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Introduction to Data Science with Python

Arvind Krishna, Lizhen Shi, Emre Besler, and Arend Kuyper

September 20, 2022

This book is developed for the course STAT303-1 (Data Science with Python-1). The first two chapters of the book are a review of python, and will be covered very quickly. Students are expected to know the contents of these chapters beforehand, or be willing to learn it quickly. Students may use the STAT201 book (https://nustat.github.io/Intro_to_programming_for_data_sci/) to review the python basics required for the STAT303 sequence. The core part of the course begins from the third chapter - Reading data .

Please feel free to let the instructors know in case of any typos/mistakes/general feedback in this book.

• Data Structures
• Linked List
• Binary Tree
• Binary Search Tree
• Segment Tree
• Disjoint Set Union
• Fenwick Tree
• Red-Black Tree
• Advanced Data Structures
• Hashing in Data Structure

Introduction to Hashing

What is hashing.

• Index Mapping (or Trivial Hashing) with negatives allowed
• Separate Chaining Collision Handling Technique in Hashing
• Open Addressing Collision Handling technique in Hashing
• Double Hashing
• Load Factor and Rehashing

Easy problems on Hashing

• Find whether an array is subset of another array
• Union and Intersection of two Linked List using Hashing
• Pair with given Sum (Two Sum)
• Maximum distance between two occurrences of same element in array
• Most frequent element in an array
• Find the only repetitive element between 1 to N-1
• How to check if two given sets are disjoint?
• Non-overlapping sum of two sets
• Check if two arrays are equal or not
• Find missing elements of a range
• Minimum number of subsets with distinct elements
• Remove minimum number of elements such that no common element exist in both array
• Count pairs with given sum
• Count quadruples from four sorted arrays whose sum is equal to a given value x
• Sort elements by frequency | Set 4 (Efficient approach using hash)
• Find all pairs (a, b) in an array such that a % b = k
• Group words with same set of characters
• k-th distinct (or non-repeating) element among unique elements in an array.

Intermediate problems on Hashing

• Find Itinerary from a given list of tickets
• Find number of Employees Under every Manager
• Longest subarray with sum divisible by K
• Find the length of largest subarray with 0 sum
• Longest Increasing consecutive subsequence
• Count distinct elements in every window of size k
• Design a data structure that supports insert, delete, search and getRandom in constant time
• Find subarray with given sum | Set 2 (Handles Negative Numbers)
• Implementing our Own Hash Table with Separate Chaining in Java
• Implementing own Hash Table with Open Addressing Linear Probing
• Maximum possible difference of two subsets of an array
• Sorting using trivial hash function
• Smallest subarray with k distinct numbers

Hard problems on Hashing

• Clone a Binary Tree with Random Pointers
• Largest subarray with equal number of 0s and 1s
• All unique triplets that sum up to a given value
• Range Queries for Frequencies of array elements
• Elements to be added so that all elements of a range are present in array
• Cuckoo Hashing - Worst case O(1) Lookup!
• Count subarrays having total distinct elements same as original array
• Maximum array from two given arrays keeping order same
• Find Sum of all unique sub-array sum for a given array.
• Length of longest strict bitonic subsequence
• Find All Duplicate Subtrees
• Find if there is a rectangle in binary matrix with corners as 1
• Top 20 Hashing Technique based Interview Questions

Hashing refers to the process of generating a fixed-size output from an input of variable size using the mathematical formulas known as hash functions. This technique determines an index or location for the storage of an item in a data structure.

Table of Content

Need for Hash data structure

Components of hashing, how does hashing work, what is a hash function.

• Types of Hash functions

Properties of a Good hash function

Complexity of calculating hash value using the hash function, problem with hashing, what is collision, how to handle collisions.

• Separate Chaining
• Linear Probing
• Quadratic Probing

What is meant by Load Factor in Hashing?

What is rehashing, applications of hash data structure, real-time applications of hash data structure, advantages of hash data structure, disadvantages of hash data structure.

