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Data Structures & Algorithms

Write a function moving_window to find the moving window average

Moving Window

Given an array and a target integer, write a function that returns the indices of two integers in the array that add up to the target integer.

Target Indices

Write a function to rotate an array by 90 degrees in the clockwise direction.

Matrix Rotation

Write an algorithm to return the character with the longest continuous repetition, breaking ties by earliest occurrence

Most Repetition

Median O(1)

Behavioral

Describing a data project and its challenges

Hurdles In Data Projects

Strategically resolving misaligned expectations with stakeholders for a successful project outcome

Stakeholder Communication

Prioritized debt reduction, process improvement, and a focus on maintainability for fintech efficiency

Decreasing Tech Debt

How to present complex data insights with clarity and adaptability tailored to a specific audience

Presentations and Insights

How would you answer when an Interviewer asks why you applied to their company?

Why Do You Want to Work With Us

A/B Testing

How would you assess the validity of the result?

Experiment Validity

Button AB Test

How would you design a two-week A/B test to determine whether a pricing increase is a good business decision

Testing Price Increase

Design an A/B test to use the marketing budget most efficiently across multiple new channels

Marketing Dollar Efficiency

An A/B test is being conducted to determine which version of a payment processing page leads to higher conversion rates. You’re responsible for analyzing the results. How would you set up and analyze this A/B test? Additionally, how would you use bootstrap sampling to calculate the confidence intervals for the test results, ensuring your conclusions are statistically valid?

A/B Testing a Checkout Button Change

Product Sense & Metrics

Google Maps Improvement

What are the top five metrics you would start tracking to understand the health of Google Docs

Docs Metrics

What are the most important metrics for WhatsApp

WhatsApp Metrics

The role of A/B testing in measuring the success rate of an analytics experiment

Success Measurement

Vision Setting and Execution Strategy

Machine Learning

Interpret coefficients of logistic regression for categorical and boolean variables

Coefficients of Logistic Regression

Bias vs. Variance Tradeoff

Implement the k-means clustering algorithm in python from scratch

k-Means from Scratch

Addressing imbalanced data in machine learning through carefully prepared techniques.

Data Preparation for Imbalanced Data

Let's say that you're training a classification model.   How would you combat overfitting when building tree-based models?

Overfit Avoidance

Given a table of product subscriptions with a subscription start date and end date for each user, write a query that returns true or false whether or not each user has a subscription date range that overlaps with any other completed subscription.

Completed subscriptions have <code>end_date</code> recorded.

Example:

Input:

<code>subscriptions</code> table

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>start_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>end_date</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>

<table>
<thead>
<tr>
<th><code>user_id</code></th>
<th><code>start_date</code></th>
<th><code>end_date</code></th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>2019-01-01</td>
<td>2019-01-31</td>
</tr>

<tr>
<td>2</td>
<td>2019-01-15</td>
<td>2019-01-17</td>
</tr>

<tr>
<td>3</td>
<td>2019-01-29</td>
<td>2019-02-04</td>
</tr>

<tr>
<td>4</td>
<td>2019-02-05</td>
<td>2019-02-10</td>
</tr>
</tbody>
</table>
Output:

<table>
<thead>
<tr>
<th><code>user_id</code></th>
<th><code>overlap</code></th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>1</td>
</tr>

<tr>
<td>2</td>
<td>1</td>
</tr>

<tr>
<td>3</td>
<td>1</td>
</tr>

<tr>
<td>4</td>
<td>0</td>
</tr>
</tbody>
</table>

Write a query to return whether each user's subscription date range overlaps with any other completed subscription

Subscription Overlap

Given a table called <code>user_experiences</code>, write a query to determine the percentage of users that held the title of <code>&#34;Data Analyst&#34;</code> immediately before holding the title <code>&#34;Data Scientist&#34;</code>.

Immediate is defined as the user holding no other titles between the <code>&#34;Data Analyst&#34;</code> and <code>&#34;Data Scientist&#34;</code> roles.

Example:

Input:

<code>user_experiences</code> table

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>position_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>start_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>end_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
Output:

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>percentage</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>

User Experience Percentage

Let’s say that your company is running a standard control and variant AB test on a feature to increase conversion rates on the landing page. The PM checks the results and finds a .04 p-value.

How would you assess the validity of the result?

A team wants to A/B test multiple different changes through a sign-up funnel.

For example, on a page, a button is currently red and at the top of the page. They want to see if changing a button from red to blue and/or from the top of the page to the bottom of the page will increase click-through.

How would you set up this test?

Your team wants to run an AB test on the color (red or blue) and position (top/bottom of the page) of a button that links to a promotion.

How many different variants of the test should you run to see the effect that a red button has on the bottom of the page, if currently the button is blue and on the top of the page.

