Prepare for and practice interview questions from MSCI across topics like SQL, Algorithms, Analytics and more.

MSCI Interview Questions

MSCI Interview Guides

Data Structures & Algorithms

Find the missing integer from a array of consequtive integers

Find the Missing Number

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

Prime to N

String Subsequence

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

Rectangle Overlap

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

Behavioral

Describing a data project and its challenges

Hurdles In Data Projects

What do you tell an interviewer when they ask you what your strengths and weaknesses are?

Your Strengths and Weaknesses

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

Why Do You Want to Work With Us

Machine Learning

Bank Fraud Model

Decision Tree Evaluation

What is the difference between Logistic and Linear Regression?

Linear vs Logistic Regression

Statistics

What are the assumptions of linear regression?

Assumptions of Linear Regression

What are confidence intervals and how are they useful

Confidence Interval Explanation

Concurrent & Distributed Systems

Design a scalable messenger system using OOP principles and write a technical design document.

Messenger Service Design

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>

Subscription Overlap

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>

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>

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

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

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

Example:

Input:

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

Output:

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

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

Given two strings, <code>string1</code> and <code>string2</code>, write a function <code>is_subsequence</code> to find out if <code>string1</code> is a subsequence of <code>string2</code>.

Bonus: A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

Example:

Input:

<pre tabindex="0" class="chroma"><code>string1 = &#39;abc&#39;
string2 = &#39;asbsc&#39;
string3 = &#39;acedb&#39;

is_subsequence(string1, string2) -&gt; True
is_subsequence(string1, string3) -&gt; False
</code></pre>

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?

Let’s say that you work at a bank that wants to build a model to detect fraud on the platform.

The bank wants to implement a text messaging service in addition that will text customers when the model detects a fraudulent transaction in order for the customer to approve or deny the transaction with a text response.

How would we build this model?

Let’s say that you work at a bank that wants to build a model to detect fraud on the platform.

The bank wants to implement a text messaging service that will text customers when the model detects a fraudulent transaction in order for the customer to approve or deny the transaction with a text response.

Which statement is true?

Let's say that you work at a bank that wants to build a model to detect fraud on the platform.

The bank wants to implement a text messaging service that will text customers when the model detects a fraudulent transaction in order for the customer to approve or deny the transaction with a text response.

Which statement is true?

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

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

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

Fair Coin

Probability

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

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

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

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

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

Example:

Input:

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

Output:

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

Explanation:

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

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

Nearest Common Ancestor

<h1>Binary Tree Validation</h1>

You are given the root of a binary tree. You need to determine if it is a valid binary search tree (BST).

A valid BST is defined as follows:

<ul>
<li>The left subtree of a node contains only nodes with values less than or equal to the node’s value.</li>
<li>The right subtree of a node contains only nodes with values greater than or equal to the node’s value.</li>
<li>Both the left and right subtrees must also be binary search trees.</li>
</ul>

Given the function <code>def is_valid_bst(root: Node) -&gt; bool:</code>, return True if the binary tree is a valid BST. Otherwise, return False.

<h3>Example:</h3>

Input:

<img src="/s3/questions/9664817c-3e12-4a40-9236-8382b13f55a0.png" alt="image"/>Converted Binary Tree.png

Output:

<pre tabindex="0" class="chroma"><code>def is_valid_bst(Node(3)) -&gt; True
</code></pre>

Given the root node, verify if a binary search tree is valid or not.

Binary Tree Validation

Write a Python function called <code>group_anagrams</code> that takes a list of strings as input and returns a list of lists, where each inner list contains a group of anagrams that were present in the input list.

An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, using all the original letters exactly once.

Note: Each of the inner lists should be ordered alphabetically and contain no duplicate values

<h3>Example:</h3>

Input:

<pre tabindex="0" class="chroma"><code>words = [&#34;eat&#34;, &#34;tea&#34;, &#34;tan&#34;, &#34;ate&#34;, &#34;nat&#34;, &#34;bat&#34;]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>[ 
 [&#34;nat&#34;,&#34;tan&#34;],
 [&#34;ate&#34;,&#34;eat&#34;, &#34;tea&#34;],
 [&#34;bat&#34;]
]
</code></pre>

Explanation:

In the example, the words “eat”, “tea”, and “ate” are anagrams of each other, as are the words “tan” and “nat”. The word “bat” does not have any anagrams in the input list, and therefore is listed on its own. The function then groups the anagrams together and returns a list of lists representing these groups.

