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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 the missing integer from a array of consequtive integers

Find the Missing Number

Find Bigrams

Minimum Change

Write a function to select only the rows where the student's favorite color is green or red and their grade is above 90.

Good Grades and Favorite Colors

Machine Learning

Interpret coefficients of logistic regression for categorical and boolean variables

Coefficients of Logistic Regression

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

Same Algorithm Different Success

Rebalancing outcome probabilities for a classifier on imbalanced data.

Rebalance Probabilities

Lasso vs Ridge

In which case would you use a bagging algorithm versus a boosting algorithm

Bagging vs Boosting

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

Subscription Overlap

Write a query to get the current salary for each employee after an ETL error.

Employee Salaries (ETL Error)

User Experience Percentage

Write a query to find the average downloads for free vs paying accounts by day, rounded to 2 decimals

Download Facts

Project Budget Error

Analytics

What metrics would you use to determine the value of each marketing channel?

Marketing Channel Metrics

We want to figure out if users are creating multiple accounts to upvote their own comments.

Fraudulent Upvotes

Create and write queries for health metrics for stack overflow 

Community Health Metrics

How would you present the performance of each subscription to an executive?

Analyzing Churn Behavior

What kind of analysis would you conduct to recommend changes to the UI?

User Journey Analysis

Behavioral

Describing a data project and its challenges

Hurdles In Data Projects

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

Decreasing Tech Debt

How would you negotiate and resolve disagreements when a client rejects your proposed solution?

Client Solution Pushback

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

Why Do You Want to Work With Us

What challenges might you face when deploying a new model to production and how would you address them?

Production Rollout Challenges

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

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>

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

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?

First to Six

Probability

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>

Given two tables: <code>accounts</code>, and <code>downloads</code>, find the average number of downloads for free vs paying accounts, broken down by day.

Note: You only need to consider accounts that have had at least one download before when calculating the average.

Note: round <code>average_downloads</code> to 2 decimal places.

Example:

Input:

<code>accounts</code> table

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

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

<tr>
<td><code>paying_customer</code></td>
<td>BOOLEAN</td>
</tr>
</tbody>
</table>
<code>downloads</code> table

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

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

<tr>
<td><code>download_date</code></td>
<td>DATETIME</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>download_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>paying_customer</code></td>
<td>BOOLEAN</td>
</tr>

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

Let’s say we have a table representing a company payroll schema.

Due to an ETL error, the employees table, instead of updating the salaries every year when doing compensation adjustments, did an insert instead. The head of HR still needs the current salary of each employee.

Write a query to get the current salary for each employee.

Note: Assume no duplicate combination of first and last names (I.E. No two John Smiths). Assume the <code>INSERT</code> operation works with <code>ID</code> autoincrement.

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>VARCHAR</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>
Output:

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

<tbody>
<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>
</tbody>
</table>

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?

Given tables <code>employees</code>,
<code>employee_projects</code>, and <code>projects</code>, find the 3 lowest-paid employees that have completed at least 2 projects.

Note: incomplete projects will have an end date of <code>NULL</code> in the projects table.

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>employee_projects</code> table

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

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

<tr>
<td><code>project_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<code>projects</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>title</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>start_date</code></td>
<td>DATE</td>
</tr>

<tr>
<td><code>end_date</code></td>
<td>DATE</td>
</tr>

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

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

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

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

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

Find the 3 lowest-paid employees that have completed at least 2 projects

Lowest Paid

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

We’re given two tables. One is named <code>projects</code> and the other maps employees to the projects they’re working on. 

We want to select the five most expensive projects by budget to employee count ratio. But let’s say that we’ve found a bug where there exist duplicate rows in the <code>employee_projects</code> table.

Write a query to account for the error and select the top five most expensive projects by budget to employee count ratio.

<h3>Schema</h3>

Input:

<code>projects</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>title</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>state_date</code></td>
<td>DATETIME</td>
</tr>

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

<tr>
<td><code>budget</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<code>employee_projects</code> table

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

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

<tr>
<td><code>employee_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>title</code></td>
<td>VARCHAR</td>
</tr>

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

<h3>Example</h3>

Input:

<code>projects</code> table

<table>
<thead>
<tr>
<th>id</th>
<th>title</th>
<th>start_date</th>
<th>end_date</th>
<th>budget</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>party</td>
<td>2006-04-17 00:00:00</td>
<td>2006-05-19 00:00:00</td>
<td>25875</td>
</tr>

<tr>
<td>2</td>
<td>diversity</td>
<td>2017-08-09 00:00:00</td>
<td>2017-09-18 00:00:00</td>
<td>77867</td>
</tr>

<tr>
<td>3</td>
<td>integration</td>
<td>2005-06-29 00:00:00</td>
<td>2005-07-19 00:00:00</td>
<td>75987</td>
</tr>

<tr>
<td>4</td>
<td>testing</td>
<td>2009-01-12 00:00:00</td>
<td>2009-05-03 00:00:00</td>
<td>35946</td>
</tr>

<tr>
<td>5</td>
<td>launch</td>
<td>2005-05-02 00:00:00</td>
<td>2005-10-16 00:00:00</td>
<td>66292</td>
</tr>

<tr>
<td>6</td>
<td>meet</td>
<td>2001-09-09 00:00:00</td>
<td>2002-04-04 00:00:00</td>
<td>71243</td>
</tr>

<tr>
<td>7</td>
<td>payroll</td>
<td>2019-09-25 00:00:00</td>
<td>2020-05-05 00:00:00</td>
<td>97071</td>
</tr>

<tr>
<td>8</td>
<td>admin</td>
<td>2000-07-08 00:00:00</td>
<td>2000-09-10 00:00:00</td>
<td>24000</td>
</tr>

<tr>
<td>9</td>
<td>petronas</td>
<td>2016-07-01 00:00:00</td>
<td>2016-11-28 00:00:00</td>
<td>37088</td>
</tr>

<tr>
<td>10</td>
<td>bel</td>
<td>2005-08-03 00:00:00</td>
<td>2006-04-29 00:00:00</td>
<td>61937</td>
</tr>
</tbody>
</table>
<code>employee_projects</code> table

<table>
<thead>
<tr>
<th>project_id</th>
<th>employee_id</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>7</td>
</tr>

<tr>
<td>1</td>
<td>9</td>
</tr>

<tr>
<td>2</td>
<td>6</td>
</tr>

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

<tr>
<td>3</td>
<td>2</td>
</tr>

<tr>
<td>4</td>
<td>5</td>
</tr>

<tr>
<td>5</td>
<td>3</td>
</tr>

<tr>
<td>5</td>
<td>4</td>
</tr>

<tr>
<td>6</td>
<td>8</td>
</tr>

<tr>
<td>8</td>
<td>10</td>
</tr>

<tr>
<td>9</td>
<td>11</td>
</tr>

<tr>
<td>10</td>
<td>12</td>
</tr>

<tr>
<td>5</td>
<td>5</td>
</tr>

<tr>
<td>9</td>
<td>11</td>
</tr>

<tr>
<td>6</td>
<td>8</td>
</tr>

<tr>
<td>4</td>
<td>5</td>
</tr>
</tbody>
</table>
Output:

<table>
<thead>
<tr>
<th>title</th>
<th>budget_per_employee</th>
</tr>
</thead>

<tbody>
<tr>
<td>diversity</td>
<td>77867</td>
</tr>

<tr>
<td>meet</td>
<td>71243</td>
</tr>

<tr>
<td>bel</td>
<td>61937</td>
</tr>

<tr>
<td>integration</td>
<td>37993.5</td>
</tr>

<tr>
<td>petronas</td>
<td>37088</td>
</tr>
</tbody>
</table>

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

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

Raining in Seattle

You have an array of integers, <code>nums</code> of length <code>n</code> spanning <code>0</code> to <code>n</code> with one missing. Write a function <code>missing_number</code> that returns the missing number in the array.

Note: Complexity of \(O(n)\) required.

Example:

Input:

<pre tabindex="0" class="chroma"><code>nums = [0,1,2,4,5] 
missing_number(nums) -&gt; 3
</code></pre>

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>

Consider a trip from one city to another that may contain many layovers. Given the list of flights out of order, each with a starting city and end city, write a function <code>plan_trip</code> to reconstruct the path of the trip so the trip tickets are in order.

Example:

For a trip from Bombay to Beijing:

Input:

<pre tabindex="0" class="chroma"><code>flights = [
 [&#39;Chennai&#39;, &#39;Bangalore&#39;], 
 [&#39;Bombay&#39;, &#39;Delhi&#39;], 
 [&#39;Goa&#39;, &#39;Chennai&#39;], 
 [&#39;Delhi&#39;, &#39;Goa&#39;], 
 [&#39;Bangalore&#39;, &#39;Beijing&#39;]
]
output = [
 [&#39;Bombay&#39;, &#39;Delhi&#39;], 
 [&#39;Delhi&#39;, &#39;Goa&#39;], 
 [&#39;Goa&#39;, &#39;Chennai&#39;], 
 [&#39;Chennai&#39;, &#39;Bangalore&#39;], 
 [&#39;Bangalore&#39;, &#39;Beijing&#39;],
]
</code></pre>

Reconstruct the path of a trip so that the trip tickets are in order.

Scrambled Tickets

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

We’re given two tables. One is named <code>projects</code> and the other maps employees to the projects they’re working on.

Write a query to get the top five most expensive projects by budget to employee count ratio.

Note: Exclude projects with 0 employees. Assume each employee works on only one project.

<code>projects</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>title</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>state_date</code></td>
<td>DATETIME</td>
</tr>

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

<tr>
<td><code>budget</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<code>employee_projects</code> table

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

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

<tr>
<td><code>employee_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>title</code></td>
<td>VARCHAR</td>
</tr>

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

Write a query to get the top five projects by budget-to-employee-count ratio

Employee Project Budgets

Let’s say we’re comparing two machine learning algorithms. In which case would you use a bagging algorithm versus a boosting algorithm? 

Give an example of the tradeoffs between the two.

In machine learning, when would you use a bagging algorithm over a boosting algorithm?

In machine learning, when would you use a bagging algorithm over a boosting algorithm?

Bagging vs. Boosting

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>

Suppose we have two coins. One is fair and the other biased where the probability of it coming up heads is 3⁄4.

Let’s say we select a coin at random and flip it two times. What is the probability that both flips result in the same side?

Suppose we have two coins. One is fair and the other biased where the probability of it coming up heads is 3/4. You select a coin at random and flip it two times. What is the probability that both flips result in the same side?

Suppose we have two coins. One is fair and the other biased where the probability of it coming up heads is 3/4. You select a coin at random and flip it two times. What is the probability that both flips result in the same side?

Same Side Probability

What is the probability that both flips result in the same side?

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

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

You’re given a dataframe of students named <code>students_df</code>:

<code>students_df</code> table

<table>
<thead>
<tr>
<th>name</th>
<th>age</th>
<th>favorite_color</th>
<th>grade</th>
</tr>
</thead>

<tbody>
<tr>
<td>Tim Voss</td>
<td>19</td>
<td>red</td>
<td>91</td>
</tr>

<tr>
<td>Nicole Johnson</td>
<td>20</td>
<td>yellow</td>
<td>95</td>
</tr>

<tr>
<td>Elsa Williams</td>
<td>21</td>
<td>green</td>
<td>82</td>
</tr>

<tr>
<td>John James</td>
<td>20</td>
<td>blue</td>
<td>75</td>
</tr>

<tr>
<td>Catherine Jones</td>
<td>23</td>
<td>green</td>
<td>93</td>
</tr>
</tbody>
</table>
Write a function named <code>grades_colors</code> to select only the rows where the student’s favorite color is green or red and their grade is above 90.

Example:

Input:

<pre tabindex="0" class="chroma"><code>import pandas as pd

students = {&#34;name&#34; : [&#34;Tim Voss&#34;, &#34;Nicole Johnson&#34;, &#34;Elsa Williams&#34;, &#34;John James&#34;, &#34;Catherine Jones&#34;], &#34;age&#34; : [19, 20, 21, 20, 23], &#34;favorite_color&#34; : [&#34;red&#34;, &#34;yellow&#34;, &#34;green&#34;, &#34;blue&#34;, &#34;green&#34;], &#34;grade&#34; : [91, 95, 82, 75, 93]}

students_df = pd.DataFrame(students)
</code></pre>

Output:

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

<table>
<thead>
<tr>
<th>name</th>
<th>age</th>
<th>favorite_color</th>
<th>grade</th>
</tr>
</thead>

<tbody>
<tr>
<td>Tim Voss</td>
<td>19</td>
<td>red</td>
<td>91</td>
</tr>

<tr>
<td>Catherine Jones</td>
<td>23</td>
<td>green</td>
<td>93</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

Write a function <code>get_ngrams</code> to take in a word (string) and return a dictionary of n-grams and their frequency in the given string.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>string = &#39;banana&#39; 
n=2
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>output = {&#39;ba&#39;:1, &#39;an&#39;:2, &#39;na&#39;:2} 
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>string = &#39;banana&#39; 
n=3 
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>output = {&#39;ban&#39;:1, &#39;ana&#39;:2, &#39;nan&#39;:1}
</code></pre>

Write a function get_ngrams to return a dictionary of n-grams and their frequency in a string

N-gram Dictionary

You have been given a table <code>tbl_numbers</code> with only one column: <code>int_numbers</code>. It can have one integer number value per row in a sequential manner.

Write a query to return the number repeated by one times its own value.

For example, the integer number 5 would appear five times in the output (1 times 5).

Example:

Input:

<code>tbl_numbers</code> table

<table>
<thead>
<tr>
<th>int_numbers</th>
</tr>
</thead>

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

<tr>
<td><code>2</code></td>
</tr>

<tr>
<td><code>3</code></td>
</tr>

<tr>
<td><code>4</code></td>
</tr>
</tbody>
</table>
Output:

<table>
<thead>
<tr>
<th>seq_numbers</th>
</tr>
</thead>

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

<tr>
<td><code>2</code></td>
</tr>

<tr>
<td><code>2</code></td>
</tr>

<tr>
<td><code>3</code></td>
</tr>

<tr>
<td><code>3</code></td>
</tr>

<tr>
<td><code>3</code></td>
</tr>

<tr>
<td><code>4</code></td>
</tr>

<tr>
<td><code>4</code></td>
</tr>

<tr>
<td><code>4</code></td>
</tr>

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

Write a query to repeat each int_numbers value by its own value in the output

Sequentially Fill in Integers

Given a list of integers, write a function <code>gcd</code> to find the greatest common denominator between them.

Example:

Input:

<pre tabindex="0" class="chroma"><code>int_list = [8, 16, 24]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def gcd(int_list) -&gt; 8
</code></pre>

Which of the following is true about the greatest common division (gcd) between three integers a, b, and c?

Which of the following is true about the greatest common division (gcd) between three integers a, b, and c?

Greatest Common Denominator Properties

Write a function gcd to find the greatest common denominator of a list of integers

Greatest Common Denominator

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

Given a <code>ListNode</code> representing the head of a linked list, write a function <code>is_cyclic</code> which returns <code>True</code> if a linked list is cyclic and <code>False</code> if it is not. A linked list is cyclic when there is no tail to the linked list, and the supposed tail is attached to another node inside the list itself, creating a cycle.

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

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

Example:

Input:

<img src="/s3/questions/1a65651d-a483-4481-b073-2738d65ab9d7.png" alt="image"/>

Output:

<pre tabindex="0" class="chroma"><code>def is_cyclic(head) -&gt; True
</code></pre>

Cyclic Detection

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.

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