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Data Structures & Algorithms

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

Merge Sorted Lists

Find Bigrams

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

Complete Addresses

Write a function friendship_timeline to generate an output that lists the pairs of friends with their corresponding timestamps of the friendship beginning and then the timestamp of the friendship ending. 

Friendship Timeline

Write a function can_shift to return whether or not A can be shifted some number of places to get B

String Shift

Probability

What is the probability that each subsequent card is larger than the previous drawn card when picking three cards from a shuffled deck of 500 cards

500 Cards

First to Six

What is the probability that it's actually raining in Seattle?

Raining in Seattle

What is the probability that item X would be found on Amazon's website?

Found Item

Compute the expected number of good ads in each scenario and the probability a bad rating came from a lazy rater

Ad Raters

Machine Learning

Interpret coefficients of logistic regression for categorical and boolean variables

Coefficients of Logistic Regression

How would you build a job recommendation feed?

Job Recommendation

Write a function calculate_rmse to calculate the root mean squared error from y_pred and y_true

RMS Error

Why can the same machine learning algorithm produce different success rates on the same dataset

Same Algorithm Different Success

Lasso vs Ridge

A/B Testing

How would you assess the validity of the result?

Experiment Validity

How would you determine if the new model predicts delivery times better than the old model

Delivery Estimate Model

Button AB Test

A/B Test Power Size

How would you make a control group and test group to account for network effects

Network Experiment Design

Statistics

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

Bucket Test Scores

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

P-value to a Layman

How many more samples are needed to decrease the margin of error to 0.3

Reducing Error Margin

What are the assumptions of linear regression?

Assumptions of Linear Regression

Design a test to determine whether the coin is biased

Possibly Biased Coin

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>

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

Empty Neighborhoods

Write a SQL query to select the 2nd highest salary in the engineering department.

Note: If more than one person shares the highest salary, the query should select the next highest salary.

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

Select the 2nd highest salary in the engineering department

2nd Highest Salary

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

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>

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

First Touch Attribution

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

Bonus: What’s the time complexity?

Example:

Input:

<pre tabindex="0" class="chroma"><code>list1 = [1,2,5]
list2 = [2,4,6]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def merge_list(list1,list2) -&gt; [1,2,2,4,5,6]
</code></pre>

You have two sorted lists, one with m elements and one with n elements. What would be the time complexity of merging the two lists via merge sort?

You have two sorted lists, one with m elements and one with n elements. What would be the time complexity of merging the two lists via merge sort? 

Merging Lists Complexity

Amy and Brad take turns in rolling a fair six-sided die. Whoever rolls a “6” first wins the game. Amy starts by rolling first.

What’s the probability that Amy wins?

Amy and Brad take turns in rolling a fair six-sided die. Whoever rolls a “6” first wins the game. Amy starts by rolling first.

What’s the probability that Amy wins?

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?

Given two strings <code>A</code> and <code>B</code>, write a function <code>can_shift</code> to return whether or not <code>A</code> can be shifted some number of places to get <code>B</code>.

Example:

Input:

<pre tabindex="0" class="chroma"><code>A = &#39;abcde&#39;
B = &#39;cdeab&#39;
can_shift(A, B) == True

A = &#39;abc&#39;
B = &#39;acb&#39;
can_shift(A, B) == False
</code></pre>

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

Imagine a deck of 500 cards numbered from 1 to 500. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what’s the probability of each subsequent card being larger than the previous drawn card?

Imagine a deck of 2000 cards numbered from 1 to 2000. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what’s the probability of each subsequent card being larger than the previously drawn card?

Imagine a deck of 2000 cards numbered from 1 to 2000. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what's the probability of each subsequent card being larger than the previously drawn card?

2000 cards

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

You are about to get on a plane to Seattle. You want to know if you should bring an umbrella. You call 3 random friends of yours who live there and ask each independently if it’s raining. Each of your friends has a 2⁄3 chance of telling you the truth and a 1⁄3 chance of messing with you by lying. All 3 friends tell you that “Yes” it is raining.

What is the probability that it’s actually raining in Seattle?

What is the main difference between the Frequentist and Bayesian methods of probabilistic analysis?

What is the **main** difference between the Frequentist and Bayesian methods of probabilistic analysis?

Frequentist Vs Bayesian Analysis

Let’s say you work at a file-hosting website. You have information on user’s daily downloads in the <code>download_facts</code> table

Use the window function <code>RANK</code> to display the top three users by downloads each day. Order your data by <code>date</code>, and then by <code>daily_rank</code>

Example:

Input:

<code>download_facts</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>date</code></td>
<td>DATE</td>
</tr>

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

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

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

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

<tr>
<td><code>date</code></td>
<td>DATE</td>
</tr>

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

Write a query to display the top three users by downloads each day

Top 3 Users

Let’s say that you’re working on a job recommendation engine. You have access to all user Linkedin profiles, a list of jobs each user applied to, and answers to questions that the user filled in about their job search.

Using this information, how would you build a job recommendation feed?

What problem can arise in job recommendation systems with regard to initial recommendations?

What problem can arise in job recommendation systems with regard to initial recommendations?

Write a function <code>minimum_change</code> to find the minimum number of coins that make up the given amount of change <code>cents</code>. Assume we only have coins of value 1, 5, 10, and 25 cents.

Example:

Input:

<pre tabindex="0" class="chroma"><code>cents = 73
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def minimum_change(cents) -&gt; 7
#(25 + 25 + 10 + 10 + 1 + 1 + 1)
</code></pre>

Minimum Change

Let’s say we have a very naive advertising platform. There is an audience of size A and a limited amount of impressions B.

Each of the impressions goes to just one user, defined at random. Every user in the audience has the same random chance of receiving each impression. 

<ol>
<li>Compute the probability that a user has exactly 0 impressions. </li>

<li>What’s the probability that every person has at least 1 impression?</li>
</ol>

Compute the probability a user gets exactly 0 impressions, and the probability everyone gets at least 1 impression

Impression Reach

A jar holds 1000 coins. Out of all of the coins, 999 are fair and one is double-sided with two heads. Picking a coin at random, you toss the coin ten times.

Given that you see 10 heads, what is the probability that the coin is double headed and the probability that the next toss of the coin is also a head?

Compute the probability the coin is double headed and the probability the next toss is a head given 10 heads

Jars and Coins

Netflix has hired people to rate movies.

Out of all of the raters, 80% of the raters carefully rate movies and rate 60% of the movies as good and 40% as bad. The other 20% are lazy raters and rate 100% of the movies as good.

Assuming all raters rate the same amount of movies, what is the probability that a movie is rated good?

There are two categories of movie raters: careful and lazy. Careful raters make up 80% of the total. They rate 60% of the movies as good and 40% as bad. Lazy raters, constitute 20% of the raters and 100% of the movies as good. Given these parameters, calculate the overall probability of a movie being rated good.

There are two categories of movie raters: careful and lazy. Careful raters make up 80% of the total. They rate 60% of the movies as good and 40% as bad. Lazy raters, constitute 20% of the raters and 100% of the movies as good. Given these parameters, calculate the overall probability of a movie being rated good.

Lazy Raters

What is the probability that a movie is rated good

Let’s say that you’re a data scientist on the engagement team. A product manager comes up to you and says that the weekly active users metric is up 5% but email notification open rates are down 2%.

What would you investigate to diagnose what’s happening?

Email Open Rate

What would you investigate to diagnose what's happening?

WAU vs Open Rates

Product Sense & Metrics

Let’s say you’re given a dataframe of standardized test scores from high schoolers from grades 9 to 12 called df_grades.

Given the dataset, write code function in Pandas called bucket_test_scores to return the cumulative percentage of students that received scores within the buckets of &lt;50, &lt;75, &lt;90, &lt;100.

Example:

Input:

<pre tabindex="0" class="chroma"><code>print(df_grades)
</code></pre>

<table>
<thead>
<tr>
<th>user_id</th>
<th>grade</th>
<th>test score</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>10</td>
<td>85</td>
</tr>

<tr>
<td>2</td>
<td>10</td>
<td>60</td>
</tr>

<tr>
<td>3</td>
<td>11</td>
<td>90</td>
</tr>

<tr>
<td>4</td>
<td>10</td>
<td>30</td>
</tr>

<tr>
<td>5</td>
<td>11</td>
<td>99</td>
</tr>
</tbody>
</table>
Output:

<pre tabindex="0" class="chroma"><code>def bucket_test_scores(df_grades) -&gt;
</code></pre>

<table>
<thead>
<tr>
<th>grade</th>
<th>test score</th>
<th>percentage</th>
</tr>
</thead>

<tbody>
<tr>
<td>10</td>
<td>&lt;50</td>
<td>33%</td>
</tr>

<tr>
<td>10</td>
<td>&lt;75</td>
<td>66%</td>
</tr>

<tr>
<td>10</td>
<td>&lt;90</td>
<td>100%</td>
</tr>

<tr>
<td>10</td>
<td>&lt;100</td>
<td>100%</td>
</tr>

<tr>
<td>11</td>
<td>&lt;50</td>
<td>0%</td>
</tr>

<tr>
<td>11</td>
<td>&lt;75</td>
<td>0%</td>
</tr>

<tr>
<td>11</td>
<td>&lt;90</td>
<td>50%</td>
</tr>

<tr>
<td>11</td>
<td>&lt;100</td>
<td>100%</td>
</tr>
</tbody>
</table>

Let’s say you want to test the close friends feature on Instagram Stories.

How would you make a control group and test group to account for network effects?

What could be a potential risk when Facebook segments the metrics of the user interface change by market or demographic groups?