• Frequently Asked Questions(FAQs) on Hashing

Hashing in Data Structures refers to the process of transforming a given key to another value. It involves mapping data to a specific index in a hash table using a hash function that enables fast retrieval of information based on its key. The transformation of a key to the corresponding value is done using a Hash Function and the value obtained from the hash function is called Hash Code .

Every day, the data on the internet is increasing multifold and it is always a struggle to store this data efficiently. In day-to-day programming, this amount of data might not be that big, but still, it needs to be stored, accessed, and processed easily and efficiently. A very common data structure that is used for such a purpose is the Array data structure.

Now the question arises if Array was already there, what was the need for a new data structure! The answer to this is in the word ” efficiency “. Though storing in Array takes O(1) time, searching in it takes at least O(log n) time. This time appears to be small, but for a large data set, it can cause a lot of problems and this, in turn, makes the Array data structure inefficient.

So now we are looking for a data structure that can store the data and search in it in constant time, i.e. in O(1) time. This is how Hashing data structure came into play. With the introduction of the Hash data structure, it is now possible to easily store data in constant time and retrieve them in constant time as well.

There are majorly three components of hashing:

• Key: A Key can be anything string or integer which is fed as input in the hash function the technique that determines an index or location for storage of an item in a data structure.
• Hash Function: The hash function receives the input key and returns the index of an element in an array called a hash table. The index is known as the hash index .
• Hash Table: Hash table is a data structure that maps keys to values using a special function called a hash function. Hash stores the data in an associative manner in an array where each data value has its own unique index.

Suppose we have a set of strings {“ab”, “cd”, “efg”} and we would like to store it in a table.

Our main objective here is to search or update the values stored in the table quickly in O(1) time and we are not concerned about the ordering of strings in the table. So the given set of strings can act as a key and the string itself will act as the value of the string but how to store the value corresponding to the key?

• Step 1: We know that hash functions (which is some mathematical formula) are used to calculate the hash value which acts as the index of the data structure where the value will be stored.
• “b”=2, .. etc, to all alphabetical characters.
• Step 3: Therefore, the numerical value by summation of all characters of the string:

“ab” = 1 + 2 = 3, “cd” = 3 + 4 = 7 , “efg” = 5 + 6 + 7 = 18

• Step 4: Now, assume that we have a table of size 7 to store these strings. The hash function that is used here is the sum of the characters in key mod Table size . We can compute the location of the string in the array by taking the sum(string) mod 7 .
• “ab” in 3 mod 7 = 3,
• “cd” in 7 mod 7 = 0, and
• “efg” in 18 mod 7 = 4.

The above technique enables us to calculate the location of a given string by using a simple hash function and rapidly find the value that is stored in that location. Therefore the idea of hashing seems like a great way to store (key, value) pairs of the data in a table.

The hash function creates a mapping between key and value, this is done through the use of mathematical formulas known as hash functions. The result of the hash function is referred to as a hash value or hash. The hash value is a representation of the original string of characters but usually smaller than the original.

For example: Consider an array as a Map where the key is the index and the value is the value at that index. So for an array A if we have index i which will be treated as the key then we can find the value by simply looking at the value at A[i].

Types of Hash functions:

There are many hash functions that use numeric or alphanumeric keys. This article focuses on discussing different hash functions :

• Division Method.
• Mid Square Method
• Folding Method.
• Multiplication Method

A hash function that maps every item into its own unique slot is known as a perfect hash function. We can construct a perfect hash function if we know the items and the collection will never change but the problem is that there is no systematic way to construct a perfect hash function given an arbitrary collection of items. Fortunately, we will still gain performance efficiency even if the hash function isn’t perfect. We can achieve a perfect hash function by increasing the size of the hash table so that every possible value can be accommodated. As a result, each item will have a unique slot. Although this approach is feasible for a small number of items, it is not practical when the number of possibilities is large.

So, We can construct our hash function to do the same but the things that we must be careful about while constructing our own hash function.

A good hash function should have the following properties:

• Efficiently computable.
• Should uniformly distribute the keys (Each table position is equally likely for each.
• Should minimize collisions.
• Should have a low load factor(number of items in the table divided by the size of the table).
• Time complexity: O(n)
• Space complexity: O(1)

If we consider the above example, the hash function we used is the sum of the letters, but if we examined the hash function closely then the problem can be easily visualized that for different strings same hash value is begin generated by the hash function.

