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Nintendo Interview Questions

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Data Structures & Algorithms

Write a function moving_window to find the moving window average

Moving Window

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

Convert a list of integers into their Roman numeral representations

Integer to Roman

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

Nearest Common Ancestor

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

Statistics

Write a function compute_deviation that returns the standard deviation of each list in a list of dictionaries

Compute Deviation

What metrics would you use to describe the distribution of time spent per day on Facebook

Time on FB Distribution

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

P-value to a Layman

Write a function that outputs the sample variance given a list of integers

Compute Variance

Write a function to bootstrap the confidence interface for a list of integers

Bootstrapping Confidence Intervals

Product Sense & Metrics

How would you measure the success of Facebook Groups

Group Success

What would you investigate to diagnose what's happening?

WAU vs Open Rates

Google Maps Improvement

Unified Inbox

What testing strategies and metrics would you use to determine the success of stories

Stories Success

Machine Learning

What kind of model did the co-worker develop, how would you measure the difference between the two credit risk models within a timeframe, and what metrics would you track to measure the success of the new model

Loan Model

What metrics would you use to track accuracy and validity of the model

Spam Classifier 

How would you evaluate whether a decision tree is the right model and assess its performance before and after deployment

Decision Tree Evaluation

How would you build a model or algorithm to generate respawn locations for an online third person shooter game like Halo?

Video Game Respawn Model

Build a k Nearest Neighbors classification model from scratch.

KNN From Scratch

Select the 2nd highest salary in the engineering department

2nd Highest Salary

Find the average yearly purchases for each product

Average Quantity

Subscription Retention

How would you design a data warehouse for a e-commerce company looking to expand internationally?

International e-Commerce Warehouse

How do you calculate weekly active paying users (WAPU) by joining gameplay and purchase activity by week?

Track Your Most Valuable Gamers

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>

Write a function <code>compute_deviation</code> that takes in a list of dictionaries with a key and list of integers and returns a dictionary with the standard deviation of each list.

Note: This should be done without using the NumPy built-in functions.

Example:

Input:

<pre tabindex="0" class="chroma"><code>input = [
 {
 &#39;key&#39;: &#39;list1&#39;,
 &#39;values&#39;: [4,5,2,3,4,5,2,3],
 },
 {
 &#39;key&#39;: &#39;list2&#39;,
 &#39;values&#39;: [1,1,34,12,40,3,9,7],
 }
]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code> output = {&#39;list1&#39;: 1.12, &#39;list2&#39;: 14.19}
</code></pre>

Given a table of <code>transactions</code>, write a query to find the average quantity of each product purchased per transaction each year.

The output should include the year, product_id, and average quantity of the product purchased per transaction that year. The output table should be sorted by year and product_id in ascending order. The value for avg_quantity should be rounded to two decimal places.

Example:

Input:
<code>transactions</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>user_id</code></td>
<td>INTEGER</td>
</tr>

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

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

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

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

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

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

<tr>
<td><code>avg_quantity</code></td>
<td>DECIMAL</td>
</tr>
</tbody>
</table>

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

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

Button AB Test

A/B Testing

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

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

Given the integer list nums with length n, create a function that converts each integer in the list into its corresponding Roman numeral representation. The Roman numeral symbols and corresponding values are provided in the table below. The function must be able to handle integers up to 1000.

<table>
<thead>
<tr>
<th>Symbols</th>
<th>Values</th>
</tr>
</thead>

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

<tr>
<td>IV</td>
<td>4</td>
</tr>

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

<tr>
<td>IX</td>
<td>9</td>
</tr>

<tr>
<td>X</td>
<td>10</td>
</tr>

<tr>
<td>XL</td>
<td>40</td>
</tr>

<tr>
<td>L</td>
<td>50</td>
</tr>

<tr>
<td>XC</td>
<td>90</td>
</tr>

<tr>
<td>C</td>
<td>100</td>
</tr>

<tr>
<td>CD</td>
<td>400</td>
</tr>

<tr>
<td>D</td>
<td>500</td>
</tr>

<tr>
<td>CM</td>
<td>900</td>
</tr>

<tr>
<td>M</td>
<td>1000</td>
</tr>
</tbody>
</table>

<h3>Examples:</h3>

Input:

<pre tabindex="0" class="chroma"><code>nums = [1, 4, 179]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>[&#34;I&#34;, &#34;IV&#34;, &#34;CLXXIX&#34;]
</code></pre>

How would you measure the success of Facebook Groups?