What could be a potential risk when Facebook segments the metrics of the user interface change by market or demographic groups?

Network Experiment Design I

What is the primary metric that Facebook should monitor if it decides to make the user interface of its posting feature more like Instagram's?

What is the primary metric that Facebook should monitor if it decides to make the user interface of its posting feature more like Instagram's?

Network Experiment Design II

If Facebook changes its user interface to mimic Instagram's, which adverse effect should they anticipate and monitor?

If Facebook changes its user interface to mimic Instagram's, which adverse effect should they anticipate and monitor?

Let’s say we want to build a new delivery time estimate model for consumers ordering food delivery.

How would you determine if the new model predicts delivery times better than the old model?

When rolling out a new delivery time estimate model in production, what is an important consideration?

When rolling out a new delivery time estimate model in production, what is an important consideration?

Delivery Estimate Model I

What is one way to measure the performance of a new delivery time estimate model for food delivery?

What is one way to measure the performance of a new delivery time estimate model for food delivery?

Delivery Estimate Model II

In an A/B test, how can you check if assignment to the various buckets was truly random?

In an A/B test, which of the following is a common method to determine if the assignment to the test groups was truly random?

In an A/B test, which of the following is a common method to determine if the assignment to the test groups was truly random?

Random Bucketing

How can you check if assignment to the various buckets was truly random

Given a string, find the first non-repeating character in it and return its index. If it doesn’t exist, return -1.

Example questions:

Consider a string where all characters are lowercase alphabets.

Example 1:

Input:

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

Output:

<pre tabindex="0" class="chroma"><code>first_uniq_char(s) -&gt; 0
</code></pre>

In the string ‘helloworld’, the first non-repeating character is ‘h’, which is at index 0.

Example 2:

Input:

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

Output:

<pre tabindex="0" class="chroma"><code>first_uniq_char(s) -&gt; 4
</code></pre>

In the string ‘concussion’, the first non-repeating character is ‘u’, which is at index 4.

This problem involves finding the first non-repeating character in a given string. The solution involves iterating over the string and keeping track of the frequency of each character. The first character that has a frequency of 1 is the first non-repeating character.

Find the First Non-Repeating Character in a String

Write a function called <code>find_bigrams</code> that takes a sentence or paragraph of strings and returns a list of all its bigrams in order.

Note: A bigram is a pair of consecutive words.

Example:

Input:

<pre tabindex="0" class="chroma"><code>sentence = &#34;&#34;&#34;
Have free hours and love children? 
Drive kids to school, soccer practice 
and other activities.
&#34;&#34;&#34;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def find_bigrams(sentence) -&gt;

 [(&#39;have&#39;, &#39;free&#39;),
 (&#39;free&#39;, &#39;hours&#39;),
 (&#39;hours&#39;, &#39;and&#39;),
 (&#39;and&#39;, &#39;love&#39;),
 (&#39;love&#39;, &#39;children?&#39;),
 (&#39;children?&#39;, &#39;drive&#39;),
 (&#39;drive&#39;, &#39;kids&#39;),
 (&#39;kids&#39;, &#39;to&#39;),
 (&#39;to&#39;, &#39;school,&#39;),
 (&#39;school,&#39;, &#39;soccer&#39;),
 (&#39;soccer&#39;, &#39;practice&#39;),
 (&#39;practice&#39;, &#39;and&#39;),
 (&#39;and&#39;, &#39;other&#39;),
 (&#39;other&#39;, &#39;activities.&#39;)]
</code></pre>

Let’s say you’re a Product Data Scientist at Instagram. How would you measure the success of the Instagram TV product?

What is the primary goal of Instagram TV as a product feature?

What is the primary goal of Instagram TV as a product feature?

Instagram TV Success

How would you measure the success of the Instagram TV product

Write a function <code>calculate_rmse</code> to calculate the root mean squared error of a regression model. The function should take in two lists, one that represents the predictions <code>y_pred</code> and another with the target values <code>y_true</code>.

Input:

Example 1: 

<pre tabindex="0" class="chroma"><code>y_pred = [3,4,5]
y_true = [3,4,5]

def calculate_rmse(y_pred,y_true) -&gt; 0
</code></pre>

Example 2:

<pre tabindex="0" class="chroma"><code>y_pred = [3,4,5]
y_true = [5,4,3]

def calculate_rmse(y_pred,y_true) -&gt; 1.63
</code></pre>

Let’s say we have a sample size of \(n\). The margin of error for our sample size is 3.

How many more samples would we need to decrease the margin of error to 0.3?

Let's say we have a sample size of N. The margin of error for our sample size is 3.

How many more samples would we need to decrease the margin of error to 0.3?

Let's say we have a sample size of N. The margin of error for our sample size is 3.

How many more samples would we need to decrease the margin of error to 0.3?

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.

Identify tachycardia runs where heart rate stays above 100 bpm for at least 10 seconds and return run start, end, and duration

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