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Sumo Logic Interview Questions

Sumo Logic Interview Guides

Data Structures & Algorithms

Given two sorted lists, write a function to merge them into one sorted list.

Merge Sorted Lists

Find the missing integer from a array of consequtive integers

Find the Missing Number

Find Bigrams

Write a function to create a single dataframe with complete addresses in the format of street, city, state, zip code.

Complete Addresses

Get Top N Frequent Words

Select the 2nd highest salary in the engineering department

2nd Highest Salary

Write a SQL query to create a histogram of the number of comments per user in the month of January 2020.

Comments Histogram

Write a query that returns all neighborhoods that have 0 users.

Empty Neighborhoods

Calculate the first touch attribution for each `user_id` that converted.

First Touch Attribution

Closest SAT Scores

Machine Learning

Encoding Categorical Features

Coefficients of Logistic Regression

Booking Regression

Job Recommendation

RMS Error

Probability

First to Six

500 Cards

Raining in Seattle

Found Item

Ad Raters

Statistics

Compute Deviation

Write a function to return the cumulative percentage of students that received scores within certain buckets.

Bucket Test Scores

P-value to a Layman

Say you are given a dataset of perfectly linearly separable data. What would happen when you run logistic regression?

Perfectly Separable

Reducing Error Margin

We’re given two tables, a <code>users</code> table with demographic information and the neighborhood they live in and a <code>neighborhoods</code> table.

Write a query that returns all neighborhoods that have 0 users. 

Example:

Input:

<code>users</code> table

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

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

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>neighborhood_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
<code>neighborhoods</code> table

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

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

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

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

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

<tbody>
<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>

Given the <code>employees</code> and <code>departments</code> table, write a query to get the top 3 highest employee salaries by department. If the department contains less that 3 employees, the top 2 or the top 1 highest salaries should be listed (assume that each department has at least 1 employee). 

Note: The output should include the full name of the employee in one column, the department name, and the salary. The output should be sorted by department name in ascending order and salary in descending order. 

Example:

Input:

<code>employees</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>first_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>last_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>department_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<code>departments</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>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
Output:

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

<tbody>
<tr>
<td><code>employee_nam</code>e</td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>department_name</code></td>
<td>VARCHAR</td>
</tr>

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

Get the top 3 highest employee salaries by department

Top Three Salaries

Let’s say we have a table with an <code>id</code> and <code>name</code> fields. The table holds over 100 million rows and we want to sample a random row in the table without throttling the database.

Write a query to randomly sample a row from this table.

Input:

<code>big_table</code> table

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

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

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>

Write a query to randomly sample a row from a big table.

Random SQL Sample

The schema below is for a retail online shopping company consisting of two tables, <code>attribution</code> and <code>user_sessions</code>.

<ul>
<li>The attribution table logs a session visit for each row.</li>

<li>If <code>conversion</code> is <code>true</code>, then the user converted to buying on that session.</li>

<li>The <code>channel</code> column represents which advertising platform the user was attributed to for that specific session.</li>

<li>Lastly the <code>user_sessions</code> table maps many to one session visits back to one user.</li>
</ul>

First touch attribution is defined as the channel with which the converted user was associated when they first discovered the website.

Calculate the first touch attribution for each <code>user_id</code> that converted. 

Example:

Input:

<code>attribution</code> table

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

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

<tr>
<td><code>channel</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>conversion</code></td>
<td>BOOLEAN</td>
</tr>
</tbody>
</table>
<code>user_sessions</code> table

<table>
<thead>
<tr>
<th>column</th>
<th>type</th>
</tr>
</thead>

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

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

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
Example output:

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

<tbody>
<tr>
<td>123</td>
<td>facebook</td>
</tr>

<tr>
<td>145</td>
<td>google</td>
</tr>

<tr>
<td>153</td>
<td>facebook</td>
</tr>

<tr>
<td>172</td>
<td>organic</td>
</tr>

<tr>
<td>173</td>
<td>email</td>
</tr>
</tbody>
</table>

Given a table of bank transactions with columns <code>id</code>, <code>transaction_value</code>, and <code>created_at</code> representing the date and time for each transaction, write a query to get the last transaction for each day.

The output should include the id of the transaction, datetime of the transaction, and the transaction amount. Order the transactions by datetime.

Example:

Input:

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

<tr>
<td><code>transaction_value</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>
Output:

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

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

<tr>
<td><code>transaction_value</code></td>
<td>FLOAT</td>
</tr>

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

Last Transaction

You’re a data scientist at Meta working on a feature that helps users discover trending books and understand borrowing behavior across the platform’s digital library.

Every time a user borrows a book, the system logs a <code>borrowed_at</code> timestamp and a <code>returned_at</code> timestamp. The team wants to measure how long books are typically kept, while also flagging which books have large inventories.

Write a SQL query to compute the following metrics for each book:

<ol>
<li><code>avg_borrow_duration_days</code>: average borrowing duration in days (rounded to 2 decimals)</li>
<li><code>has_over_10_copies</code>: <code>&#39;Yes&#39;</code> if the book has more than 10 copies available, otherwise <code>&#39;No&#39;</code></li>
</ol>

Only include completed borrows where <code>returned_at</code> is not NULL.