Considering the purpose of Facebook Groups as a platform for connecting users through shared interests or real-life relationships, which metrics would be appropriate to measure the success of these groups?

Considering the purpose of Facebook Groups as a platform for connecting users through shared interests or real-life relationships, which metrics would be appropriate to measure the success of these groups?

One of your favorite sports teams is playing at a local stadium, but you waited until the last minute to buy a ticket.

You can buy a scalped (second-hand) ticket for $50, which has a 20% chance of not working. If the scalped ticket doesn’t work, you’ll have to buy a box office ticket for $70 at the stadium.

<ol>
<li>How much do you expect to pay to go to the sports game?</li>
<li>How much money should you set aside for the game?</li>
</ol>

How much do you expect to pay and how much money should you set aside for the game

Scalped Ticket

Let’s say you have a time series dataset grouped monthly for the past five years.

How would you find out if the difference between this month and the previous month was significant or not?

How would you find out if the difference between this month and the previous month was significant or not

Significance Time Series

Forecasting & Time Series

Write a function that outputs the (sample) variance given a list of integers.

Note: round the result to 2 decimal places.

Example:

Input:

<pre tabindex="0" class="chroma"><code>test_list = [6, 7, 3, 9, 10, 15]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>get_variance(test_list) -&gt; 13.89
</code></pre>

Given that $X$ and $Y$ are independent random variables with normal distributions, what is the mean and variance of the distribution of $2X - Y$ when the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$?

Given that $X$ and $Y$ are independent random variables with normal distributions, and the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$, what is the mean of the distribution of $2X - Y$?

Given that $X$ and $Y$ are independent random variables with normal distributions, and the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$, what is the mean of the distribution of $2X - Y$?

Distribution of 2X - Y I

Given that $X$ and $Y$ are independent random variables with normal distributions, and the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$, what is the variance of the distribution of $2X - Y$?

Given that $X$ and $Y$ are independent random variables with normal distributions, and the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$, what is the variance of the distribution of $2X - Y$?

Distribution of 2X - Y II

What is the mean and variance of 2X - Y when X~N(3, 4) and Y~N(1, 4)

Distribution of 2X - Y

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>

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>

Blizzard Entertainment operates a global network of games and services, each generating massive volumes of real-time gameplay and infrastructure events, everything from player actions in Overwatch to server status updates for World of Warcraft. You are tasked with building a centralized system to reliably ingest, process, and distribute these events across the company for analytics, live operations, and player-facing features.

How would you architect the data ingestion and processing pipeline for this event system?

Design a scalable event data pipeline for real-time, multi-application ingestion and processing.

Centralized Event Ingestion

Data Pipelines

You’re an analyst at Ubisoft Gaming. Leadership wants to track Weekly Active Paying Users (WAPU), players who record at least one game session and at least one in-app purchase in the same calendar week.

Write a SQL query that returns, for each week in the dataset:

<ol>
<li><code>week_start</code>- the Monday of that calendar week 
</li>
<li><code>wapu</code>- the number of distinct users who qualify as WAPU in that week 
</li>
</ol>

Note: Assume all timestamps are in UTC. Output should be ordered by <code>week_start</code> ascending.

<h3>Schema:</h3>

Input:

<code>game_sessions</code> table

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

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

<tr>
<td>session_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>session_start</td>
<td>TIMESTAMP</td>
</tr>

<tr>
<td>country</td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<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>user_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>purchase_time</td>
<td>TIMESTAMP</td>
</tr>

<tr>
<td>amount</td>
<td>DECIMAL(10,2)</td>
</tr>
</tbody>
</table>
Output:

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

<tbody>
<tr>
<td>week_start</td>
<td>TIMESTAMP</td>
</tr>

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

<h3>Example:</h3>

Input:

<code>game_sessions</code> table

<table>
<thead>
<tr>
<th>user_id</th>
<th>session_id</th>
<th>session_start</th>
<th>country</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>101</td>
<td>2023-10-02</td>
<td>USA</td>
</tr>

<tr>
<td>2</td>
<td>102</td>
<td>2023-10-03</td>
<td>USA</td>
</tr>

<tr>
<td>1</td>
<td>103</td>
<td>2023-10-04</td>
<td>USA</td>
</tr>

<tr>
<td>3</td>
<td>104</td>
<td>2023-10-05</td>
<td>USA</td>
</tr>
</tbody>
</table>
<code>purchases</code> table

