Prepare for and practice interview questions from Twin health.

Twin health Interview Questions

Twin health Interview Guides

Data Structures & Algorithms

Given an integer N, write a function that returns all of the prime numbers up to N

Prime to N

Write a function str_map to determine if there exists a one-to-one correspondence between characters of string1 and string2

String Mapping

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

Target Indices

Write a function to retrieve the combination that allows you to spend all of your store credit while getting at least two books at the lowest weight.

Book Combinations

Write a function `sorting` from scratch to sort a list of strings in ascending alphabetical order

Sort Strings

Machine Learning

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

Bagging vs Boosting

How does random forest generate the forest and why use it over logistic regression

Random Forest Explanation

choosing k value during k-means clustering

Choosing k

How would you justify the complexity of building such a model and explain the predictions to non-technical stakeholders

Justify a Neural Network

Design a function to detect anomalies in univariate and bivariate data

Variate Anomalies

Select the 2nd highest salary in the engineering department

2nd Highest Salary

Get the top 3 highest employee salaries by department

Top Three Salaries

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

Employee Salaries (ETL Error)

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

Top 3 Users

Create top_ads with the top 3 ads and return the row counts for inner, left, right, and cross joins with ads

Size of Joins

Behavioral

Strategically resolving misaligned expectations with stakeholders for a successful project outcome

Stakeholder Communication

Describing a data project and its challenges

Hurdles In Data Projects

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

How would you analyze and optimize a low-performing marketing automation workflow?

Marketing Workflow Optimization

A/B Testing

How would you assess the validity of the result?

Experiment Validity

Button AB Test

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

Network Experiment Design

What kind of analysis would you run and how would you measure which variant won

Non-Normal AB Testing

How would you approach limited testing time before a major app release?

Testing Constraints

If given a univariate dataset, how would you design a function to detect anomalies?

What if the data is bivariate?

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>

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 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>

Given an integer <code>N</code>, write a function that returns a list of all of the prime numbers up to <code>N</code>.

Note: Return an empty list there are no prime numbers less than or equal to <code>N</code>.

Example:

Input:

<pre tabindex="0" class="chroma"><code>N = 3
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def prime_numbers(N) -&gt; [2,3]
</code></pre>

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 a dictionary with weights, write a function <code>random_key</code> that returns a key at random with a probability proportional to the weights.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>weights = {&#39;A&#39;: 1, &#39;B&#39;: 2}
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>random_key(weights) -&gt; return A 1/3 of the time, B 2/3 of the time
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>weights = {&#39;A&#39;: 1, &#39;B&#39;: 1}
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>random_key(weights) -&gt; return A 1/2 of the time, B 1/2 of the time
</code></pre>

Weighted Keys

Probability

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

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

How would you set up this test?

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

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

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

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

A/B Test Variants

Let’s say 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>

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

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?

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

Detecting ECG Tachycardia Runs

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

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

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

Let’s say that you’re looking at the metrics of a job board. You see that the number of job postings per day has more or less remained the same the last few months but the number of applicants that have applied to jobs has steadily been decreasing.

Why would this be happening?

Why would the number of applicants be steadily decreasing while job postings remain the same

Declining Applicants

Business Case

How does random forest generate the forest? Additionally, why would we use it over other algorithms such as logistic regression?

What happens when you average the output on multiple decision trees?

What happens when you average the output on multiple decision trees?

Average Trees

Given a list of strings, write a function, <code>sorting</code> from scratch to sort the list in ascending alphabetical order.

Notes:
- Do NOT use the built-in <code>sorted</code> function
- Return the new sorted list, rather than modifying the list in-place

Bonus: Have your solution be \(O(n log(n))\).

Example:

Input:

<pre tabindex="0" class="chroma"><code>array = [&#34;apple&#34;, &#34;cat&#34;, &#34;banana&#34;, &#34;zoo&#34;, &#34;football&#34;]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def sorting(array) -&gt; [&#34;apple&#34;, &#34;banana&#34;, &#34;cat&#34;, &#34;football&#34;, &#34;zoo&#34;]
</code></pre>

Given two strings, <code>string1</code> and <code>string2</code>, write a function <code>str_map</code> to determine if there exists a one-to-one correspondence (bijection) between the characters of <code>string1</code> and <code>string2</code>.

For the two strings, our correspondence must be between characters in the same position/index.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>string1 = &#39;qwe&#39;
string2 = &#39;asd&#39;

string_map(string1, string2) == True

# q = a, w = s, and e = d
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>string1 = &#39;donut&#39;
string2 = &#39;fatty&#39;

string_map(string1, string2) == False
# cannot map two distinct characters to two equal characters
</code></pre>

Example 3:

Input:

<pre tabindex="0" class="chroma"><code>string1 = &#39;enemy&#39;
string2 = &#39;enemy&#39;

string_map(string1, string2) == True
# there exists a one-to-one correspondence between equivalent strings
</code></pre>

Example 4:

Input:

<pre tabindex="0" class="chroma"><code>string1 = &#39;enemy&#39;
string2 = &#39;ymene&#39;

string_map(string1, string2) == False
# since our correspondence must be between characters of the same index, this case returns &#39;False&#39; as we must map e = y AND e = e
</code></pre>

Given a 2-D matrix P of predicted values and actual values, write a function precision_recall to calculate precision and recall metrics.

Return the ordered pair (precision, recall).

Example:

Input:

<pre tabindex="0" class="chroma"><code>
P = [[121, 9],
 [17, 144]]
</code></pre>

where P represents the following table

<table>
<thead>
<tr>
<th></th>
<th>Predicted =TRUE</th>
<th>Predicted =FALSE</th>
</tr>
</thead>

<tbody>
<tr>
<td>Actual =TRUE</td>
<td>121</td>
<td>9</td>
</tr>

<tr>
<td>Actual =FALSE</td>
<td>17</td>
<td>144</td>
</tr>
</tbody>
</table>
Output:

<pre tabindex="0" class="chroma"><code>def precision_recall(P) -&gt; (0.931, 0.877,)
</code></pre>

Write a function to calculate precision and recall metrics.

Precision and Recall

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

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

Example 1:

Input:

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

Example 2:

Input:

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

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

Most Repetition

Given two strings, write a function to return <code>True</code> if the strings are anagrams of each other and <code>False</code> if they are not.

Note: A word is not an anagram of itself.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>string_1 = &#34;listen&#34;
string_2 = &#34;silent&#34;
</code></pre>

Output:

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

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>string_1 = &#34;banana&#34;
string_2 = &#34;bandana&#34;
</code></pre>

Output:

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

Write a function to return True if two strings are anagrams of each other and False if they are not

Valid Anagram

Given a list of integers, identify all the duplicate values in the list. Assume that the list can contain both positive and negative numbers, and the order of the list does not matter. A number is considered a duplicate if it appears more than once in the list. Return a list of the duplicate numbers.

Example 1:

Input:

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

Output:

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

The numbers 1, 2, and 3 all appear more than once in the list, so they are considered duplicates.

Example 2:

Input:

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

Output:

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

The numbers -1 and 3 both appear more than once in the list, so they are considered duplicates. Note that the order of the output does not matter.

Example 3:

Input:

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

Output:

<pre tabindex="0" class="chroma"><code>find_duplicates(nums) -&gt; []
</code></pre>

None of the numbers in the list appear more than once, so there are no duplicates.

This problem involves identifying duplicate numbers in a list of integers. The function should return a list of the duplicate numbers.

Find Duplicate Numbers in a List

Explain the difference between the XGBoost and random forest algorithms and give an example where you would use one over the other.

Why might a data scientist choose to use XGBoost instead of Random Forest for a particular machine learning task?

Why might a data scientist choose to use XGBoost instead of Random Forest for a particular machine learning task?

XGBoost vs Random Forest: Choice

Explain the difference between XGBoost and random forest and give an example where you would use one over the other

Xgboost vs Random Forest

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

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

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

Example 1:

Input:

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

Output:

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

Example 2:

Input:

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

Output:

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

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

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. It is often used in algorithm examples, and is defined by the following formula: F(n) = F(n-1) + F(n-2), with F(0) = 0 and F(1) = 1.

Your task is to implement the Fibonacci algorithm in three different methods:
1. Recursively
2. Iteratively
3. Using Memoization

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>n = 5
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>fibonacci(n) -&gt; 5
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>n = 10
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>fibonacci(n) -&gt; 55
</code></pre>

The Fibonacci sequence starts as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

This question requires the implementation of the Fibonacci sequence using three different methods: recursively, iteratively, and using memoization.

Implementing the Fibonacci Sequence in Three Different Methods

Priority queues are an abstract data structure responsible for allowing enqueuing items with an attached priority. While typically implemented with a heap, implement a priority queue using a linked list.

The Priority Queue implementation should support the following operations:

<ul>
<li><code>insert</code>(element, priority): This operation should be able to insert an element into the Priority Queue, along with its corresponding priority.</li>
<li><code>delete()</code>: This operation should remove and return the element with the highest priority. If multiple elements share the same highest priority, the element first enqueued should be returned. In the case that the queue is empty, return None.</li>
<li><code>peek()</code>: This operation should return the element with the highest priority without removing it from the Priority Queue. Again, in the case of equal highest priorities, the element first enqueued should be returned. In the case that the queue is empty, return None.</li>
</ul>

Note: Smaller priority values imply that they have higher priority.

<h3>Input</h3>

<pre tabindex="0" class="chroma"><code>queue.insert(2, 1)
queue.insert(3, 3)
</code></pre>

<h3>Output:</h3>

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

Implementing a priority queue used linked lists.

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