Sort results by <code>avg_borrow_duration_days</code> DESC, then by <code>book_id</code> ASC.

Note: Every book that has at least one completed borrow should appear in the output.

<h3>Schema</h3>

Input

<code>books</code> Table

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

<tbody>
<tr>
<td>book_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>title</td>
<td>VARCHAR</td>
</tr>

<tr>
<td>copies_available</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<code>borrows</code> Table

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

<tbody>
<tr>
<td>borrow_id</td>
<td>INTEGER</td>
</tr>

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

<tr>
<td>book_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>borrowed_at</td>
<td>DATETIME</td>
</tr>

<tr>
<td>returned_at</td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
Output

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

<tbody>
<tr>
<td>book_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>avg_borrow_duration_days</td>
<td>DECIMAL</td>
</tr>

<tr>
<td>has_over_10_copies</td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>

<h3>Example</h3>

Input

<code>books</code> Table

<table>
<thead>
<tr>
<th>book_id</th>
<th>title</th>
<th>copies_available</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>Dune</td>
<td>12</td>
</tr>

<tr>
<td>2</td>
<td>Sapiens</td>
<td>8</td>
</tr>

<tr>
<td>3</td>
<td>Clean Code</td>
<td>15</td>
</tr>
</tbody>
</table>
<code>borrows</code> Table

<table>
<thead>
<tr>
<th>borrow_id</th>
<th>user_id</th>
<th>book_id</th>
<th>borrowed_at</th>
<th>returned_at</th>
</tr>
</thead>

<tbody>
<tr>
<td>101</td>
<td>10</td>
<td>1</td>
<td>2026-01-01 09:00:00</td>
<td>2026-01-06 09:00:00</td>
</tr>

<tr>
<td>102</td>
<td>11</td>
<td>1</td>
<td>2026-01-10 10:00:00</td>
<td>2026-01-13 22:00:00</td>
</tr>

<tr>
<td>103</td>
<td>12</td>
<td>2</td>
<td>2026-01-02 12:00:00</td>
<td>2026-01-04 12:00:00</td>
</tr>

<tr>
<td>104</td>
<td>13</td>
<td>2</td>
<td>2026-01-05 09:00:00</td>
<td>NULL</td>
</tr>

<tr>
<td>105</td>
<td>14</td>
<td>3</td>
<td>2026-01-03 08:00:00</td>
<td>2026-01-10 08:00:00</td>
</tr>
</tbody>
</table>
Output

<table>
<thead>
<tr>
<th>book_id</th>
<th>avg_borrow_duration_days</th>
<th>has_over_10_copies</th>
</tr>
</thead>

<tbody>
<tr>
<td>3</td>
<td>7.00</td>
<td>Yes</td>
</tr>

<tr>
<td>1</td>
<td>4.25</td>
<td>Yes</td>
</tr>

<tr>
<td>2</td>
<td>2.00</td>
<td>No</td>
</tr>
</tbody>
</table>
Explanation

For book 1, there are two completed borrows. The durations are 5.00 days (Jan 1 → Jan 6) and 3.50 days (Jan 10 10:00 → Jan 13 22:00). The average borrowing duration is (5.00 + 3.50) / 2 = 4.25 days. Since <code>copies_available = 12</code>, the book is flagged as <code>&#39;Yes&#39;</code>.

For book 2, only one borrow is completed (the other has <code>returned_at = NULL</code> and is excluded). The completed duration is 2.00 days. Since <code>copies_available = 8</code>, it is flagged as <code>&#39;No&#39;</code>.

For book 3, there is one completed borrow lasting 7.00 days, and <code>copies_available = 15</code>, so it is flagged as <code>&#39;Yes&#39;</code>.

Write a SQL query to compute the average borrowing duration and identify books with over 10 copies.

Digital Library Borrowing Metrics

A digital health startup is analyzing ECG sensor data captured from wearable heart monitors. Each row in the dataset represents one heartbeat, including its timestamp and calculated heart rate at that moment.

The clinical team wants to detect tachycardia runs, periods where a patient’s heart rate stays above 100 bpm continuously for at least 10 seconds .

Write a SQL query to identify every valid tachycardia run and return:

<ol>
<li><code>patient_id</code></li>
<li><code>run_start</code>: timestamp of the first beat in the run</li>
<li><code>run_end</code>: timestamp of the last beat in the run</li>
<li><code>duration_seconds</code>: difference in seconds between start and end (rounded to 2 decimals)</li>
</ol>

Sort results by <code>patient_id</code>, then <code>run_start</code>.

Definition of a Tachycardia Run

<ul>
<li>All consecutive heartbeats must have <code>heart_rate &gt; 100</code></li>
<li>Total duration ≥ 10 seconds</li>
<li>Any gap ≥ 3 seconds between consecutive beats breaks the run</li>
</ul>

Note: A patient may have multiple separate runs.