<table>
<thead>
<tr>
<th>purchase_id</th>
<th>user_id</th>
<th>purchase_time</th>
<th>amount</th>
</tr>
</thead>

<tbody>
<tr>
<td>201</td>
<td>1</td>
<td>2023-10-02</td>
<td>5.99</td>
</tr>

<tr>
<td>202</td>
<td>2</td>
<td>2023-10-03</td>
<td>10.00</td>
</tr>

<tr>
<td>203</td>
<td>1</td>
<td>2023-10-04</td>
<td>2.99</td>
</tr>

<tr>
<td>204</td>
<td>3</td>
<td>2023-10-05</td>
<td>7.49</td>
</tr>
</tbody>
</table>
Output:

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

<tbody>
<tr>
<td>week_start</td>
<td>2023-10-02</td>
</tr>

<tr>
<td>wapu</td>
<td>3</td>
</tr>
</tbody>
</table>
Explanation:

All sessions and purchases occur during the same calendar week:

<ul>
<li>Week start: Monday 2023-10-02</li>
</ul>

Users who qualify as WAPU (≥1 session AND ≥1 purchase in the same week):

<ul>
<li>User 1 - sessions on Oct 2 &amp; 4; purchases on Oct 2 &amp; 4</li>
<li>User 2 - session on Oct 3; purchase on Oct 3</li>
<li>User 3 - session on Oct 5; purchase on Oct 5</li>
</ul>

Total WAPU = 3 users

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>

Write a function that takes an input as the number of tosses and a probability of heads and return a list of randomly generated results equal in length to the number of tosses. Each result represents the outcome of a coin toss, where ‘H’ represents heads and ’T’ represents tails.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>tosses = 5
probability_of_heads = 0.6
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>coin_toss(tosses, probability_of_heads) -&gt; [&#39;H&#39;, &#39;T&#39;, &#39;H&#39;, &#39;H&#39;, &#39;T&#39;]
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>tosses = 3
probability_of_heads = 0.2
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>coin_toss(tosses, probability_of_heads) -&gt; [&#39;T&#39;, &#39;T&#39;, &#39;T&#39;]
</code></pre>

The output may vary due to the randomness of coin tosses.

Simulate a series of coin tosses given the number of tosses and the probability of getting heads.

Simulating Coin Tosses

Let’s say you’re given all the different marketing channels along with their respective marketing costs at a company called Mode, that sells B2B analytics dashboards.

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

When determining the value of each marketing channel for the company Mode, which metric is considered the key metric?

When determining the value of each marketing channel for the company Mode, which metric is considered the key metric?

Marketing Channel Metrics

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

Analytics

What do you think the distribution of time spent per day on Facebook looks like? What metrics would you use to describe that distribution?

Tower of Hanoi is a fun puzzle game that consists of a set of <code>3</code> pegs (<code>A</code>, <code>B</code>, <code>C</code>) and <code>n</code> number of disks. You are required to move all disks from the source peg <code>A</code> to destination peg <code>C</code>, under the following conditions:

<ul>
<li>You can only move one disk for each action.</li>
<li>You can only move the disk onto the top of another peg; you cannot place it off to the side or under existing disks.</li>
<li>You cannot place a larger disk onto a smaller disk.</li>
</ul>

Initially, all disks are on the source <code>A</code> peg and sorted by decreasing width from bottom to the top (widest on the bottom, smallest on the top).

You must develop an algorithm to move all disks from <code>A</code> to the destination peg <code>C</code> with the optimal solution. Also, return every step made from the starting state to the final state.

<img src="https://i.ibb.co/my0Vm13/initail.png" alt="alt"/>

<img src="https://i.ibb.co/0Ftzs7D/final.png" alt="alt"/>

Example

Input:

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

Output:

<pre tabindex="0" class="chroma"><code>#return list of {&#34;A&#34;:[],&#34;B&#34;:[],&#34;C&#34;:[]} 
tower_of_hanoi_solver(n) -&gt; [
 {&#34;A&#34;: [1, 2, 3], &#34;B&#34;: [], &#34;C&#34;: []},
 {&#34;A&#34;: [2, 3], &#34;B&#34;: [], &#34;C&#34;: [1]},
 {&#34;A&#34;: [3], &#34;B&#34;: [2], &#34;C&#34;: [1]},
 {&#34;A&#34;: [3], &#34;B&#34;: [1, 2], &#34;C&#34;: []},
 {&#34;A&#34;: [], &#34;B&#34;: [1, 2], &#34;C&#34;: [3]},
 {&#34;A&#34;: [1], &#34;B&#34;: [2], &#34;C&#34;: [3]},
 {&#34;A&#34;: [1], &#34;B&#34;: [], &#34;C&#34;: [2, 3]},
 {&#34;A&#34;: [], &#34;B&#34;: [], &#34;C&#34;: [1, 2, 3]}
 ]
</code></pre>

What is the minimal number of steps needed to solve the Tower of Hanoi problem with n disks?