Your team wants to run an AB test on the color (red or blue) and position (top/bottom of the page) of a button that links to a promotion.

How many different variants of the test should you run to see the effect that a red button has on the bottom of the page, if currently the button is blue and on the top of the page.

A/B Test Variants

Let’s say we are given a table <code>user_logins</code>.

Using this table, calculate how many users logged in an identical number of times on January 1st, 2022.

For example, it may be the case that on that date three users logged in seven times, four users logged in five times, two users logged in ten times, etc.

Example:

Input:

<code>user_logins</code> table

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>login_date</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
Output:

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>number_of_logins</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>number_of_users</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>

Find how many users logged in a certain number of times on a given day

Daily Logins

Tell me about a data project that didn’t go the way you expected. What did you set out to do, what surprised you, and how did you handle it?

Let’s say that you work at a B2B SAAS company that’s interested in testing the pricing of different levels of subscriptions.

Your project manager comes to you and asks you to run a two-week-long A/B test to test an increase in pricing.

How would you approach designing this test? How would you determine whether the increase in pricing is a good business decision?

How would you explain what a p-value is to someone who is not technical?

What does a p-value in a statistical test represent?

What does a p-value in a statistical test represent?

P-value to a Layman I

In a statistical test, how does a low p-value (less than 0.05) influence our decision about the null hypothesis?

In a statistical test, how does a low p-value (less than 0.05) influence our decision about the null hypothesis?

P-value to a Layman II

Explain what a p-value is to someone who is not technical

P-value to a Layman

Statistics

In the context of hypothesis testing, what are type I errors (type one errors) and type II errors (type two errors)? What is the difference between the two?

Bonus: Describe the probability of making each type of error mathematically.

What is the difference between type I and type II errors?

Type I and II Errors

Let’s say that you’re the PM on Google Maps.

<ol>
<li>How would you improve Google Maps?</li>

<li>What metrics would you check to see if your feature improvements are successful?</li>
</ol>

<h1>Binary Tree Validation</h1>

You are given the root of a binary tree. You need to determine if it is a valid binary search tree (BST).

A valid BST is defined as follows:

<ul>
<li>The left subtree of a node contains only nodes with values less than or equal to the node’s value.</li>
<li>The right subtree of a node contains only nodes with values greater than or equal to the node’s value.</li>
<li>Both the left and right subtrees must also be binary search trees.</li>
</ul>

Given the function <code>def is_valid_bst(root: Node) -&gt; bool:</code>, return True if the binary tree is a valid BST. Otherwise, return False.

<h3>Example:</h3>

Input:

<img src="/s3/questions/9664817c-3e12-4a40-9236-8382b13f55a0.png" alt="image"/>Converted Binary Tree.png

Output:

<pre tabindex="0" class="chroma"><code>def is_valid_bst(Node(3)) -&gt; True
</code></pre>

Given the root node, verify if a binary search tree is valid or not.

Binary Tree Validation

Write a Python function called <code>longest_increasing_subsequence</code> that takes a list of integers as input and returns as output the length of the longest increasing subsequence in the list.

Note: An increasing subsequence is a subset of a list where the elements are in strictly increasing order. The subsequence does not have to be contiguous or unique.

<h3>Example:</h3>

Input:

<pre tabindex="0" class="chroma"><code>nums = [10, 9, 2, 5, 3, 3, 7, 101, 18]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>4
</code></pre>

Explanation:

The longest increasing subsequence is <code>[2, 3, 7, 101]</code>, for a total length of 4.

Find the longest increasing subsequence in a list of integers.

Longest Increasing Subsequence

Given an array and a target integer, write a function <code>sum_pair_indices</code> that returns the indices of two integers in the array that add up to the target integer. If not found, just return an empty list.

Note: Can you do it on \(O(n)\) time?

Note: Even though there could be many solutions, only one needs to be returned.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>array = [1 2 3 4] 
target = 5 
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def sum_pair_indices(array, target) -&gt; [0 3] or [1 2]
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>array = [3]
target = 6 
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>Do NOT return [0 0] as you can&#39;t use an index twice.
</code></pre>

Given a string <code>str</code> of any length, write an algorithm <code>max_repeating</code> to return which character has the longest string of continuous repetition.

If two characters are tied for most continuous repetition, return the character whose longest continuous repetition occurs earliest in <code>str</code>.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>str = &#39;aabbaaccbbbaa&#39;
def max_repeating(str) -&gt; b
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>str = &#39;adccccbbbbc&#39;
def max_repeating(str) -&gt; c
</code></pre>

What are the assumptions of linear regression?

Which assumption of the residuals of the standard linear regression model can not be overcome by increasing the sample size?

Regression assumptions

What are the assumptions of linear regression?

Assumptions of Linear Regression

How would you interpret coefficients of logistic regression for categorical and boolean variables?

Why is one-hot encoding recommended for categorical variables in logistic regression models?

Why is one-hot encoding recommended for categorical variables in logistic regression models?

You’re a data scientist at YouTube. Leadership wants to revisit how the platform measures success, not for a specific new feature, but for the product as a whole given its current state.

How would you define and measure success for YouTube? Identify your primary and secondary metrics, explain your rationale for each, and discuss how you would choose the right thresholds for any engagement-based metrics you propose.

Let’s say you’re a data scientist at LinkedIn where you’re working on a product that sends qualified job candidates to companies. The team has launched a new feature that allows candidates to message hiring managers at companies directly during the interview process to get updates on their status.

Due to engineering constraints, the company can’t AB test the feature before launching it.

How would you analyze how the feature is performing?

How would you analyze the performance of a new LinkedIn feature that lets candidates message hiring managers during the interview process

Recruiting Leads

Analytics

You’re given a table called <code>annual_payments</code> for an annually billed B2B SAAS subscription product.

<code>annual_payments</code> table

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>status</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>amount</code></td>
<td>FLOAT</td>
</tr>

<tr>
<td><code>amount_refunded</code></td>
<td>FLOAT</td>
</tr>

<tr>
<td><code>product</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>last_updated</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
Users pay for the three different products: <code>&#39;PDF Editor&#39;</code>, <code>&#39;Cloud Storage&#39;</code>, and <code>&#39;Mobile CRM&#39;</code>.

How would you formulate a query to calculate the average annual retention, for each subsequent year, at the end of the year?

Retention rate is calculated as a percentage of active subscriptions at the end of the year \(T\) in the active subscriptions at the end of the previous year \((T-1)\).

Example 1:

User 1 bought a subscript to <code>PDF editor</code> in 2019 for the first time and renewed their subscription in 2020. In 2021, they canceled their subscription.
Retention rates should be calculated as:

<table>
<thead>
<tr>
<th>2019</th>
<th>2020</th>
<th>2021</th>
</tr>
</thead>

<tbody>
<tr>
<td>0.00</td>
<td>1.00</td>
<td>0.00</td>
</tr>
</tbody>
</table>
Example 2:

User 2 bought a subscription to <code>&#39;PDF Editor&#39;</code> in 2019 for the first time, renewed their subscription in 2020, and canceled a few days later in 2020.
Retention rates should be calculated as:

<table>
<thead>
<tr>
<th>2019</th>
<th>2020</th>
<th>2021</th>
</tr>
</thead>

<tbody>
<tr>
<td>0.00</td>
<td>0.00</td>
<td>0.00</td>
</tr>
</tbody>
</table>
Notes:

<ol>
<li>The status column may contain the values <code>&#39;paid&#39;</code>, <code>&#39;refunded&#39;</code>, or <code>&#39;failed&#39;</code>.</li>
<li>A <code>&#39;failed&#39;</code> payment equates to a user canceling their subscription on the date the next payment is due.</li>
<li>If a user refunds a successful payment, then the row gets updated, and the status becomes <code>&#39;refunded&#39;</code>. The date of refund is recorded in <code>last_updated</code>.</li>
<li>When a refund occurs in year \(T\), the subscription is canceled. Users may purchase the same product again in the subsequent years, and it is considered a new purchase.</li>
</ol>

Annual Retention

You’re given a list of sorted integers in which more than 50% of the list is comprised of the same repeating integer.

Write a function to return the median value of the list in \(O(1)\) computational time and space.

Note: the lists are all non-empty

Example:

Input:

<pre tabindex="0" class="chroma"><code>li = [1,2,2]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>median(li) -&gt; 2
</code></pre>

You work for an insurance SAAS company that sells leads to insurance agents.

The VP of sales at your company asks you to dig into whether more leads delivered to the agents provides more value and retains customers for longer periods of time. They point to a graph that shows agents at month three receiving more than 3x the leads than agents in month one as proof.

What is potentially flawed with the VP’s approach?

What is potentially flawed with the VP's approach?

Insurance Leads

Business Case

Let’s say that you are leading the development of an internal chatbot for operations support at Thomson Reuters, an internal tooling in their news division for referencing articles.

How would you design a system given a choice between fine-tuning the LLM or using Retrieval-Augmented Generation (RAG)?

Fine-Tuning VS RAG

AI & Agentic Systems

Given an array filled with random values, write a function <code>rotate_matrix</code> to rotate the array by 90 degrees in the clockwise direction.