For example: {“ab”, “ba”} both have the same hash value, and string {“cd”,”be”} also generate the same hash value, etc. This is known as collision and it creates problem in searching, insertion, deletion, and updating of value.

Collision in Hashing occurs when two different keys map to the same hash value. Hash collisions can be intentionally created for many hash algorithms. The probability of a hash collision depends on the size of the algorithm, the distribution of hash values and the efficiency of Hash function.

The hashing process generates a small number for a big key, so there is a possibility that two keys could produce the same value. The situation where the newly inserted key maps to an already occupied, and it must be handled using some collision handling technology.

There are mainly two methods to handle collision:

• Open Addressing

1) Separate Chaining

The idea is to make each cell of the hash table point to a linked list of records that have the same hash function value. Chaining is simple but requires additional memory outside the table.

Example: We have given a hash function and we have to insert some elements in the hash table using a separate chaining method for collision resolution technique.

Let’s see step by step approach to how to solve the above problem:

Hence In this way, the separate chaining method is used as the collision resolution technique.

2) Open Addressing

In open addressing, all elements are stored in the hash table itself. Each table entry contains either a record or NIL. When searching for an element, we examine the table slots one by one until the desired element is found or it is clear that the element is not in the table.

2.a) Linear Probing

In linear probing, the hash table is searched sequentially that starts from the original location of the hash. If in case the location that we get is already occupied, then we check for the next location.

Calculate the hash key. i.e. key = data % size Check, if hashTable[key] is empty store the value directly by hashTable[key] = data If the hash index already has some value then check for next index using key = (key+1) % size Check, if the next index is available hashTable[key] then store the value. Otherwise try for next index. Do the above process till we find the space.

Example: Let us consider a simple hash function as “key mod 5” and a sequence of keys that are to be inserted are 50, 70, 76, 85, 93.

2.b) Quadratic Probing

Quadratic probing is an open addressing scheme in computer programming for resolving hash collisions in hash tables. Quadratic probing operates by taking the original hash index and adding successive values of an arbitrary quadratic polynomial until an open slot is found.

An example sequence using quadratic probing is:

H + 1 2 , H + 2 2 , H + 3 2 , H + 4 2 …………………. H + k 2

This method is also known as the mid-square method because in this method we look for i 2 ‘th probe (slot) in i’th iteration and the value of i = 0, 1, . . . n – 1. We always start from the original hash location. If only the location is occupied then we check the other slots.

Let hash(x) be the slot index computed using the hash function and n be the size of the hash table.

If the slot hash(x) % n is full, then we try (hash(x) + 1 2 ) % n. If (hash(x) + 1 2 ) % n is also full, then we try (hash(x) + 2 2 ) % n. If (hash(x) + 2 2 ) % n is also full, then we try (hash(x) + 3 2 ) % n. This process will be repeated for all the values of i until an empty slot is found

Example: Let us consider table Size = 7, hash function as Hash(x) = x % 7 and collision resolution strategy to be f(i) = i 2 . Insert = 22, 30, and 50

2.c) Double Hashing

Double hashing is a collision resolving technique in Open Addressed Hash tables. Double hashing make use of two hash function,

• The first hash function is h1(k) which takes the key and gives out a location on the hash table. But if the new location is not occupied or empty then we can easily place our key.
• But in case the location is occupied (collision) we will use secondary hash-function h2(k) in combination with the first hash-function h1(k) to find the new location on the hash table.

This combination of hash functions is of the form

• i is a non-negative integer that indicates a collision number,
• k = element/key which is being hashed
• n = hash table size.

Complexity of the Double hashing algorithm:

Example: Insert the keys 27, 43, 692, 72 into the Hash Table of size 7. where first hash-function is h1​(k) = k mod 7 and second hash-function is h2(k) = 1 + (k mod 5)

The load factor of the hash table can be defined as the number of items the hash table contains divided by the size of the hash table. Load factor is the decisive parameter that is used when we want to rehash the previous hash function or want to add more elements to the existing hash table.

