fix it by prefetching all users and finding the right user in memory.

students = Student.where(section: 'A')

user_ids = students.pluck(:user_id)

users = User.where(id: user_ids)

students.each do |student|
  user = users.find { |user| user.id == student.user_id }
  puts user.username

You run two queries now, and page loads faster on the development database. Your code is merged, but the production feels more sluggish.

That doesn’t make sense!



Here are benchmarks for the above and two other implementations - Hash and ORM API (discussed below) on a local database:

N (N + 1) Query Prefetch Hash ORM API
10 0.0163 0.0055 0.0053 0.0048
50 0.0557 0.0108 0.0082 0.0089
100 0.1005 0.0197 0.0120 0.0140
500 0.4517 0.1505 0.0428 0.0564
1,000 0.9273 0.4634 0.0767 0.0927
5,000 4.9729 10.572 0.3522 0.3989
10,000 9.3168 60.571 0.6063 0.8187

Observations from the above table:

  1. Hash and ORM API approach scale well - taking less than a second for 10,000 records.
  2. Prefetch performs better for small values of N (< 2000) which is typical for development
  3. (N + 1) query functions better for larger N, present in the production database.

The benchmark depends on many factors - notably the round trip time from the database. Local databases respond in ~2 ms, whereas a remote database responds in ~150ms, which completely changes the benchmark results.


Here’s understand the costs involved in both methods:

Costs of (N + 1) query   = (Fetch students) + N * (Fetch user)
                         = O(N) queries
Costs of prefetch method = (Fetch students) + (Pluck user_ids) 
                           + (Fetch users) +  ((N * (N - 1)/2) * iterations
                         = O(N^2) iterations

Cost of iterations is much smaller than the cost of queries (10^-4ms « 0.5ms).

For small N, the cost of N queries dominates over the N^2 iterations. But for larger and larger N, the cost of N^2 iterations adds up and increases quadratically.

Profiling is the only way to be sure about performance.

Let’s see two better ways to solve this problem.

Hash approach

Here’s the critical realization - Each of the users match precisely one of the students. Hashes are a great way to store one to one mappings.

Using hashes converts O(n) inner iteration of prefetch method to O(1) hash table lookup.


  1. Fetch all students in section A from the database.
  2. Fetch all user_id from such students from the database (using SELECT students.user_id or the ORM equivalent).
  3. Fetch all users using user_id in step 2.
  4. Create a hash using the foreign key as key and the object itself as the value.
  5. For each student, look up the hash table and find the user.


# Step 1
students = Student.where(section: 'A')

# Step 2 - Avoid a query using preloaded students
user_ids = students.pluck(:user_id)

# Step 3
users = User.where(id: user_ids)

# Step 4
users = users.to_h { |user| [user.id, user] }

# Step 5
students.each do |student|
  puts users[student.user_id].username


Databases and ORMs have recognized the need to work with relations efficiently. Rails has includes whereas Django has prefetch_related for fetching related records efficiently.

students = Student.where(section: 'A').includes(:user)

students.each do |student|
  puts student.user.username

Phew! That was shorter and is just as fast as the hash approach.