Schema

Input

<code>ecg_readings</code> table

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

<tbody>
<tr>
<td>patient_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>timestamp</td>
<td>DATETIME</td>
</tr>

<tr>
<td>heart_rate</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
Output

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

<tbody>
<tr>
<td>patient_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>run_start</td>
<td>DATETIME</td>
</tr>

<tr>
<td>run_end</td>
<td>DATETIME</td>
</tr>

<tr>
<td>duration_seconds</td>
<td>DECIMAL</td>
</tr>
</tbody>
</table>
Example

Input

<code>ecg_readings</code> table

<table>
<thead>
<tr>
<th>patient_id</th>
<th>timestamp</th>
<th>heart_rate</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>2025-03-01 10:00:00</td>
<td>98</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:02</td>
<td>105</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:04</td>
<td>110</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:07</td>
<td>108</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:12</td>
<td>107</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:15</td>
<td>85</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:20</td>
<td>120</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:28</td>
<td>122</td>
</tr>
</tbody>
</table>
Output

<table>
<thead>
<tr>
<th>patient_id</th>
<th>run_start</th>
<th>run_end</th>
<th>duration_seconds</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>2025-03-01 10:00:02</td>
<td>2025-03-01 10:00:12</td>
<td>10.00</td>
</tr>
</tbody>
</table>

<h3>Explanation</h3>

The high-rate streak from 10:00:02 to 10:00:12 forms one continuous sequence because each gap between timestamps (2 to 4, 4 to 7, and 7 to 12) is less than three seconds. This creates a valid 10-second run. The later high values at seconds 20 and 28 are separated by an eight-second gap, so they form a different sequence that is shorter than 10 seconds and is therefore ignored.

Write a SQL query to identify every valid tachycardia run.

Detecting ECG Tachycardia Runs

Given a string, write a function <code>recurring_char</code> to find its first recurring character. Return <code>None</code> if there is no recurring character.

Treat upper and lower case letters as distinct characters.

You may assume the input string includes no spaces.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>input = &#34;interviewquery&#34;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>output = &#34;i&#34;
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>input = &#34;interv&#34;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>output = None
</code></pre>

Given a string, write a function to find its first recurring character.

Recurring Character

You’re a data analyst working for Burlington studying customer behavior during the annual Black Friday shopping spree. Each customer may visit the store multiple times throughout the day and make several purchases across different product categories. The marketing team wants to understand which customer segments were most engaged.

Write a SQL query to compute the following metrics for each product category:

<ol>
<li>Total number of unique customers who purchased from that category</li>
<li>Average spend per customer (rounded to 2 decimal places)</li>
<li>Percentage of customers who made more than one purchase in that category (rounded to 2 decimal places)</li>
</ol>

Sort the final results in descending order by average spend per customer.

Notes:

<ul>
<li>A “purchase” means a single row in the purchases table.</li>
<li>A customer who buys multiple items in one visit still counts as multiple purchases.</li>
<li>If a customer purchased from a category only once, they should not count toward the “multiple purchase” percentage.</li>
<li>Every category present in the purchases table should appear in the output.</li>
</ul>

Schema

Input

<code>purchases</code> table

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

<tbody>
<tr>
<td>purchase_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>customer_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>category</td>
<td>VARCHAR</td>
</tr>

<tr>
<td>amount</td>
<td>DECIMAL</td>
</tr>

<tr>
<td>purchase_time</td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
Output

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

<tbody>
<tr>
<td>category</td>
<td>VARCHAR</td>
</tr>

<tr>
<td>unique_customers</td>
<td>INTEGER</td>
</tr>

<tr>
<td>avg_spend_per_customer</td>
<td>DECIMAL</td>
</tr>

<tr>
<td>pct_multi_purchase_customers</td>
<td>DECIMAL</td>
</tr>
</tbody>
</table>
Example

Input

<code>purchases</code> table

<table>
<thead>
<tr>
<th>purchase_id</th>
<th>customer_id</th>
<th>category</th>
<th>amount</th>
<th>purchase_time</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>101</td>
<td>Electronics</td>
<td>120</td>
<td>2025-11-28 09:10:00</td>
</tr>

<tr>
<td>2</td>
<td>101</td>
<td>Electronics</td>
<td>80</td>
<td>2025-11-28 10:00:00</td>
</tr>

<tr>
<td>3</td>
<td>102</td>
<td>Clothing</td>
<td>40</td>
<td>2025-11-28 11:15:00</td>
</tr>

<tr>
<td>4</td>
<td>103</td>
<td>Electronics</td>
<td>300</td>
<td>2025-11-28 13:30:00</td>
</tr>

<tr>
<td>5</td>
<td>102</td>
<td>Electronics</td>
<td>150</td>
<td>2025-11-28 14:10:00</td>
</tr>

<tr>
<td>6</td>
<td>102</td>
<td>Clothing</td>
<td>10</td>
<td>2025-11-28 16:20:00</td>
</tr>

<tr>
<td>7</td>
<td>103</td>
<td>Clothing</td>
<td>50</td>
<td>2025-11-28 17:20:00</td>
</tr>
</tbody>
</table>
Output

<table>
<thead>
<tr>
<th>category</th>
<th>unique_customers</th>
<th>avg_spend_per_customer</th>
<th>pct_multi_purchase_customers</th>
</tr>
</thead>

<tbody>
<tr>
<td>Electronics</td>
<td>3</td>
<td>216.67</td>
<td>33.33</td>
</tr>

<tr>
<td>Clothing</td>
<td>2</td>
<td>50.00</td>
<td>50.00</td>
</tr>
</tbody>
</table>
Explanation

For Electronics, there are three unique customers: 101, 102, and 103. Their spend amounts are 200 for customer 101 (120 + 80), 150 for customer 102, and 300 for customer 103, giving an average spend of 216.67. Only customer 101 made more than one purchase, so the multi-purchase rate is 33.33%.