It helps us in determining the efficiency of the hash function i.e. it tells whether the hash function which we are using is distributing the keys uniformly or not in the hash table.

As the name suggests, rehashing means hashing again. Basically, when the load factor increases to more than its predefined value (the default value of the load factor is 0.75), the complexity increases. So to overcome this, the size of the array is increased (doubled) and all the values are hashed again and stored in the new double-sized array to maintain a low load factor and low complexity.

• Hash is used in databases for indexing.
• Hash is used in disk-based data structures.
• In some programming languages like Python, JavaScript hash is used to implement objects.
• Hash is used for cache mapping for fast access to the data.
• Hash can be used for password verification.
• Hash is used in cryptography as a message digest.
• Rabin-Karp algorithm for pattern matching in a string.
• Calculating the number of different substrings of a string.
• Hash provides better synchronization than other data structures.
• Hash tables are more efficient than search trees or other data structures
• Hash provides constant time for searching, insertion, and deletion operations on average.
• Hash is inefficient when there are many collisions.
• Hash collisions are practically not avoided for a large set of possible keys.
• Hash does not allow null values.

Frequently Asked Questions(FAQs) on Hashing:

1. what is a hash function.

Hashing refers to the process of transforming a given key to another value. It involves mapping data to a specific index in a hash table using a hash function that enables fast retrieval of information based on its key.

2. What is a Hash function?

Hash function is a function that takes an input and return a fixed-size string of bytes. The hash function receives the input key and returns the index of an element in an array called a hash table. The index is known as the hash index.

3. What are Hash collisions?

Hash collisions occur when two different inputs passed to the hash function produce the same hash value. The lesser the number of hash collisions, the better the hash function is.

4. What are hash tables?

Hash tables are data structures that use hash functions to map keys to values, allowing for efficient retrieval of data when needed. Hash table maps keys to values using a special function called a hash function. Hash stores the data in an associative manner in an array where each data value has its own unique index.

5. What are some applications of Hashing?

Hashing is used in databases for indexing, disk-based data structures and  data compression algorithms. Hashing is also used to store passwords securely by applying a hash function to the password and storing the hashed result, rather than the plain text password.

From the above discussion, we conclude that the goal of hashing is to resolve the challenge of finding an item quickly in a collection. For example, if we have a list of millions of English words and we wish to find a particular term then we would use hashing to locate and find it more efficiently. It would be inefficient to check each item on the millions of lists until we find a match. Hashing reduces search time by restricting the search to a smaller set of words at the beginning.

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Coursera Course - Introduction of Data Science in Python Assignment 1

I'm taking this course on Coursera, and I'm running some issues while doing the first assignment. The task is to basically use regular expression to get certain values from the given file. Then, the function should output a dictionary containing these values:

This is just a screenshot of the file. Due to some reasons, the link doesn't work if it's not open directly from Coursera. I apologize in advance for the bad formatting. One thing I must point out is that for some cases, as you can see in the first example, there's no username. Instead '-' is used.

This is what I currently have right now. However, the output is None. I guess there's something wrong in my pattern.

2 Answers 2

You can use the following expression:

See the regex demo . See the Python demo :

• Thank you so much!!! It worked!!! However, may I just ask a question regarding your solution? It probably sounds stupid, but don't you need to include everything in the parenthesis? For example, ("?P<request>[^"]*"). Or are they the same? Also, may you please explain the meaning of "?:" in your regular expression –  BryantHsiung Commented Oct 19, 2020 at 13:20
• @BryantHsiung You can't use ("?P<request>[^"]*") , it is an invalid regex construct. See more about non-capturing groups here . –  Wiktor Stribiżew Commented Oct 19, 2020 at 13:42
• 1 Just did! Thanks again! –  BryantHsiung Commented Oct 20, 2020 at 12:42
• 1 I am working on the same question but I don't know why my for loop doesn't give me an output! I check my regex pattern on regex101 and they are all seem to be working the way they should. –  Anoushiravan R Commented Jan 9, 2022 at 20:22
• @AnoushiravanR Without seeing your code, I can't help. –  Wiktor Stribiżew Commented Jan 9, 2022 at 20:29