Each of the lists representing a group of anagrams is sorted in alphabetical order.

Identify the groups of anagrams in a list of words

Groups of Anagrams

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

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

You are given two non-empty linked lists representing two non-negative integers. Each list contains a single number, where each item in the list is one digit. The digits are stored in reverse order.

Task: Add the two numbers and return the sum as a linked list, also with the digits in reverse order. You may assume the two numbers do not contain any leading zeros, except the number 0 itself.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>l1 = 2-&gt;4-&gt;3-&gt;null
l2 = 5-&gt;6-&gt;4-&gt;null
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>addTwoNumbers(l1, l2) = 7-&gt;0-&gt;8-&gt;null
</code></pre>

Explanation: 342 + 465 = 807.

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>l1 = 0-&gt;null
l2 = 0-&gt;null
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>addTwoNumbers(l1, l2) -&gt; 0-&gt;null
</code></pre>

Explanation: 0 + 0 = 0.

In this problem, we are given two linked lists representing two non-negative integers, with each item in the list holding one digit. The digits are stored in reverse order, and each of their nodes contains a single digit. We are required to add the two numbers and return the sum as a linked list.

Radix Addition

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>

Most Repetition

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>

Implement Dijkstra’s shortest path algorithm for a given graph with a known source node.

A graph format is a dictionary of nodes as key and the value is a dictionary of neighbors to that node with the distance between them as follow.

Note: set the previous node of the source node to <code>None</code>.

Example:

Input:

<pre tabindex="0" class="chroma"><code>
source_node = &#39;A&#39;

graph = {
 &#39;A&#39;: {
 &#39;D&#39;: 1,
 &#39;B&#39;: 6
 },
 &#39;B&#39;: {
 &#39;A&#39;: 6,
 &#39;D&#39;: 2,
 &#39;E&#39;: 2,
 &#39;C&#39;: 5
 },
 &#39;C&#39;: {
 &#39;B&#39;: 5,
 &#39;E&#39;: 5
 },
 &#39;D&#39;: {
 &#39;A&#39;: 1,
 &#39;B&#39;: 2,
 &#39;E&#39;: 1
 },
 &#39;E&#39;: {
 &#39;C&#39;: 5,
 &#39;B&#39;: 2
 }

 }


</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>
output_table = {
 &#39;A&#39;: {
 &#39;ShortestDistance&#39;: 0,
 &#39;PreviousVertex&#39;: None
 },
 &#39;B&#39;: {
 &#39;ShortestDistance&#39;: 3,
 &#39;PreviousVertex&#39;: &#39;D&#39;
 },
 &#39;C&#39;: {
 &#39;ShortestDistance&#39;: 7,
 &#39;PreviousVertex&#39;: &#39;E&#39;
 },
 &#39;D&#39;: {
 &#39;ShortestDistance&#39;: 1,
 &#39;PreviousVertex&#39;: &#39;A&#39;
 },
 &#39;E&#39;: {
 &#39;ShortestDistance&#39;: 2,
 &#39;PreviousVertex&#39;: &#39;D&#39;
 }
 }
</code></pre>

<img src="/s3/questions/785715d4-3305-4b9f-bdd7-33d5cf987bdb.png" alt="image"/>

Implement Dijkstra's shortest path algorithm for a given graph with a known source node.

Dijkstra implementation

What are the assumptions of linear regression?

Which assumption of the residuals of the standard linear regression model can not be overcome by increasing the sample size?

Regression assumptions

You’re given a list of sorted integers in which more than 50% of the list is comprised of the same repeating integer.

Write a function to return the median value of the list in \(O(1)\) computational time and space.

Note: the lists are all non-empty

Example:

Input:

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

Output:

<pre tabindex="0" class="chroma"><code>median(li) -&gt; 2
</code></pre>

Median O(1)

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>

5th Largest Number

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

You work as a backend engineer at a growing messaging startup. The team is tasked with building a scalable messenger service that supports individual and group chats, message delivery receipts, and media attachments.

How would you architect the core messaging components using object-oriented principles?

Write a technical design document describing your approach.

Let’s say you’re in a supermarket.

You’ve found out that there is a huge discount on some items you want; unfortunately, you only have one bag with a certain <code>bag_capacity</code>. Each of the items has its own <code>value</code> and <code>capacity</code>, stored in lists called <code>values</code> and <code>capacities</code> contained in a dictionary called <code>items</code>.

Write a function to pick the items that maximize the total value without exceeding the bag’s capacity and return the total value.

Note: You can’t take more than one copy of each item home. Also, you do not need to fill the entire bag to capacity.

Example:

Input:

<pre tabindex="0" class="chroma"><code>items = {
 &#34;values&#34;:[2,3,1,4],
 &#34;capacities&#34;:[2, 4, 6, 5]
}

bag_capacity = 8
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>max_profit(items,bag_capacity) -&gt; 6
</code></pre>

We choose the first and last item with a total profit of 6 and a capacity of 7, which is less than the <code>bag_capacity</code>.

Write a function to pick the items that maximize the total value without exceeding the bag’s capacity

Filling Supermarket Bag

Given a string, write a function to determine if it is palindrome or not.

Note: A palindrome is a word/string that is read the same way forward as it is backward, e.g. <code>&#39;reviver&#39;</code>, <code>&#39;madam&#39;</code>, <code>&#39;deified&#39;</code> and <code>&#39;civic&#39;</code> are all palindromes, while <code>&#39;tree&#39;</code>, <code>&#39;music&#39;</code> and <code>&#39;person&#39;</code> are not palindromes.

Example:

Input:

<pre tabindex="0" class="chroma"><code>word1 = &#34;tree&#34;
word2 = &#34;radar&#34;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def is_palindrome(word1) -&gt; False
def is_palindrome(word2) -&gt; True
</code></pre>

Given a string, write a function to determine if it is palindrome or not.

String Palindromes

Given an integer \(n\), write a function <code>traverse_count</code> to determine the number of paths from the top left corner of an \(n\times n\) grid to the bottom right. You may only move right or down.

Example:

Input:

<pre tabindex="0" class="chroma"><code>n = 2
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def traverse_count(n) -&gt; 2
</code></pre>

As our two options for a 2x2 grid:

<table>
<thead>
<tr>
<th>start</th>
<th></th>
</tr>
</thead>

<tbody>
<tr>
<td></td>
<td>end</td>
</tr>
</tbody>
</table>
are only to go right then down, or down then right. So there are two possible paths.

NxN Grid Traversal

Write a function <code>data_stream_median</code> to calculate the new median from a stream of ordered integers and the new element which is not yet inserted into the stream.

The median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value, so the median is the mean of the two middle values.

Example:

<pre tabindex="0" class="chroma"><code>new_value = 2
stream = [1, 2, 3, 4, 5, 6]
def data_stream_median(new_value, stream): -&gt; 3
</code></pre>

Write a function data_stream_median to calculate the median from a stream of integers.

Data Stream Median

What is a confidence interval for a statistic? Why is it useful to know the confidence interval for a statistic and how do you calculate it?

When an interviewer asks a question along the lines of:

<ul>
<li>What would your current manager say about you? What constructive criticisms might he give?</li>
<li>What are your three biggest strengths and weaknesses you have identified in yourself?</li>
</ul>

How would you respond?

When asked about your strengths in an interview, what is an effective way to respond?

When asked about your strengths in an interview, what is an effective way to respond?

Your Strengths and Weaknesses I

Which of the following is an acceptable strategy when discussing weaknesses in an interview?

Which of the following is an acceptable strategy when discussing weaknesses in an interview?

Your Strengths and Weaknesses II

Given a string <code>n</code>, a multi-digit number, write a function <code>rearranging_digits</code> to return a string of the smallest number larger than <code>n</code> that can be created by rearranging the digits in <code>n</code>. Return <code>None</code> if no such number exists.

Example:

Input:

<pre tabindex="0" class="chroma"><code>n = &#39;395&#39;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def rearranging_digits(n) -&gt; &#39;539&#39;
</code></pre>

Given a string n, a multi-digit number, write a function to return a string of the smallest number larger than n that can be created by rearranging the digits in n.

Rearranging Digits

Write a function <code>fib</code> which takes an integer <code>n</code> and returns the nth fibonacci number. For this question, <code>fib</code> MUST be recursively defined.

Note: <code>for</code> and <code>while</code> keywords are disabled for this question, as well as <code>functools</code>. Any workarounds around this restriction is prohibited.

Example:

Input:

<pre tabindex="0" class="chroma"><code>n = 4
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def fib(n) -&gt; 3
# the sequence is [1, 1, 2, 3, 5, 8...]
</code></pre>

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