For Clothing, there are two unique customers: 102 and 103. Customer 102 spent a total of 50 (40 + 10), while customer 103 spent 50, resulting in an average of 50.00. Customer 102 is the only one with multiple purchases, leading to a multi-purchase rate of 50.00%.

Write a SQL query to compute metrics for each product category.

Black Friday Shopping Spree

You’re a data scientist working for a smart grocery platform that helps families automatically plan their Christmas dinner based on their dietary preferences and pantry availability.

Each Christmas recipe consists of several ingredients, and each ingredient has different brands with different prices. Families want the cheapest possible ingredient combination but only using brands they have marked as acceptable and only those ingredients they do not already have in their pantry.

Write a SQL query to determine the cheapest valid shopping cost for each recipe for family_id = 1, while also identifying whether the recipe is feasible to make.

For each recipe, compute:

<ol>
<li><code>missing_ingredients</code>: number of ingredients the family does not already have in their pantry</li>
<li><code>min_total_cost</code>: total minimum cost required to buy missing ingredients</li>
<li>feasible:

<ul>
<li><code>&#39;Yes&#39;</code> if every missing ingredient has at least one acceptable brand available</li>
<li><code>&#39;No&#39;</code> otherwise (and <code>min_total_cost</code> should be <code>NULL</code>)</li>
</ul></li>
</ol>

Note: Sort results by <code>missing_ingredients</code> ASC and <code>min_total_cost</code> ASC (NULLS LAST)

Schema

Input

<code>recipes</code> Table

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

<tbody>
<tr>
<td>recipe_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>ingredient_id</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<code>ingredient_brands</code> Table

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

<tbody>
<tr>
<td>ingredient_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>brand_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>price</td>
<td>DECIMAL</td>
</tr>
</tbody>
</table>
<code>pantry</code> Table

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

<tbody>
<tr>
<td>family_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>ingredient_id</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<code>acceptable_brands</code> Table

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

<tbody>
<tr>
<td>family_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>brand_id</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
Output

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

<tbody>
<tr>
<td>recipe_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>missing_ingredients</td>
<td>INTEGER</td>
</tr>

<tr>
<td>min_total_cost</td>
<td>DECIMAL</td>
</tr>

<tr>
<td>feasible</td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
Example

Input

<code>recipes</code> Table

<table>
<thead>
<tr>
<th>recipe_id</th>
<th>ingredient_id</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>100</td>
</tr>

<tr>
<td>1</td>
<td>200</td>
</tr>

<tr>
<td>1</td>
<td>300</td>
</tr>

<tr>
<td>2</td>
<td>200</td>
</tr>

<tr>
<td>2</td>
<td>400</td>
</tr>
</tbody>
</table>
<code>pantry</code> Table

<table>
<thead>
<tr>
<th>family_id</th>
<th>ingredient_id</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>100</td>
</tr>
</tbody>
</table>
<code>ingredient_brands</code> Table

<table>
<thead>
<tr>
<th>ingredient_id</th>
<th>brand_id</th>
<th>price</th>
</tr>
</thead>

<tbody>
<tr>
<td>200</td>
<td>10</td>
<td>3.50</td>
</tr>

<tr>
<td>200</td>
<td>11</td>
<td>2.99</td>
</tr>

<tr>
<td>300</td>
<td>20</td>
<td>8.50</td>
</tr>

<tr>
<td>400</td>
<td>30</td>
<td>6.75</td>
</tr>
</tbody>
</table>
<code>acceptable_brands</code> Table

<table>
<thead>
<tr>
<th>family_id</th>
<th>brand_id</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>10</td>
</tr>

<tr>
<td>1</td>
<td>20</td>
</tr>

<tr>
<td>1</td>
<td>30</td>
</tr>
</tbody>
</table>
Output

<table>
<thead>
<tr>
<th>recipe_id</th>
<th>missing_ingredients</th>
<th>min_total_cost</th>
<th>feasible</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>12.00</td>
<td>Yes</td>
</tr>

<tr>
<td>2</td>
<td>2</td>
<td>10.25</td>
<td>Yes</td>
</tr>
</tbody>
</table>

<h3>Explanation</h3>

For Recipe 1, the required ingredients are 100, 200, and 300. The pantry already contains ingredient 100, so only 200 and 300 are missing. The cheapest acceptable option for ingredient 200 is brand 10 at $3.50, since brand 11 is not allowed. For ingredient 300, the cheapest acceptable option is brand 20 at $8.50. This makes the total cost $12.00, and the recipe is feasible.

For Recipe 2, the required ingredients are 200 and 400. The cheapest acceptable choice for ingredient 200 is again $3.50, and for ingredient 400 it is $6.75. The total comes to $10.25, and this recipe is also feasible.

Write a SQL query to determine the cheapest valid shopping cost for each recipe for family_id = 1, while also identifying whether the recipe is feasible to make.

Christmas Dinner Ingredient Optimization

You are given two rectangles <code>a</code> and <code>b</code> each defined by four ordered pairs denoting their corners on the <code>x</code>, <code>y</code> plane. Write a function <code>rectangle_overlap</code> to determine whether or not they overlap. Return <code>True</code> if so, and <code>False</code> otherwise.

Note: If the two rectangles border one another, or share a corner like two diagonally adjacent positions on a chessboard, they are said to overlap.

Note: The lists of ordered pairs are in no particular order. The first entry in list <code>a</code> could be the top left corner while the first in list <code>b</code> is the bottom right.

Example:

Input:

<pre tabindex="0" class="chroma"><code>
a = [(-3,5), (-3,2),(0,5),(0,2)]
b = [(-1,4), (3,4), (3,1), (-1,1)]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def rectangle_overlap(a, b) -&gt; True
</code></pre>

As point <code>(0,2)</code> is fully contained in rectangle <code>b</code> and point <code>(-1,4)</code> is fully contained in a rectangle <code>a</code>.

Write a function to determine whether or not two rectangles overlap.

Rectangle Overlap

You’re given a string that may contain the characters <code>{</code>, <code>}</code>, <code>[</code>, <code>]</code>, <code>(</code>, and <code>)</code>.

Task: Verify that the string is balanced. A balanced string is one where every opening character, <code>{</code>, <code>[</code>, or <code>(</code>, has a corresponding closing character, <code>}</code>, <code>]</code>, or <code>)</code>.

Write a function called <code>is_balanced(string: str) -&gt; bool</code> which verifies the balance of a string.

Example:

<pre tabindex="0" class="chroma"><code>is_balanced(&#39;(())[]{}&#39;) -&gt; True
</code></pre>

<pre tabindex="0" class="chroma"><code>is_balanced(&#39;{([(){}])()}&#39;) -&gt; True
</code></pre>

<pre tabindex="0" class="chroma"><code>is_balanced(&#39;{}[]())&#39;) -&gt; False
</code></pre>

<hr/>

Write a function that tests whether a string of brackets is balanced.

The Brackets Problem

Given a table of employees, write a query to identify all managers.

A manager is defined as any employee who directly supervises at least one other employee.

Manager Definition:

<ul>
<li>An employee is considered a manager if at least one other employee has them listed as their supervisor.</li>
<li>Each employee has a unique ID, and supervisors are referenced by their employee ID.</li>
</ul>

<h2>Schema:</h2>

<h3>Input:</h3>

Table <code>employees</code>

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

<tbody>
<tr>
<td>employee_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>name</td>
<td>VARCHAR</td>
</tr>

<tr>
<td>supervisor_id</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>

<h3>Output:</h3>

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

<tbody>
<tr>
<td>name</td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>

<h2>Example:</h2>

<h3>Input:</h3>

<code>employees</code> table

<table>
<thead>
<tr>
<th>employee_id</th>
<th>name</th>
<th>supervisor_id</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>Alice</td>
<td>NULL</td>
</tr>

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

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

<tr>
<td>4</td>
<td>David</td>
<td>2</td>
</tr>

<tr>
<td>5</td>
<td>Eve</td>
<td>NULL</td>
</tr>
</tbody>
</table>

<h3>Output:</h3>

<table>
<thead>
<tr>
<th>name</th>
</tr>
</thead>

<tbody>
<tr>
<td>Alice</td>
</tr>

<tr>
<td>Bob</td>
</tr>
</tbody>
</table>

<h3>Explanation:</h3>

<ul>
<li>Alice is a manager because both Bob and Carol report directly to her (<code>supervisor_id = 1</code>).</li>
<li>Bob is a manager because David reports directly to him (<code>supervisor_id = 2</code>).</li>
<li>Eve is not a manager because no employees report to her.</li>
</ul>

Identify Managers

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>

Google Maps Improvement

Product Sense & Metrics

You are given a binary tree of unique positive numbers. Each node in the binary tree is represented as a dictionary with the following keys:

<ul>
<li><code>data</code>: integer value stored in the node</li>
<li><code>left</code>: reference to the left child (or <code>None</code>)</li>
<li><code>right</code>: reference to the right child (or <code>None</code>)</li>
</ul>

<pre tabindex="0" class="chroma"><code>node = {
 &#34;data&#34;: 6,
 &#34;left&#34;: {
 &#34;data&#34;: 3,
 &#34;left&#34;: {...},
 &#34;right&#34;: {...}
 },
 &#34;right&#34;: {
 &#34;data&#34;: 9,
 &#34;left&#34;: {...},
 &#34;right&#34;: {...}
 }
}
</code></pre>

Given two node values as input (<code>value1</code> and <code>value2</code>), write a function to return the value of the nearest common ancestor (lowest node in the tree that has both nodes as descendants).

Note: If one of the nodes doesn’t exist in the tree, return <code>-1</code>.

Example:

Input:

<pre tabindex="0" class="chroma"><code># Diagram of the binary tree
&#39;&#39;&#39;
 6 
 / \ 
 3 9 
 / \
 2 11
 / \
 5 8
&#39;&#39;&#39;
value1 = 8
value2 = 2
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>common_ancestor(root,value1,value2) -&gt; 3
</code></pre>

Explanation:

<ul>
<li>Ancestors of <code>8</code>: <code>11 → 3 → 6</code></li>
<li>Ancestors of <code>2</code>: <code>3 → 6</code></li>
<li>Common ancestors: <code>3</code> and <code>6</code></li>
<li>The nearest common ancestor is <code>3</code>.</li>
</ul>

Write a function to return the value of the nearest node that is a parent to both nodes.

Nearest Common Ancestor

Let’s say you work at an advertising firm. You have a table of users’ impressions of ad campaigns over time. Each <code>impression_id</code> consists of values of user engagement specified by <code>Excited</code>, <code>OK</code>, and <code>Bored</code>.

Write a query to find all users who were at some point “Excited” and have never been “Bored” with a campaign.

Example:

Input:

<code>ad_impressions</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>dt</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>campaign_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>impression_id</code></td>
<td>TEXT</td>
</tr>
</tbody>
</table>
Output:

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

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

Write a query to find all users that were at some point "Excited" and have never been "Bored" with a campaign.

Always Excited Users

Say you are tasked with designing a data mart or data warehouse for a new online retailer.

How would you design the system?

Note: Sketch a star schema to explain your design.

Design a data warehouse for a new online retailer

Retailer Data Warehouse

Data Modeling

Write a query to create a new table, named flight routes, that displays unique pairs of two locations.

Note: Duplicate pairs from the <code>flights</code> table, such as Dallas to Seattle and Seattle to Dallas, should have one entry in the flight routes table.

<h3>Schema</h3>

<code>flights</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>source_location</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>destination_location</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
Output:

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

<tbody>
<tr>
<td><code>destination_one</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>destination_two</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>

<h3>Example</h3>

Input:

<code>flights</code> table

<table>
<thead>
<tr>
<th>id</th>
<th>source_location</th>
<th>destination_location</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>Seattle, WA</td>
<td>Dallas, TX</td>
</tr>

<tr>
<td>2</td>
<td>Dallas, TX</td>
<td>Seattle, WA</td>
</tr>

<tr>
<td>3</td>
<td>Seattle, WA</td>
<td>San Francisco, CA</td>
</tr>

<tr>
<td>4</td>
<td>San Francisco, CA</td>
<td>Dallas, TX</td>
</tr>

<tr>
<td>5</td>
<td>San Francisco, CA</td>
<td>Portland, OR</td>
</tr>

<tr>
<td>6</td>
<td>Seattle, WA</td>
<td>Dallas, TX</td>
</tr>

<tr>
<td>7</td>
<td>Portland, OR</td>
<td>San Francisco, CA</td>
</tr>

<tr>
<td>8</td>
<td>San Francisco, CA</td>
<td>Los Angeles, CA</td>
</tr>
</tbody>
</table>
Output:

<table>
<thead>
<tr>
<th>destination_one</th>
<th>destination_two</th>
</tr>
</thead>

<tbody>
<tr>
<td>Dallas, TX</td>
<td>Seattle, WA</td>
</tr>

<tr>
<td>Portland, OR</td>
<td>San Francisco, CA</td>
</tr>

<tr>
<td>San Francisco, CA</td>
<td>Seattle, WA</td>
</tr>

<tr>
<td>Dallas, TX</td>
<td>San Francisco, CA</td>
</tr>

<tr>
<td>Los Angeles, CA</td>
<td>San Francisco, CA</td>
</tr>
</tbody>
</table>

Flight Records

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.

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

Success Measurement

Given the head of a singly linked list represented as a <code>ListNode</code>, and two zero-indexed positions <code>x</code> and <code>y</code>, write a function <code>swap_node</code> which swaps the positions of nodes <code>x</code> and <code>y</code> and returns the new head. Note that you cannot simply swap the values of these nodes, as these nodes do not have values. Instead, you must swap these two using pointer manipulation (i.e., modifying the <code>next</code> references of the involved nodes inside the list).

A <code>ListNode</code> is defined as:

<pre tabindex="0" class="chroma"><code>class ListNode:
 next: ListNode = None
</code></pre>

Example:

Input:

<pre tabindex="0" class="chroma"><code>linked_list = ListNode(0x01) -&gt; ListNode(0x02) -&gt; ListNode(0x03) 
# Here, imagine that &#39;0x0_&#39; refer to their memory locations.
head = 0x01
x = 1
y = 2
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def swap_node(head, x, y) -&gt; ListNode(0x01) -&gt; ListNode(0x03) -&gt; ListNode(0x02)
</code></pre>

Swapping Nodes

You are tasked with keeping track of a customer’s addresses in your database.

However, customer’s addresses change whenever they move. We want to keep track of their moving history as well as the person that moves in afterwards.

How would you create or modify a schema to keep track of these address changes?

Create a schema to keep track of customer address changes

Address Schema

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

Walmart is analyzing how product performance changes across American seasons: Spring, Summer, Fall, Winter. The company stores sales records and seasonal product assignments in separate tables. A product may belong to different seasonal collections in different years.