What is the minimal number of steps needed to solve the Tower of Hanoi problem with *n* disks?

Linear Data Structures

Write an algorithm to solve Tower of Hanoi optimally and return every step from A to C

Tower of Hanoi

Let’s say you’re working on a building a better search engine for Google. You build it and want to see if it serves better results than the existing one in production.

How would you determine which search engine performed better? Which metrics would you track?

How would you determine which search engine performed better and which metrics would you track

Comparing Search Engines

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.

Let’s say you are tasked with building a spam classifier for emails. Assume that you’ve built a V1 of the model.

What metrics would you use to track accuracy and validity of the model?

Let’s say that you’re in charge of Square’s small business division. 

The CEO wants to hire a customer success manager to help manage a new software product. Another executive thinks that it’s worth just instituting a free trial instead.

What would be your recommendation on utilizing a customer success manager versus just a free trial to get new or existing customers to use the new product?

What would be your recommendation on utilizing a customer success manager versus just a free trial to get new or existing customers to use the new product

Customer Success vs. Free Trial

Business Case

Let’s say we’re testing a new UI with the goal to increase conversion rates. We test it by giving the new UI to a random subset of users.

The test variant wins by 5% on the target metric. What would you expect to happen after the new UI is applied to all users? Will the metric actually go up by ~5%, more, or less?

Note: Assume there is no novelty effect.

What would you expect to happen after the new UI is applied to all users?

New UI Effect

How would you build a model or algorithm to generate respawn locations for an online third person shooter game like Halo?

When designing an algorithm to generate respawn locations in an online game, what aspects must be considered to ensure long-term player engagement?

When designing an algorithm to generate respawn locations in an online game, what aspects must be considered to ensure long-term player engagement?

Video Game Respawn Model I

Why should respawn locations in a game like Halo not be constant?

Why should respawn locations in a game like Halo not be constant?

Video Game Respawn Model II

Build a $k$ Nearest Neighbors classification model from scratch with the following conditions:

<ul>
<li>Use Euclidian distance (aka, the “2 norm”) as your closeness metric</li>
<li>Your function should be able to handle data frames of arbitrary many rows and columns</li>
<li>If there is a tie in the class of the $k$ nearest neighbors, rerun the search using $k-1$ neighbors instead</li>
<li>You may use <code>pandas</code> and <code>numpy</code> but NOT <code>scikit-learn</code></li>
</ul>

Example:

Input:

<pre tabindex="0" class="chroma"><code>k = 5
new_point = [0.5,-2,8]
print(data)
...
 Var1 Var2 Var3 Target
0 -3.279536 3.362223 2.847892 2
1 -0.791565 1.742475 2.151587 2
2 -0.785992 -0.938681 -0.459770 0
3 -1.068190 1.461051 0.127130 3
4 -0.367568 -0.870240 -0.225734 0
.. ... ... ... ...
95 -1.327175 1.971085 -0.690689 2
96 -3.203714 1.847649 0.778901 2
97 -0.587640 0.647458 2.094385 2
98 0.363644 -0.509795 2.514191 1
99 -0.673498 2.955285 2.102122 4

[100 rows x 4 columns]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def kNN(k, new_point, data) -&gt; 2
</code></pre>

You are given an array of numerical values, bootstrap samples, and size for a confidence interval.

Write a function that performs bootstrap sampling on the given array and calculates the confidence interval based on the given size.

Note: The function should return a tuple containing the minimum and maximum values of the confidence interval rounded to the tenths place.

Example

Input:

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

Output

<pre tabindex="0" class="chroma"><code>bootstrap_conf_interval(values, 1000, 0.95) -&gt; (1.2, 4.8)
</code></pre>

In this case, the function returns a tuple indicating that we are 95% confident that the population parameter lies between 1.2 and 4.8 based on our bootstrap samples.

Note: Results may vary due to the randomness of bootstrap sampling.

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