Check using following code:

For more information regarding regex, read the following documentation, it would be very useful for beginners: https://docs.python.org/3/library/re.html#module-re

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GSI - QMSS 201 (Fall 2024)

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Applicants must submit a cover letter, curriculum vitae (CV) or resume, copies of previous teaching evaluations (if applicable), and a copy of your unofficial transcript(s) from current and/or previous institutions that showcase your current and previous coursework in social sciences and/or quantitative methods. In your cover letter, please explain why you would like to GSI for QMSS (including which course(s), if applicable) and the skills (e.g., analytical tools such as Excel, R, Tableau, Python, etc.) and experiences (e.g., jobs, internships, research, coursework, teaching, etc.) that contribute to your qualifications. If the files you need to upload in 1 document exceed the size limit of the application portal, please send them directly to the QMSS Program Manager at [email protected] .

About QMSS: The Quantitative Methods in the Social Science (QMSS) program in the College of Literature, Science, and the Arts at the University of Michigan aims to train undergraduate students in the theories and methods needed to be successful data literate social scientists. Todays job market is saturated with opportunities that either desire or require skills in data literacy, whether that means being able to find data, analyze data, or know how and when to use data; and this is true even for jobs outside of the data science or analyst fields specifically.

QMSS was designed to teach students how data can be used to generate solutions for social problems of today and tomorrow and give students opportunities to apply and practice their skills to hit the ground running in their internships and careers in the future. QMSS is unique relative to programs in statistics or data science in that we teach data-based skills from a social science perspective. We are strongly committed to meeting students where they R [are], and providing ample time and resources to help them succeed so they can leave our courses and minor program with both competence and confidence in applied data and statistical skills for the social world.  

Course Description

These Graduate Student Instructor (GSI) positions in QMSS are 50% effort positions. There are 4 available positions for Fall 2024. Between Winter 2021 and Winter 2024, QMSS received an average of 22 applications for available GSI positions.

QMSS 201 - Introduction to Quantitative Methods in the Social Sciences: This course includes training in descriptive statistics, data collection, data management, and data cleaning. It provides an overview of research design and hands-on experience with using data to ask and answer research questions from various social science disciplines, and educates students about ethical issues around data, data analysis, and reporting. Students will be taught and asked to use Excel, Tableau, and R in this course.

For information about class size, please refer to the LSA GSI Class Size policy here: LSA GSI Class Size Policy .

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Duties for these positions include, but are not limited to: 

• Attend course lectures (3 hours/week) 
• Teach 2 x 1-hour lab sections each week. Lab times are scheduled so that GSIs may be able to teach 2 back-to-back sections in the same room for ease of planning, though this is not guaranteed. 
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Required Qualifications*

To be appointed as a GSI or GSSA, a graduate student must be in good standing in their degree program and for Terms I and II, must be registered for not less than six (6) credit hours. With written approval of the student's faculty advisor, five (5) credit hours may be acceptable.

Proficiency with analytic tools (Excel, Tableau, Stata, R, Python, etc.) is required. You do not have to be proficient in all analytic tools associated with QMSS 201 to be considered or qualified.  

Desired Qualifications*

LSA doctoral students within their funding package. A mastery of quantitative methods in the social sciences, pursuing a graduate degree in a quantitative methods- or social sciences-related field, and real-world job/internship, teaching, and/or research experience that will help in teaching undergraduate students how to perform quantitative analyses using common analytical tools in order to answer social science questions is desired. A strong commitment to serving as a resource for undergraduate students and ability to make quantitative methods in the social sciences accessible to students of all levels of previous experience (including none at all) is preferred.

Contact Information

For any questions, students can reach out to [email protected] .

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The Director of Quantitative Methods in the Social Sciences awards all GSI positions based on stated qualifications, criteria, and academic discretion. Priority will be given to LSA doctoral students within their five year funding commitment, with a preference for students pursuing degrees in a social science discipline.  

For any questions, students can reach out to [email protected] .  

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