Write a SQL query to compute the total revenue for each (season, year) pair by joining the two tables on multiple columns. Your final output should include <code>season</code>, <code>year</code> and <code>total_revenue</code> (rounded to 2 decimals)

Sort results by <code>year</code> ascending, then by season order: Spring → Summer → Fall → Winter.

Notes

<ul>
<li>The join must match on <code>product_id</code> AND <code>year</code>.</li>
<li>Seasonal assignment varies by year.</li>
<li>Revenue is computed from: <code>quantity * price</code></li>
<li>Every season/year combination appearing in the data must be included.</li>
</ul>

Schema

Input

<code>seasonal_products</code> table

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

<tbody>
<tr>
<td>product_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>season</td>
<td>VARCHAR</td>
</tr>

<tr>
<td>year</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<code>sales</code> table

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

<tbody>
<tr>
<td>sale_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>product_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>year</td>
<td>INTEGER</td>
</tr>

<tr>
<td>quantity</td>
<td>INTEGER</td>
</tr>

<tr>
<td>price</td>
<td>DECIMAL</td>
</tr>
</tbody>
</table>
Output

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

<tbody>
<tr>
<td>season</td>
<td>VARCHAR</td>
</tr>

<tr>
<td>year</td>
<td>INTEGER</td>
</tr>

<tr>
<td>total_revenue</td>
<td>DECIMAL</td>
</tr>
</tbody>
</table>
Example

Input

<code>seasonal_products</code> table

<table>
<thead>
<tr>
<th>product_id</th>
<th>season</th>
<th>year</th>
</tr>
</thead>

<tbody>
<tr>
<td>10</td>
<td>Spring</td>
<td>2024</td>
</tr>

<tr>
<td>10</td>
<td>Summer</td>
<td>2024</td>
</tr>

<tr>
<td>20</td>
<td>Fall</td>
<td>2024</td>
</tr>

<tr>
<td>30</td>
<td>Winter</td>
<td>2024</td>
</tr>
</tbody>
</table>
<code>sales</code> table

<table>
<thead>
<tr>
<th>sale_id</th>
<th>product_id</th>
<th>year</th>
<th>quantity</th>
<th>price</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>10</td>
<td>2024</td>
<td>2</td>
<td>50</td>
</tr>

<tr>
<td>2</td>
<td>10</td>
<td>2024</td>
<td>1</td>
<td>40</td>
</tr>

<tr>
<td>3</td>
<td>20</td>
<td>2024</td>
<td>3</td>
<td>30</td>
</tr>

<tr>
<td>4</td>
<td>30</td>
<td>2024</td>
<td>1</td>
<td>100</td>
</tr>
</tbody>
</table>
Output

<table>
<thead>
<tr>
<th>season</th>
<th>year</th>
<th>total_revenue</th>
</tr>
</thead>

<tbody>
<tr>
<td>Spring</td>
<td>2024</td>
<td>140.00</td>
</tr>

<tr>
<td>Summer</td>
<td>2024</td>
<td>140.00</td>
</tr>

<tr>
<td>Fall</td>
<td>2024</td>
<td>90.00</td>
</tr>

<tr>
<td>Winter</td>
<td>2024</td>
<td>100.00</td>
</tr>
</tbody>
</table>
Explanation

In Spring 2024, product 10 appears with total sales of (2 × 50) + (1 × 40) = 140. In Summer 2024, the same product is assigned to a different season within the same year, so its total is again 140. In Fall 2024, only product 20 appears, giving 3 × 30 = 90. In Winter 2024, only product 30 appears with 1 × 100 = 100.

The key detail:

A product may appear in multiple seasons in the same year, but JOIN must match both the product_id and year, ensuring that seasonal assignment is year-specific.

Write a SQL query to compute the total revenue for each (season, year) pair by joining two tables on multiple columns.

Seasonal Product Performance Analysis

Given a sorted list, create a function <code>convert_to_bst</code> that converts the list into a binary tree. <code>convert_to_bst</code> returns a <code>TreeNode</code> holding the root of the binary tree. A <code>TreeNode</code> is defined as the following:

<pre tabindex="0" class="chroma"><code>from dataclasses import dataclass

class TreeNode:
 pass

@dataclass
class TreeNode:
 value: int
 left: TreeNode = None
 right: TreeNode = None
</code></pre>

The output binary tree should be balanced, meaning the height difference between the left and right subtree of all the nodes should be at most one.

Example:

Input:

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

Output:

<img src="/s3/questions/46a1a245-47bf-4b7e-8356-6019ef9af27b.png" alt="image"/>Converted Binary Tree.png

Note: The output in the test cases will return an in-order traversal of your tree.

Binary Tree Conversion

Suppose there are one million users and we want to expose 1000 users per day to a test. The same user can be selected twice for the test.

<ol>
<li>What’s the expected value of how long someone will have to wait before they receive the test?</li>

<li>What is the likelihood they get selected after the first day? Is that closer to 0 or 1?</li>
</ol>

Suppose there are one million users and we want to expose 1000 users per day to a test. The same user can be selected twice for the test.What's the expected value of how long someone will have to wait before they receive the test?

Suppose there are one million users and we want to expose 1000 users per day to a test. The same user can be selected twice for the test.What's the expected value of how long someone will have to wait before they receive the test?

Expected Tests

Given a table of <code>subscriptions</code>, write a query to get the retention rate of each monthly cohort for each <code>plan_id</code> for the three months after sign-up.

Order your output by <code>start_month</code>, <code>plan_id</code>, then <code>num_month</code>.

If an <code>end_date</code> is in the same month as <code>start_date</code> we say the subscription was not retained in the first month.

If the <code>end_date</code> occurs in the month after the month of <code>start_date</code>, the subscription was not retained in the second month. And so on for the third.

The <code>end_date</code> field is <code>NULL</code> if the user has not canceled.

<h3>Schema:</h3>

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>

<tr>
<td><code>plan_id</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
Output:

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

<tbody>
<tr>
<td><code>start_month</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>num_month</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>plan_id</code></td>
<td>VARCHAR</td>
</tr>

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

<h3>Example</h3>

Input:

<code>subscriptions</code> table

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

<tbody>
<tr>
<td>1</td>
<td>2020-01-10 00:00:00</td>
<td>2020-03-31 23:59:59</td>
<td>plan1</td>
</tr>

<tr>
<td>2</td>
<td>2020-01-10 00:00:00</td>
<td>2020-02-01 23:59:59</td>
<td>plan1</td>
</tr>

<tr>
<td>3</td>
<td>2020-01-10 00:00:00</td>
<td>2020-07-31 23:59:59</td>
<td>plan1</td>
</tr>
</tbody>
</table>
Output:

<table>
<thead>
<tr>
<th>start_month</th>
<th>num_month</th>
<th>plan_id</th>
<th>retained</th>
</tr>
</thead>

<tbody>
<tr>
<td>2020-01-01</td>
<td>1</td>
<td>plan1</td>
<td>1.0</td>
</tr>

<tr>
<td>2020-01-01</td>
<td>2</td>
<td>plan1</td>
<td>0.67</td>
</tr>

<tr>
<td>2020-01-01</td>
<td>3</td>
<td>plan1</td>
<td>0.33</td>
</tr>
</tbody>
</table>
Explanation:

<ul>
<li>Cohort: All subscriptions starting in January 2020.</li>
<li>Month 1 retention: All 3 users were active in the first month → 3⁄3 = 1.0</li>
<li>Month 2 retention: Only users 1 and 3 were active in Feb → 2⁄3 ≈ 0.67</li>
<li>Month 3 retention: Only user 3 was active in Mar → 1⁄3 ≈ 0.33</li>
</ul>

Subscription Retention

You are asked to implement a simple regex parser which supports two operations: <code>&#39;.&#39;</code> and <code>&#39;*&#39;</code>. The <code>&#39;.&#39;</code> operation matches any single character, while the <code>&#39;*&#39;</code> operation matches zero or more of the preceding element. The matching should cover the entire input string (not partial).

Write a function <code>isMatch(s,p)</code> which takes in two parameters, the string and the regex pattern. It should return a Boolean output indicating a ‘match success’ or a ‘match failure’.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>s = &#39;aa&#39;
p = &#39;a&#39;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>isMatch(s, p) -&gt; False
</code></pre>

Explanation: ‘a’ does not match the entire string ‘aa’.

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>s = &#39;aa&#39;
p = &#39;a*&#39;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>isMatch(s, p) -&gt; True
</code></pre>

Explanation: ‘*’ means zero or more of the preceding element, ‘a’. Therefore, by repeating ‘a’ once, it becomes ‘aa’.

Note: There is no need to consider the delimiting of characters ‘.’ and ‘*’

Implement a simple regex parser with operator support for '.' and '*'.

Basic Regex

Let’s say you’re interning at a fintech startup that’s building a platform for online games of chance. During testing, one of your simulations flips a coin 10 times and gets 8 tails and 2 heads.

How would you determine if the coin is fair, and what statistical approach would you use to support your conclusion?

How would you assess if a coin is fair after observing 8 tails in 10 flips?

Fair Coin

You are given a list of integers called <code>numbers</code>. Write a function to return any subset of <code>numbers</code> where the elements <code>sum</code> to <code>zero</code> and that does not contain the number <code>0</code>.

If there are no combinations of elements that sum to zero, return an empty list.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>numbers = [1,-2,6,7,1]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def zero_sum(numbers) -&gt; [1,-2,1] # only possible combination
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>numbers = [0,0,1,3,6,-4,-1]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def zero_sum(numbers) -&gt; [1,3,-4]
</code></pre>

or

<pre tabindex="0" class="chroma"><code>def zero_sum(numbers) -&gt; [1,-1]
</code></pre>

or any other subset that sums to zero and doesn’t include <code>0</code>.

Write a function to return any subset of the input list where the elements sum to zero and that does not contain the number 0.

Sum to Zero

Let’s say we’re building a transformer-based model for text generation, and we want to understand how it computes self-attention at each layer.

How does the model mathematically compute self-attention using queries $Q$, keys $K$, and values $V$, and why do we need to apply a masking layer in the decoder when training on sequences?

How does the transformer compute self-attention and why is decoder masking necessary during training?

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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