Example:

Input:

<pre tabindex="0" class="chroma"><code>import numpy as np

array = np.array( [[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7], [4, 5, 6, 7, 8], [5, 6, 7, 8, 9]] )

</code></pre>

array
<table><tbody><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr><tr><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td></tr><tr><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr></tbody></table>

Output:

<table><tbody><tr><td>5</td><td>4</td><td>3</td><td>2</td><td>1</td></tr><tr><td>6</td><td>5</td><td>4</td><td>3</td><td>2</td></tr><tr><td>7</td><td>6</td><td>5</td><td>4</td><td>3</td></tr><tr><td>8</td><td>7</td><td>6</td><td>5</td><td>4</td></tr><tr><td>9</td><td>8</td><td>7</td><td>6</td><td>5</td></tr></tbody></table>

You’re given <code>numlists</code>, a list where each element is a list of at least five numbers.

Write a function <code>list_fifths</code> that returns a list of the fifth-largest number from each element in <code>numlists</code>. Return the list in ascending order.

Example:

Input:

<pre tabindex="0" class="chroma"><code>numlists = [ [1,2,3,4,5], [3,1,2,5,4], [1,2,3,4,5,6,7], 
[99, 320, 400, 100.25, 55.2, 0.1] ]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def list_fifths(numlists) -&gt; [1, 1, 3, 55.2]
</code></pre>

Write a function list_fifths that returns the fifth-largest number from each list in numlists in ascending order

5th Largest Number

Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand.

You are given a target value to search. If the value is in the array, then return its index; otherwise, return -1. 

Notes:

<ul>
<li>Rotating an array at pivot \(n\) gives you a new array that begins with the elements after position \(n\) and ends with the elements up to position \(n\).</li>
<li>You may assume no duplicate exists in the array.</li>
</ul>

Bonus: Your algorithm’s runtime complexity should be in the order of \(O(\log n)\).

Example:

Input: 

<pre tabindex="0" class="chroma"><code>sample_input = [0,1,2,4,5,6,7] 
rotated_input = [4,5,6,7,0,1,2]
target_value = 6
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def target_value_search(rotated_input, target_value) -&gt; 2
</code></pre>

Search for a value in log(n) over a sorted array that has been shifted.

Target Value Search

Let’s say you’re in a supermarket.

You’ve found out that there is a huge discount on some items you want; unfortunately, you only have one bag with a certain <code>bag_capacity</code>. Each of the items has its own <code>value</code> and <code>capacity</code>, stored in lists called <code>values</code> and <code>capacities</code> contained in a dictionary called <code>items</code>.

Write a function to pick the items that maximize the total value without exceeding the bag’s capacity and return the total value.

Note: You can’t take more than one copy of each item home. Also, you do not need to fill the entire bag to capacity.

Example:

Input:

<pre tabindex="0" class="chroma"><code>items = {
 &#34;values&#34;:[2,3,1,4],
 &#34;capacities&#34;:[2, 4, 6, 5]
}

bag_capacity = 8
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>max_profit(items,bag_capacity) -&gt; 6
</code></pre>

We choose the first and last item with a total profit of 6 and a capacity of 7, which is less than the <code>bag_capacity</code>.

Write a function to pick the items that maximize the total value without exceeding the bag’s capacity

Filling Supermarket Bag

Imagine you are asked to build a machine learning model to decide new loan approvals for a
financial firm. You ask the data department in the company for a subset of data to get started
working on the problem. The data includes different features about applicants such as age,
occupation, zip code, height, number of children, favorite color, etc. You decide to build
multiple machine learning models to test out different ideas before settling on the best one.

How would you explain the bias-variance tradeoff with regards to
building and choosing a model to use?

How would you handle the data preparation for building a machine learning model using imbalanced data?

Given a list of numbers <code>nums</code> and an integer <code>window_size</code>, write a function <code>moving_window</code> to find the moving window average.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>nums = [1,2,3,4,5,6]
window_size = 3
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def moving_window(input, window_size) -&gt; [1, 1.5, 2, 3, 4, 5]
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>nums = [1,2,3,4,5,6]
window_size = 4
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def moving_window(input, window_size) -&gt; [1, 1.5, 2, 2.5, 3.5, 4.5]
</code></pre>

You’re drawing from a random variable that is normally distributed \(X \sim \mathcal{N}(0,1)\)  once per day.

What is the expected number of days that it takes to draw a value that’s higher that 2?

How many draws from a standard normal distribution would you expect to take to obtain a value higher than 2?

How many draws from a standard normal distribution would you expect to take to obtain a value higher than 2?

Calculate Moving Average	SQL	Easy
Predict Customer Churn	Machine Learning	Medium
A/B Test Significance	Statistics	Medium
Optimize Query Performance	SQL	Hard
Feature Importance Analysis	Machine Learning	Medium
Clean Missing Data	Python	Easy
Neural Network Architecture	Deep Learning	Hard
Calculate Cohort Retention	SQL	Medium
Bayesian Probability	Statistics	Easy
Recommend Similar Products	Machine Learning	Hard

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