1. Write a function to calculate all possible assignment vectors of 2n users, where n users are assigned to group 0 (control), and n users are assigned to group 1 (treatment).

• Recursive programming (sol in code)

  2. Given a list of tweets, determine the top 10 most used hashtags.

• Store all the hashtags in a dictionary and get the top 10 values

  3. Program an algorithm to find the best approximate solution to the knapsack problem1 in a given time.

• Greedy solution (add the best v/w as much as possible and move on to the next)

  4. Program an algorithm to find the best approximate solution to the travelling salesman problem2 in a given time.

• Greedy

  5. You have a stream of data coming in of size n, but you don’t know what n is ahead of time. Write an algorithm that will take a random sample of k elements. Can you write one that takes O(k) space?

• https://en.wikipedia.org/wiki/Reservoir_sampling

6. Write an algorithm that can calculate the square root of a number.

• https://www.quora.com/What-is-the-method-to-calculate-a-square-root-by-hand?redirected_qid=664405

• 7. Given a list of numbers, can you return the outliers?

• 8. When can parallelism make your algorithms run faster?

  When could it make your algorithms run slower?

9. What are the different types of joins? What are the differences between them?

• (INNER) JOIN: Returns records that have matching values in both tables
  LEFT (OUTER) JOIN: Return all records from the left table, and the matched records from the right table
  RIGHT (OUTER) JOIN: Return all records from the right table, and the matched records from the left table
  FULL (OUTER) JOIN: Return all records when there is a match in either left or right table

10. Why might a join on a subquery be slow? How might you speed it up?

• Change the subquery to a join.

  11. Describe the difference between primary keys and foreign keys in a SQL database.

• Primary keys are columns whose value combinations must be unique in a specific table so that each row can be referenced uniquely. Foreign keys are columns that references columns (often primary keys) in other tables.

  12. Given a COURSES table with columns course_id and course_name, a FACULTY table with columns faculty_id and faculty_name, and a COURSE_FACULTY table with columns faculty_id and course_id, how would you return a list of faculty who teach a course given the name of a course?

• select faculty_name from faculty_id c join (select faculty_id from (select course_id from COURSES where course_name=xxx) as a join COURSE_FACULTY b on a.course_id = b.course_id) d on c.faculty_id = d.faculty_id

  13. Given a IMPRESSIONS table with ad_id, click (an indicator that the ad was clicked), and date, write a SQL query that will tell me the click-through-rate of each ad by month.

• select id, average(click) from (select count(click) as click from IMPRESSIONS group by id,month(date)) group by id

  14. Write a query that returns the name of each department and a count of the number of employees in each: