What are the 5 areas of personal development? It's important to note that personal development is something that requires dedication, time, and effort. It's not something that will happen overnight. The five categories are: - mental - social - spiritual - emotional - physical Covered 1. The 7 Habits of Highly Effective People by Stephen Covey Learn powerful principles for personal and interpersonal effectiveness. 2. The Power of Now: A Guide to Spiritual Enlightenment by Eckhart Tolle Explore the concept of living in the present moment and finding inner peace. 3. The Subtle Art of Not Giving a F*ck: A Counterintuitive Approach to Living a Good Life by Mark Manson Learn to focus on what truly matters and let go of unnecessary worries. 4. You Are a Badass: How to Stop Doubting Your Greatness and Start Living an Awesome Life by Jen Sincero Empowering advice to boost self-confidence and achieve your goals. --- To be read - Mindset: The New Psychology of Success by Carol S. Dweck Understand the importance of having a growth mindset and how it can impact your achievements. - Atomic Habits: An Easy and Proven Way to Build Good Habits and Break Bad Ones by James Clear Discover practical strategies to develop positive habits and eliminate harmful ones. - Daring Greatly: How the Courage to Be Vulnerable Transforms the Way We Live, Love, Parent, and Lead by Brené Brown Embrace vulnerability and courage to lead a more fulfilling life. - Grit: The Power of Passion and Perseverance by Angela Duckworth Understand the role of passion and perseverance in achieving long-term success.
Monday, December 18, 2023
Personal Development Books (List From Dec 2023)
Sunday, December 17, 2023
Demystifying the book '12 Rules For Life'
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Tags: Psychology,Book Summary,1: Stand up straight with your shoulders back
The phrase "Stand up straight with your shoulders back" is often used metaphorically to convey a deeper meaning beyond its literal interpretation. This phrase is associated with the idea of adopting a confident and assertive posture, both physically and metaphorically, in the face of life's challenges. Metaphorically, it suggests that one should face difficulties and adversities with resilience, courage, and a positive attitude. Standing up straight symbolizes facing life with confidence and integrity, while having your shoulders back implies carrying yourself with strength and resilience. The moral of "Stand up straight with your shoulders back" might encourage individuals to confront life's challenges head-on, maintaining a posture of strength, confidence, and self-assuredness. It's a call to face adversity with courage and resilience, ultimately contributing to personal growth and well-being. This moral aligns with the idea that maintaining a positive attitude and facing challenges with strength can lead to better outcomes and a more fulfilling life.2: Treat Yourself Like Someone You Are Responsible For Helping
The moral "Treat yourself like someone you are responsible for helping" emphasizes the importance of self-care, self-compassion, and personal responsibility. This moral suggests that individuals should extend the same care, kindness, and consideration to themselves as they would to someone they are responsible for helping or taking care of. In many cases, people tend to prioritize the well-being of others over their own. This moral encourages a shift in perspective, urging individuals to recognize their own value and take responsibility for their own care and happiness. It implies that just as we have a sense of responsibility to help and care for others, we should also apply that level of care to ourselves. Practically, this moral promotes self-love, self-respect, and self-nurturing. It suggests that individuals should make choices that prioritize their physical and mental health, engage in activities that bring them joy and fulfillment, and treat themselves with the same empathy and kindness they would extend to a friend or someone they care for. In summary, "Treat yourself like someone you are responsible for helping" encourages a balanced and compassionate approach to self-care, reminding individuals that taking care of themselves is a responsibility worth prioritizing.3: MAKE FRIENDS WITH PEOPLE WHO WANT THE BEST FOR YOU
The moral "Make friends with people who want the best for you" underscores the importance of choosing relationships that are positive, supportive, and beneficial for your well-being. This moral encourages individuals to be selective about the people they surround themselves with, emphasizing the value of friendships that contribute positively to personal growth and happiness. In essence, this moral suggests that cultivating relationships with individuals who genuinely care about your well-being and success can have a positive impact on your life. True friends are those who celebrate your achievements, support you during challenges, and genuinely want to see you thrive and be your best self. On a deeper level, this moral encourages reflection on the nature of friendships and the impact they can have on one's life. It prompts individuals to be discerning in their choice of friends and to prioritize relationships that foster a positive and uplifting environment. By making friends with those who have your best interests at heart, you're more likely to experience meaningful connections and a supportive social network. Ultimately, the moral "Make friends with people who want the best for you" guides individuals to invest time and energy in relationships that contribute positively to their personal development and overall happiness.4: COMPARE YOURSELF TO WHO YOU WERE YESTERDAY, NOT TO WHO SOMEONE ELSE IS TODAY
The moral "Compare yourself to who you were yesterday, not to who someone else is today" encourages a healthy and constructive perspective on personal growth and self-improvement. This moral is rooted in the idea that the most meaningful and relevant measure of progress is your own development over time, rather than comparing yourself to others. By focusing on your past self, you acknowledge the journey of personal improvement and growth. It promotes a mindset of continuous self-reflection and self-improvement. Comparing yourself to who you were yesterday implies setting personal benchmarks and goals, and striving to be a better version of yourself. Conversely, comparing yourself to someone else can be counterproductive and may lead to feelings of inadequacy or unwarranted pride. Everyone's life path and circumstances are unique, and comparisons to others may not accurately reflect your own progress or challenges. In essence, this moral story encourages individuals to be their own point of reference for growth, learning, and achievement. It promotes a positive and forward-looking mindset, emphasizing personal development and the realization that the journey of self-improvement is a continuous and individualized process.5: DO NOT LET YOUR CHILDREN DO ANYTHING THAT MAKES YOU DISLIKE THEM
The statement "Do not let your children do anything that makes you dislike them" carries a message about parenting and the importance of guiding children toward positive behavior and character development. This perspective suggests that parents have a role in shaping their children's behavior and values, and they should actively discourage actions or behaviors that lead to dislike or disapproval. On one level, this advice underscores the idea that parents should set boundaries and teach their children right from wrong. It encourages the cultivation of positive qualities such as respect, responsibility, and kindness. By discouraging behaviors that are likely to result in dislike, parents aim to guide their children toward actions that promote positive relationships and well-being. However, it's crucial to interpret this statement with a balanced approach. While parents play a significant role in shaping their children's behavior, it's also important to allow children to make mistakes and learn from them. Parenting involves a delicate balance between providing guidance and allowing for independence and personal growth. In summary, the advice "Do not let your children do anything that makes you dislike them" suggests a proactive and positive approach to parenting, emphasizing the importance of instilling values and behaviors that contribute to a healthy and harmonious family environment.6: SET YOUR HOUSE IN PERFECT ORDER BEFORE YOU CRITICIZE THE WORLD
The statement "Set your house in perfect order before you criticize the world" conveys a moral lesson about personal responsibility, self-improvement, and the idea that one should address their own issues before passing judgment on others or the world at large. This phrase is often associated with Canadian clinical psychologist Jordan B. Peterson, who uses it as a guiding principle for personal development. At its core, this advice suggests that individuals should focus on improving their own lives, behaviors, and circumstances before being quick to criticize external factors, societal issues, or other people. It implies that one's ability to make a positive impact on the world is closely tied to their ability to manage and improve their own life first. The metaphor of "setting your house in perfect order" refers to the idea of addressing personal challenges, developing resilience, and cultivating a sense of responsibility for one's own well-being. It doesn't necessarily mean achieving perfection but rather striving for personal improvement and stability. In practical terms, this moral encourages self-reflection, self-discipline, and a proactive approach to dealing with personal challenges. It promotes the idea that by becoming a better and more responsible individual, a person is better equipped to contribute positively to the world and address larger issues effectively.7: PURSUE WHAT IS MEANINGFUL (NOT WHAT IS EXPEDIENT)
The statement "Pursue what is meaningful (not what is expedient)" encourages individuals to prioritize actions and pursuits that have long-term significance and purpose over those that provide quick and easy solutions or immediate gratification. "Pursue what is meaningful" suggests a focus on activities, goals, or values that align with a deeper sense of purpose, fulfillment, and personal values. This could involve pursuing meaningful relationships, meaningful work, or engaging in activities that contribute positively to personal growth and the well-being of others. On the other hand, "not what is expedient" implies avoiding shortcuts or quick fixes that may bring temporary relief or benefits but lack a lasting and substantial impact. It encourages individuals to resist the temptation of immediate gains if they come at the expense of long-term fulfillment or personal values. In essence, this moral advice advocates for a thoughtful and intentional approach to life, urging individuals to make choices that resonate with their core beliefs and contribute to a sense of meaningfulness and purpose. It aligns with the idea that enduring satisfaction often comes from pursuing what is truly important and valuable, even if it requires more effort and time.8: TELL THE TRUTH—OR, AT LEAST, DON'T LIE
The statement "Tell the truth—or, at least, don't lie" is a moral directive that emphasizes the importance of honesty and integrity in communication. At its core, it encourages individuals to be truthful and transparent in their interactions with others. "Telling the truth" is a straightforward concept, advocating for the practice of conveying information that is accurate and honest. It implies a commitment to authenticity and sincerity in one's communication. The latter part, "at least, don't lie," recognizes that while telling the absolute truth may not always be possible due to various factors, refraining from intentional deception is a fundamental principle. It suggests that if sharing the complete truth is challenging or inappropriate in a given situation, it is still important to avoid deliberate falsehoods. This moral advice aligns with the values of honesty, trustworthiness, and ethical communication. It acknowledges that truth-telling can be complex in certain circumstances, but it underscores the importance of maintaining one's integrity by avoiding intentional deception and falsehoods. The underlying message is to prioritize honesty in communication and, at the very least, abstain from engaging in deceitful practices.9: ASSUME THAT THE PERSON YOU ARE LISTENING TO MIGHT KNOW SOMETHING YOU DON'T
The statement "Assume that the person you are listening to might know something you don't" encourages an open-minded and humble approach to communication and learning. At its core, this advice suggests that when engaging in conversations or receiving information from others, it is beneficial to approach the interaction with the assumption that the other person may possess valuable insights, knowledge, or perspectives that you may not be aware of. This mindset promotes active listening and a willingness to consider alternative viewpoints. It emphasizes the idea that everyone has unique experiences and expertise, and there is always an opportunity to learn from others. By assuming that the person you are listening to has something valuable to contribute, you are more likely to approach the conversation with respect and an eagerness to broaden your understanding. In a broader sense, this advice fosters a culture of continuous learning and intellectual humility. It discourages arrogance or the assumption that one already knows everything, encouraging individuals to remain receptive to new information and diverse perspectives. Overall, the statement encourages a positive and collaborative approach to communication, where individuals are open to the possibility of gaining insights from others.10: BE PRECISE IN YOUR SPEECH
The moral lesson "Be precise in your speech" emphasizes the importance of clarity, accuracy, and specificity when communicating. This advice encourages individuals to express themselves in a way that minimizes ambiguity and ensures that their intended message is accurately conveyed. By being precise in speech, individuals can avoid misunderstandings and misinterpretations. It involves choosing words carefully, providing details, and articulating thoughts in a clear and unambiguous manner. Precision in speech is particularly important in professional settings, interpersonal relationships, and any situation where effective communication is crucial. This moral lesson is often associated with the idea that clear communication is a responsibility, and it helps build trust and understanding among people. It suggests that using vague or imprecise language can lead to confusion and may not effectively convey the intended message. In essence, "Be precise in your speech" encourages individuals to take the time to articulate their thoughts thoughtfully, using language that accurately reflects their intentions. This practice contributes to better communication, fosters understanding, and reduces the likelihood of miscommunication or misinterpretation.11: DO NOT BOTHER CHILDREN WHEN THEY ARE SKATEBOARDING
The moral lesson "Do not bother children when they are skateboarding" is often associated with the idea of allowing individuals, particularly children, the freedom to engage in activities they enjoy without unnecessary interference or disruption. This advice carries several potential meanings: Respect for Autonomy: It suggests that children, like anyone else, should be allowed the autonomy to pursue their interests and hobbies without unnecessary interference or criticism. Skateboarding, in this context, serves as an example of an activity that some individuals enjoy for recreation and personal fulfillment. Encouragement of Independence: The advice may also imply the importance of fostering independence and self-expression in children. Allowing them to pursue activities like skateboarding without unnecessary interference can contribute to their sense of autonomy and confidence. Understanding Different Interests: It encourages adults to recognize and appreciate the diverse interests and activities that children may engage in, even if those activities might seem unconventional or risky to adults. It underscores the importance of understanding and respecting the choices of others, especially when those choices involve harmless activities that contribute to personal enjoyment and growth. In a broader sense, this moral lesson might be a metaphor for respecting others' choices and interests in general, even if those choices don't align with one's own preferences or may seem unconventional. It advocates for a supportive and open-minded approach to individual pursuits and hobbies.12: PET A CAT WHEN YOU ENCOUNTER ONE ON THE STREET
The moral lesson "Pet a cat when you encounter one on the street" might carry a metaphorical meaning rather than a literal one. In a broader sense, it could be interpreted as an encouragement to appreciate and engage with moments of joy or serenity that present themselves unexpectedly in life. Here are a few potential interpretations: Appreciate the Small Pleasures: This advice might suggest taking the time to enjoy simple and pleasant moments that come your way, even in the midst of a busy or challenging day. Much like stopping to pet a cat, it encourages acknowledging and appreciating the small, positive aspects of life. Embrace Spontaneity: The idea of encountering a cat on the street is often associated with a spontaneous and unplanned occurrence. This moral lesson could be promoting the value of embracing spontaneity, being open to unexpected joys, and finding happiness in the little things. Practice Mindfulness: The act of petting a cat can be calming and mindful. This moral lesson might suggest incorporating mindfulness into daily life, being present in the moment, and finding joy in simple interactions. Promote Kindness: It could also symbolize the importance of kindness and connection. Taking a moment to interact with a cat, or by extension, being kind to others, even in passing, can contribute to a positive and compassionate outlook. In summary, "Pet a cat when you encounter one on the street" may serve as a reminder to find joy in the present moment, appreciate the small pleasures in life, and embrace spontaneity and kindness. ChatGPT can make mistakes. Consider checking important information.
Saturday, December 16, 2023
NLP Interview Preparation - Seeking help from ChatGPT on Technical Aspects - Day 1
ChatGPT Prompt: I'm interviewing for NLP developer at an MNC. I have 7 years of experience as an ML engineer. What are the technical aspects that need to be covered for the technical interview? Give me a list in order. Response: Congratulations on your interview opportunity! Here's a list of technical aspects that you may want to cover for an NLP developer role, ordered from foundational to more advanced topics. Keep in mind that the specific emphasis may vary based on the job description and the interviewer's preferences: Topic Covered Here... 1. Fundamental NLP Concepts: Tokenization Stemming and Lemmatization Named Entity Recognition (NER) Part-of-Speech (POS) tagging 2. Text Representation: Bag of Words (BoW) Term Frequency-Inverse Document Frequency (TF-IDF) Word Embeddings (e.g., Word2Vec, GloVe) Pre-trained language models (e.g., BERT, GPT) Topics to be covered in future posts in this series... 3. NLP Libraries and Frameworks: NLTK SpaCy scikit-learn TensorFlow or PyTorch for deep learning 4. Text Classification: Binary and Multiclass classification Evaluation metrics (accuracy, precision, recall, F1 score) Handling imbalanced datasets 5. Sequence-to-Sequence Models: Recurrent Neural Networks (RNNs) Long Short-Term Memory networks (LSTMs) Attention mechanisms Transformer architecture 6. Named Entity Recognition (NER) and Entity Linking: CRF-based models Evaluation metrics for NER Handling overlapping entities 7. Language Model Fine-Tuning: Transfer learning for NLP Fine-tuning pre-trained models Domain adaptation techniques 8. Text Generation: Techniques for text generation tasks GPT-like models for creative text generation Controlling generated text (e.g., temperature in softmax) 9. Deep Learning for NLP: Understanding neural network architectures Hyperparameter tuning Model optimization techniques 10. Deployment and Productionization: Model deployment using containers (e.g., Docker) RESTful APIs for NLP models Scalability and performance considerations 11. NLP Challenges and Trends: Stay current on the latest advancements in NLP Familiarity with recent NLP papers and breakthroughs Ability to adapt to evolving technologies 12. Problem-Solving and Critical Thinking: Approach to solving real-world NLP challenges Handling noisy and unstructured data Scalable and efficient solutions for large datasets During the interview, be prepared to demonstrate your practical experience with projects, discuss challenges you've faced, and showcase your problem-solving skills. Accenture may also focus on how well you can communicate technical concepts and work within a team. Good luck with your interview! What is tokenization? ChatGPT: Tokenization is the process of breaking down a text into smaller units, which can be words, phrases, symbols, or other meaningful elements referred to as tokens. In the context of natural language processing (NLP) and computational linguistics, tokenization is a crucial step in the pre-processing of textual data. Here are some key points about tokenization: Basic Units: Tokens are the basic units resulting from tokenization. In English and many other languages, tokens are often equivalent to words. However, depending on the requirements of the task, tokens could also be sub-words, characters, or even phrases. Text to Tokens Conversion: The process involves taking a text document or sentence and segmenting it into individual tokens. For example, the sentence "Tokenization is important" might be tokenized into three tokens: "Tokenization," "is," and "important." Whitespace Tokenization: The simplest form of tokenization involves splitting text based on whitespace, such as spaces or tabs. In this case, each word becomes a token. However, this method may not handle punctuation or special characters well. Punctuation Handling: Tokenization often includes rules for handling punctuation marks. For instance, a period at the end of a sentence might be treated as a separate token, or it might be attached to the preceding word. Challenges: Tokenization can be challenging in languages where words are not separated by spaces, or in languages with complex compound words. Different languages and text types may require specific tokenization strategies. Importance in NLP: Tokenization is a fundamental step in various NLP tasks, including text analysis, machine translation, and sentiment analysis. It helps convert unstructured text into a format that can be easily processed and analyzed by algorithms. Tokenization Libraries: Many programming languages and NLP frameworks provide built-in tokenization libraries. For example, NLTK and SpaCy in Python offer powerful tokenization tools that handle various linguistic nuances. In summary, tokenization is a critical preprocessing step in NLP, enabling the transformation of raw text into a format suitable for further analysis and modeling. The choice of tokenization strategy depends on the specific requirements of the NLP task and the characteristics of the language being processed. Please describe an algorithm for tokenization of english language text. ChatGPT: Tokenization of English language text involves breaking down the text into individual units, typically words or subwords. While there are various approaches to tokenization, a common algorithm for English language tokenization involves the following steps: Whitespace Tokenization: The initial step is often to split the text based on whitespace (spaces, tabs, line breaks). This basic tokenization provides a list of words in the text. Example: "Tokenization is important" becomes ["Tokenization", "is", "important"]. Punctuation Handling: Separate punctuation marks from words. Punctuation can either be treated as separate tokens or attached to adjacent words based on specific rules. Example: "I love NLP!" becomes ["I", "love", "NLP", "!"]. Special Cases Handling: Address special cases such as contractions and possessives. For example, tokenize "can't" into ["can", "'t"] and "John's" into ["John", "'s"]. This step requires language-specific rules to handle common contractions. Numeric Handling: Decide whether to treat numbers as individual tokens or combine them with surrounding words. For example, tokenize "2023" into ["2023"] or ["20", "23"] based on the desired granularity. Consideration may be given to handling decimal points, commas, and other numeric symbols. Lowercasing: Convert all tokens to lowercase to ensure consistency. This helps in treating words with different cases as the same token. Example: "Tokenization" becomes "tokenization." Stopword Removal (Optional): Optionally, remove common stopwords (e.g., "the," "and," "is") if they are not relevant for the analysis. This step may depend on the specific requirements of the NLP task. Lemmatization or Stemming (Optional): Optionally, apply lemmatization or stemming to reduce words to their base or root forms. This can help in treating different inflections of a word as the same token. Example: "running" becomes "run." Handling Compound Words (Optional): Address the challenge of compound words, especially in languages like German where compound words are prevalent. Decide whether to split or keep compound words as a single token. Example: "apple pie" might be kept as ["apple", "pie"] or treated as ["apple pie"]. Customization for Domain-Specific Text (Optional): Depending on the application and domain, consider custom rules for tokenization to handle specific terms or acronyms. Implementing these steps will give you a basic tokenization algorithm for English language text. Libraries like NLTK, SpaCy, and scikit-learn in Python provide pre-built tokenization functions that you can leverage in your projects. What is Stemming and Lemmatization? ChatGPT: Stemming and lemmatization are both techniques used in natural language processing (NLP) and information retrieval to reduce words to their base or root forms. The goal is to normalize words, making it easier to analyze and compare variations of a word. While they serve a similar purpose, there are key differences between stemming and lemmatization. Stemming: Definition: Stemming is the process of removing suffixes or prefixes from a word to obtain its root form, known as the stem. The stem may not be a valid word on its own, but it represents the core meaning shared by related words. Example: Word: "running" Stem: "run" Algorithmic Approach: Stemming algorithms use heuristics and rules to strip away affixes. Common stemming algorithms include Porter Stemmer, Snowball Stemmer, and Lancaster Stemmer. Benefits: Computational efficiency: Stemming is often faster than lemmatization. Reduction in word dimensions: Stemming can simplify the vocabulary by collapsing similar words to a common stem. Drawbacks: Over-stemming: Stemming may result in the stem being a non-real word or losing some meaning. Under-stemming: Some words may not be reduced to a common stem, leading to variations that are not recognized as related. Lemmatization: Definition: Lemmatization is the process of reducing words to their base or dictionary form, known as the lemma. The lemma is a valid word, and the goal is to map inflected forms to a common root. Example: Word: "running" Lemma: "run" Algorithmic Approach: Lemmatization involves more sophisticated linguistic analysis compared to stemming. It typically uses dictionaries and morphological analysis to identify the base form of a word. Benefits: Linguistic accuracy: Lemmatization provides valid words as lemmas, retaining the semantic meaning. Better for downstream applications: Lemmatization is often preferred in tasks where the interpretability of words is crucial, such as information retrieval or question answering. Drawbacks: Computational cost: Lemmatization is usually more computationally intensive than stemming. May not reduce words as much: While lemmatization retains more meaning, it may not collapse as many similar words as stemming. When to Use Each: Stemming: If you need a quick and computationally efficient solution and you are less concerned about retaining valid words, stemming may be suitable. It's often used in information retrieval or search engine applications. Lemmatization: If linguistic accuracy and interpretability are crucial, especially in applications like question answering or text summarization, lemmatization is a better choice. In summary, stemming and lemmatization are text normalization techniques used to preprocess textual data in NLP. The choice between them depends on the specific requirements of the task at hand. What is named entity recognition? ChatGPT Named Entity Recognition (NER) is a subtask of natural language processing (NLP) that involves identifying and classifying entities (specific pieces of information) within a text. These entities can be anything from names of people, organizations, and locations to date expressions, numerical values, and more. The goal of Named Entity Recognition is to extract and categorize these entities to better understand the meaning and structure of the text. Here are key components and concepts associated with Named Entity Recognition: Entities: Entities are real-world objects or concepts that can be denoted by proper nouns or expressions in a text. Examples include names of persons, organizations, locations, dates, times, percentages, and more. Categories: NER systems categorize entities into predefined classes or categories. Common categories include: Person: Names of individuals. Organization: Names of companies, institutions, etc. Location: Names of places, cities, countries, etc. Date: Expressions of dates. Time: Expressions of time. Money: Monetary values. Percentage: Percentage values. Miscellaneous: Any other entity type not falling into the above categories. Example: Given the sentence "Apple Inc. was founded by Steve Jobs in Cupertino on April 1, 1976," a Named Entity Recognition system would identify: Organization: "Apple Inc." Person: "Steve Jobs" Location: "Cupertino" Date: "April 1, 1976" Applications: Named Entity Recognition is a crucial component in various NLP applications, including: Information retrieval and extraction. Question answering systems. Summarization. Chatbots and virtual assistants. Language translation. Event extraction. Challenges: Ambiguity: Some words may have multiple meanings or interpretations. Variability: Entities may be expressed in various forms or variations. Named entity boundaries: Determining the start and end of an entity in the text. Context dependence: The meaning of an entity may depend on the surrounding context. Approaches: Rule-Based Approaches: Using handcrafted rules to identify entities based on patterns, capitalization, or linguistic features. Machine Learning Approaches: Training models (e.g., Conditional Random Fields, Support Vector Machines, or more recently, deep learning models like Bidirectional LSTMs or Transformers) on labeled datasets to learn patterns for entity recognition. Named Entity Recognition plays a vital role in extracting structured information from unstructured text, enabling more advanced and meaningful analysis of textual data. What is Part-of-Speech (POS) tagging? ChatGPT Part-of-Speech (POS) tagging, also known as grammatical tagging or word-category disambiguation, is a natural language processing (NLP) task that involves assigning a specific grammatical category (or part of speech) to each word in a given text. The grammatical categories include nouns, verbs, adjectives, adverbs, pronouns, prepositions, conjunctions, and interjections, among others. The primary goal of POS tagging is to analyze and understand the syntactic structure of a sentence, which is crucial for various downstream NLP tasks, such as parsing, machine translation, and information retrieval. Key aspects of Part-of-Speech tagging: Part-of-Speech Categories: Noun (NN): Represents a person, place, thing, or idea. Verb (VB): Denotes an action or a state of being. Adjective (JJ): Describes a noun. Adverb (RB): Describes a verb, adjective, or another adverb. Pronoun (PRP): Represents a specific person, object, or group without naming them. Preposition (IN): Indicates relationships between words, often in terms of time or space. Conjunction (CC): Connects words, phrases, or clauses. Interjection (UH): Expresses strong emotions or sudden exclamations. Example: Given the sentence "The quick brown fox jumps over the lazy dog," a POS tagging would assign part-of-speech tags to each word: "The" (DT) quick (JJ) brown (NN) fox (NN) jumps (VBZ) over (IN) the (DT) lazy (JJ) dog (NN). Applications: POS tagging is a fundamental step in many NLP applications, including: Information retrieval and extraction. Sentiment analysis. Text summarization. Question answering systems. Machine translation. Challenges: Ambiguity: Some words may have multiple meanings or interpretations based on context. Homographs: Words with the same spelling but different meanings may have different POS tags. Context dependence: The meaning and POS category of a word can depend on its surrounding context. Approaches: Rule-Based Approaches: Use handcrafted rules based on linguistic patterns and context to assign POS tags. Machine Learning Approaches: Train models (e.g., Hidden Markov Models, Maximum Entropy Models, or more recently, deep learning models like Bidirectional LSTMs or Transformers) on labeled datasets to learn patterns for POS tagging. POS tagging is a crucial preprocessing step that provides valuable information about the grammatical structure of a text, enabling more advanced analysis and understanding of natural language. Please explain Bag of Words (BoW) model ChatGPT: The Bag of Words (BoW) model is a simplified representation used in natural language processing (NLP) and information retrieval. It's a way of converting text data into numerical vectors, disregarding the order and structure of words in the text but focusing on their frequency of occurrence. The model is called "bag of words" because it treats a document as an unordered set of words, ignoring grammar and word order but keeping track of word frequency. Here's how the Bag of Words model works: Vocabulary Construction: Create a vocabulary, which is a list of unique words present in the entire corpus (collection of documents). Tokenization: Break down each document in the corpus into individual words or tokens. Word Frequency: Count the frequency of each word in each document. Vectorization: Represent each document as a numerical vector, where each element of the vector corresponds to the frequency of a specific word in the vocabulary. The order of words is ignored; the vector only reflects the presence and frequency of words. Sparse Matrix: Since most documents use only a small subset of the vocabulary, the resulting matrix is typically sparse (containing mostly zeros). Example: Consider two documents: Document 1: "The cat in the hat." Document 2: "The quick brown fox jumps over the lazy dog." Vocabulary: ["The", "cat", "in", "hat", "quick", "brown", "fox", "jumps", "over", "lazy", "dog"] Bag of Words vectors: Document 1: [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0] Document 2: [2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1] The BoW model is a straightforward and effective way to represent text data for various NLP tasks, such as text classification and sentiment analysis. However, it has limitations, including the loss of word order and semantic meaning. Advanced models like TF-IDF (Term Frequency-Inverse Document Frequency) and word embeddings (e.g., Word2Vec, GloVe) address some of these limitations by incorporating additional information about the importance of words in the corpus.
Please explain TF-IDF model.
TF-IDF, which stands for Term Frequency-Inverse Document Frequency, is a numerical statistic used in information retrieval and text mining to evaluate the importance of a word in a document relative to a collection of documents (corpus). TF-IDF combines two components: Term Frequency (TF) and Inverse Document Frequency (IDF).
Key Points:
Higher Weight for Important Terms: Terms that are frequent in a document (high TF) but rare across the entire corpus (high IDF) receive higher TF-IDF scores. These terms are considered more important in distinguishing the document.
Lower Weight for Common Terms: Common terms that appear in many documents are penalized with lower TF-IDF scores, as they may not contribute as much to document distinctiveness.
Sparse Vector Representation: The TF-IDF scores for all terms in a document can be combined into a vector, resulting in a sparse vector representation where most entries are zero.
Applications: TF-IDF is used in information retrieval, document classification, clustering, and other text mining tasks to identify important terms in a document and improve the accuracy of text-based tasks.
TF-IDF is a powerful technique for representing and ranking the importance of terms in a document relative to a larger corpus, providing a way to capture the specificity and uniqueness of terms within the context of a collection of documents.
What is a word embedding?
A word embedding is a numerical representation of a word in a continuous vector space, where the position of each word is learned based on its linguistic context. Word embeddings are designed to capture semantic relationships between words, making them a fundamental component in natural language processing (NLP) and machine learning tasks involving textual data.
Key characteristics of word embeddings:
Continuous Vector Representation:
Unlike traditional one-hot encoding, where words are represented as sparse vectors with a single "1" and the rest as "0," word embeddings are dense vectors with real-valued numbers. Each dimension of the vector corresponds to a feature or aspect of the word's meaning.
Semantic Similarity:
Words with similar meanings are represented by vectors that are close together in the vector space. The distances and directions between word vectors reflect semantic relationships.
Contextual Information:
Word embeddings are learned from the context in which words appear in a given dataset. The idea is that words with similar meanings will have similar distributions of neighboring words in sentences.
Word2Vec, GloVe, and FastText:
Word embeddings are often generated using algorithms like Word2Vec, GloVe (Global Vectors for Word Representation), and FastText. These algorithms utilize neural networks or co-occurrence statistics to learn vector representations.
Pre-trained Embeddings:
Pre-trained word embeddings are models that have already been trained on large corpora and can be used in downstream tasks without further training. Examples include Word2Vec and GloVe embeddings.
Word Similarity and Analogy:
Word embeddings can capture word similarity and analogies. For example, in a well-trained embedding space, the vector for "king" minus the vector for "man" plus the vector for "woman" might be close to the vector for "queen."
Dimensionality:
The dimensionality of word embeddings is a hyperparameter that determines the size of the vector space. Common choices are between 50 and 300 dimensions.
Applications:
Word embeddings are used in a wide range of NLP tasks, including text classification, sentiment analysis, machine translation, information retrieval, and more. They are also employed in deep learning models as the input representation for textual data.
Word embeddings play a crucial role in transforming words into continuous numerical representations that capture semantic information, allowing models to better understand and generalize from textual data.
Explain Word2Vec
Word2Vec is a popular technique in natural language processing (NLP) that is used to learn distributed representations (word embeddings) of words in a continuous vector space. Developed by a team at Google, Word2Vec captures semantic relationships between words by representing them as dense vectors in a way that preserves their contextual similarities.
Key Concepts:
Distributed Representations:
Word2Vec represents words as vectors in a high-dimensional space, where the position of each word is learned based on its context in the training data.
Context and Similarity:
The underlying idea is that words appearing in similar contexts have similar meanings. Word2Vec captures this by learning vector representations in such a way that the distance and direction between vectors reflect the semantic relationships between words.
Skip-gram and Continuous Bag of Words (CBOW):
Word2Vec has two main architectures: Skip-gram and Continuous Bag of Words (CBOW). Skip-gram predicts the context words given a target word, while CBOW predicts the target word given its context. Both approaches aim to optimize the likelihood of predicting surrounding words based on the target word.
Neural Network Architecture:
Word2Vec is implemented as a shallow neural network with one hidden layer. The weights of the hidden layer are the word vectors. The network is trained to predict the surrounding words or target word, and during this process, the word vectors are adjusted to capture semantic relationships.
Training Process:
The training process involves feeding a large corpus of text into the Word2Vec model. The model learns to adjust the word vectors to maximize the likelihood of predicting context words given a target word (Skip-gram) or predicting the target word given its context (CBOW).
Word Similarity:
After training, words with similar meanings or contexts end up having similar vector representations. This property allows Word2Vec to capture semantic relationships, such as "king" and "queen" being close in vector space.
Dimensionality of Vectors:
The dimensionality of word vectors is a hyperparameter that can be tuned based on the specific task and dataset. Common choices are between 50 and 300 dimensions.
Applications:
Word2Vec embeddings have been widely used in various NLP tasks, including text classification, sentiment analysis, machine translation, and information retrieval. The pre-trained Word2Vec embeddings can also be used as features in downstream tasks.
Word2Vec has been influential in the development of more advanced word embeddings and has paved the way for powerful pre-trained models like GloVe (Global Vectors for Word Representation) and contextual embeddings like ELMo and BERT.
Explain GloVe.
GloVe, which stands for Global Vectors for Word Representation, is an unsupervised learning algorithm for obtaining word embeddings. Developed by researchers at Stanford University, GloVe aims to capture global statistical information about word co-occurrences in a corpus, enabling the generation of meaningful and contextually rich word vectors.
Key Characteristics and Concepts:
Global Co-occurrence Statistics:
GloVe is based on the idea that meaningful word representations can be derived from the global statistical information of word co-occurrences in a large corpus. It considers the overall word co-occurrence patterns rather than local context.
Training Process:
GloVe uses stochastic gradient descent to minimize the cost function. During training, word vectors are updated based on their ability to reconstruct the observed word co-occurrence probabilities.
Dimensionality:
The dimensionality of the word vectors in GloVe is a hyperparameter that can be adjusted based on the specific task and dataset. Common choices include 50, 100, 200, or 300 dimensions.
Pre-trained Embeddings:
Similar to Word2Vec, GloVe can be used to train word embeddings from scratch on a specific corpus, or pre-trained embeddings can be utilized for downstream tasks.
Applications:
GloVe embeddings are widely used in various NLP tasks, such as text classification, sentiment analysis, machine translation, and information retrieval. They provide dense, meaningful representations that capture semantic relationships between words.
GloVe has gained popularity for its ability to produce high-quality word embeddings by leveraging global co-occurrence statistics. It has been shown to be effective in capturing semantic relationships and has become a standard choice for word embedding generation in many NLP applications.
What is a Pre-trained language model?
A pre-trained language model is a model that has been trained on a large corpus of text data before being fine-tuned for a specific downstream natural language processing (NLP) task. These models are typically trained on massive amounts of diverse textual data to learn general language patterns, syntactic structures, and semantic relationships. Once pre-trained, these models can be fine-tuned on smaller, task-specific datasets for various NLP applications.
There are two main types of pre-trained language models:
Feature-Based Models:
These models learn fixed-size representations (features) for words or sub-word units. Examples include Word2Vec, GloVe, and FastText. These models generate embeddings for words based on contextual information but do not capture more complex syntactic or semantic structures.
Contextualized Models:
Contextualized language models, on the other hand, capture context-dependent representations for words. These models consider the surrounding context of each word in a sentence and generate embeddings that vary based on the context in which the word appears. Examples include ELMo (Embeddings from Language Models), GPT (Generative Pre-trained Transformer), and BERT (Bidirectional Encoder Representations from Transformers).
Pre-trained Language Models Workflow:
Pre-training:
The model is pre-trained on a large and diverse corpus of text. During pre-training, the model learns to predict missing words in a sentence or other related tasks. For example, BERT is pre-trained using a masked language model (MLM) objective, where some words are randomly masked, and the model is trained to predict these masked words based on the surrounding context.
Fine-tuning:
After pre-training, the model can be fine-tuned on smaller, task-specific datasets for various NLP applications. Fine-tuning adjusts the model's parameters to better suit the specific requirements of the downstream task, such as sentiment analysis, named entity recognition, or machine translation.
Transfer Learning:
The key advantage of pre-trained language models is transfer learning. By pre-training on a large and general dataset, the models learn useful language representations. Fine-tuning allows these models to adapt to specific tasks with relatively small amounts of task-specific data.
Benefits of Pre-trained Language Models:
Effective Transfer Learning:
Pre-trained models capture general language patterns, allowing for effective transfer learning to downstream tasks with limited labeled data.
Context-Aware Representations:
Contextualized models generate embeddings that take into account the surrounding context of each word, allowing them to capture more nuanced semantic relationships.
State-of-the-Art Performance:
Pre-trained language models have achieved state-of-the-art performance on various NLP benchmarks and competitions.
Reduced Need for Annotated Data:
Fine-tuning on task-specific data requires less annotated data compared to training models from scratch.
Examples of popular pre-trained language models include OpenAI's GPT-3, BERT (developed by Google), RoBERTa, and T5. These models have demonstrated remarkable success in a wide range of NLP tasks and have significantly contributed to advancements in natural language understanding.
Explain BERT.
BERT, which stands for Bidirectional Encoder Representations from Transformers, is a natural language processing (NLP) model developed by Google in 2018. It represents a significant advancement in the field of language understanding and has been widely adopted in various NLP applications.
Here are the key components and concepts associated with BERT:
Transformer Architecture: BERT is based on the transformer architecture, which was introduced by Vaswani et al. in the paper "Attention is All You Need." Transformers use self-attention mechanisms to process input data in parallel, making them highly efficient for handling sequential data like text.
Bidirectional Context: Unlike previous language models that processed text in a left-to-right or right-to-left manner, BERT considers the entire context of a word by using bidirectional context. This means that during training, BERT looks at both the left and right context of each word in a sentence, allowing it to capture richer semantic information.
Pre-training: BERT is pre-trained on large amounts of unlabeled text data. During pre-training, the model learns to predict missing words in a sentence by considering the surrounding context. This task is known as the Masked Language Model (MLM) objective, where certain words in a sentence are randomly masked, and the model is trained to predict those masked words.
Two-Stage Training: BERT follows a two-stage training process. In the pre-training stage, the model is trained on a massive corpus of text data. In the fine-tuning stage, the pre-trained model is further trained on a smaller dataset with labeled examples for specific NLP tasks, such as text classification, named entity recognition, question answering, etc.
Contextual Word Embeddings: BERT produces contextualized word embeddings, meaning that the embedding of a word can vary depending on its context within a sentence. This enables BERT to capture the nuances of word meanings in different contexts.
Application in NLP Tasks: BERT's pre-trained representations have been shown to be highly effective for a wide range of NLP tasks. By fine-tuning the pre-trained model on task-specific data, BERT can achieve state-of-the-art performance in tasks like sentiment analysis, named entity recognition, question answering, and more.
BERT Variants: Since the introduction of BERT, several variants and improvements have been proposed, including models like GPT-3, RoBERTa, and ALBERT, each with specific modifications to enhance performance or address certain limitations.
BERT has played a crucial role in advancing the capabilities of natural language processing models and has become a cornerstone in the development of various language understanding applications.
Explain GPT.
GPT, or Generative Pre-trained Transformer, is a series of natural language processing (NLP) models developed by OpenAI. The GPT models are based on the transformer architecture and are designed for a wide range of natural language understanding and generation tasks. As of my last knowledge update in January 2022, the latest version is GPT-3.
Here are the key features and concepts associated with GPT:
Transformer Architecture: GPT is built on the transformer architecture, which was introduced by Vaswani et al. in the paper "Attention is All You Need." The transformer architecture uses self-attention mechanisms to process input data in parallel, making it highly efficient for handling sequential data like text.
Pre-training: Similar to BERT, GPT models are pre-trained on large amounts of unlabeled text data. During pre-training, the model learns to predict the next word in a sentence given its context. This is known as the autoregressive language modeling objective.
Generative Approach: GPT is a generative model, meaning it is capable of generating coherent and contextually relevant text. Given a prompt or an initial sequence of text, GPT can continue generating text in a way that is contextually appropriate.
Layer-wise Training: GPT models have a layer-wise training approach, where each layer of the model is trained to understand different levels of context. This allows the model to capture hierarchical patterns and dependencies in the input data.
Attention Mechanism: The attention mechanism in transformers enables the model to focus on different parts of the input sequence when making predictions. This attention mechanism contributes to the model's ability to capture long-range dependencies in the data.
Large-Scale Models: GPT models, especially in later iterations like GPT-3, are characterized by their large number of parameters. GPT-3, for example, has 175 billion parameters, making it one of the largest language models to date. The large scale contributes to the model's ability to capture complex patterns and nuances in language.
Transfer Learning: GPT models are designed with a pre-training and fine-tuning paradigm. After pre-training on a large corpus of text data, the model can be fine-tuned on smaller, task-specific datasets for a variety of downstream NLP tasks, such as text completion, question answering, translation, and more.
Zero-Shot and Few-Shot Learning: GPT-3 introduced the capability of zero-shot and few-shot learning. This means the model can perform tasks with minimal task-specific training examples or even without any examples by providing a prompt or instruction.
GPT models have demonstrated state-of-the-art performance on a wide range of NLP benchmarks and tasks, showcasing the effectiveness of transformer-based architectures and large-scale pre-training for language understanding and generation.
Tags: Natural Language Processing,Interview Preparation,Technology,Bonus Question: what is the difference between word embedding and language model?
ChatGPT Word embedding and language models are both concepts in natural language processing (NLP) that involve representing and understanding words in a mathematical or computational way, but they serve different purposes and operate at different levels of language understanding. Word Embedding: Definition: Word embedding is a technique to represent words as vectors of real numbers in a continuous vector space. Each word is mapped to a high-dimensional vector where the relationships between words are preserved. Purpose: The primary goal of word embedding is to capture semantic relationships between words based on their context in a given corpus. Words with similar meanings or contextual usage are represented as vectors that are close to each other in the embedding space. Examples: Word2Vec, GloVe (Global Vectors for Word Representation), and FastText are popular word embedding models. Language Model: Definition: A language model is a type of artificial intelligence model that assigns probabilities to sequences of words. It models the likelihood of a sequence occurring in a given language and can be used for various NLP tasks such as speech recognition, machine translation, and text generation. Purpose: Language models aim to capture the syntactic and semantic structure of a language. They learn patterns and relationships between words and can generate coherent and contextually relevant text. They are trained to predict the next word in a sequence given the preceding context. Examples: OpenAI's GPT (Generative Pre-trained Transformer) models, BERT (Bidirectional Encoder Representations from Transformers), and ELMO (Embeddings from Language Models) are examples of language models. In summary, word embedding focuses on representing individual words in a continuous vector space, capturing semantic relationships, while language models focus on understanding and generating coherent sequences of words, capturing both syntactic and semantic structures in a given language. Word embedding can be a component of a language model, but a language model involves a broader understanding of language beyond individual word representations.
Thursday, December 14, 2023
Swap The Elements (A problem on counting elements)
Swap The Elements
Problem
Problem: You are given an integer m (1 <= m <= 1 000 000) and two non-empty, zero-indexed arrays A and B of n integers, a0, a1, … , a(n-1) and b0, b1, ... , b(n-1) respectively (0 <= ai , bi <= m).
The goal is to check whether there is a swap operation which can be performed on these arrays in such a way that the sum of elements in array A equals the sum of elements in array B after the swap. By swap operation we mean picking one element from array A and one element from array B and exchanging them.
Example
x = [3, 4, 2, 1, 0]
y = [3, 1, 4, 2, 2]
print(sum(x))
print(sum(y))
Out:
10
12
# Swapping '2 from y' with '1 from x'.
x = [3, 4, 2, 2, 0]
y = [3, 1, 4, 2, 1]
print(sum(x))
print(sum(y))
Out:
11
11
# Also, on swapping '3 from y' and '2 from x'.
x = [3, 4, 3, 1, 0]
y = [2, 1, 4, 2, 2]
print(sum(x))
print(sum(y))
Out:
11
11
# Also, on swapping '4 from y' and '3 from x'.
x = [4, 4, 2, 1, 0]
y = [3, 1, 3, 2, 2]
print(sum(x))
print(sum(y))
Out:
11
11
Hint
After the swap operation, the two sums (sum_a and sum_b) should become equal.
And if initially, sum_b - sum_a = d
This is total change we want.
Now, since sum_b + sum_a = Constant (before and after the swap), we can then say:
Half of this change (viz. d/2) will come from side 'b' and half (viz. d/2) will come from side 'a'.
(This is equivalent to saying side 'a' and side 'b' will meet the halfway.)
Since side 'b' is higher, we would have to swap a value B[i] with B[i] - d/2
Now for this, we will loop through side 'b' to find that B[i] for which 'B[i] - d/2' is in side 'a'.
Brute Force Solution
Solution O(n^2): The simplest method is to swap every pair of elements and calculate the totals. Using that approach gives us O(n^3) time complexity. A better approach is to calculate the sums of elements at the beginning, and check only how the totals change during the swap operation.
Linear Time Complexity Solution
Solution O(n + m): The best approach is to count the elements of array A and calculate the difference d between the sums of the elements of array A and B.
For every element of array B, we assume that we will swap it with some element from array A. The difference d tells us the value from array A that we are interested in swapping, because only one value will cause the two totals to be equal. The occurrence of this value can be found in constant time from the array used for counting.
Code
def fast_solution(A, B, m): n = len(A) sum_a = sum(A) sum_b = sum(B) d = sum_b - sum_a if d % 2 == 1: return False d //= 2 count = counting(A, m) for i in xrange(n): if 0 <= B[i] - d and B[i] - d <= m and count[B[i] - d] > 0: return True return False Note: counting() is: def counting(A, m): n = len(A) count = [0] * (m + 1) for k in xrange(n): count[A[k]] += 1 return count 'counting()' can be replaced with 'Counter': >>> l = ['A', 'B', 'C'] >>> from collections import Counter >>> Counter(l) Counter({'A': 1, 'B': 1, 'C': 1}) >>>
Wednesday, December 13, 2023
Tape Equilibrium (A problem in time complexity)
Tape Equilibrium: Minimize the value |(A[0] + ... + A[P-1]) - (A[P] + ... + A[N-1])|
Problem
A non-empty array A consisting of N integers is given. Array A represents numbers on a tape.
Any integer P, such that 0 < P < N, splits this tape into two non-empty parts:
A[0], A[1], … , A[P − 1] and A[P], A[P + 1], … , A[N − 1].
The difference between the two parts is the value of: |(A[0] + A[1] + ... + A[P − 1]) − (A[P] + A[P + 1] + ... + A[N − 1])|
In other words, it is the absolute difference between the sum of the first part and the sum of the second part.
Write a function:
def solution(A)
that, given a non-empty array A of N integers, returns the minimal difference that can be achieved.
Write an efficient algorithm for the following assumptions:
N is an integer within the range [2..100,000];
each element of array A is an integer within the range [−1,000..1,000].
Example
For example, consider array A such that:
A[0] = 3
A[1] = 1
A[2] = 2
A[3] = 4
A[4] = 3
We can split this tape in four places:
P = 1, difference = |3 − 10| = 7
P = 2, difference = |4 − 9| = 5
P = 3, difference = |6 − 7| = 1
P = 4, difference = |10 − 3| = 7
In this example, the function should return 1
Hint
A naive way to think how to solve this problem is to go through each element from second index to second last index, split the array into two parts: left and right and then compute the sum of both left side and right side to get the absolute difference for this split.
But the way we optimize this code is to do away with the need to compute the sum of left side and right side again and again.
In the a better approach, we change what we store in our left and right variable (viz integers, instead of lists).
This is achieved by maintaining two integer variables as left and right that contain the current value of sum of left and right side.
In each step, we update the values left and right by the amount of element which is changing the side from right to left.
Code
def solution(A): left = A[0] right = sum(A) - A[0] g_diff = abs(left - right) for i in range(1, len(A) - 1): left = left + A[i] right = right - A[i] l_diff = abs(left - right) if (l_diff < g_diff): g_diff = l_diff return g_diff
Complexity
O(n)
Tuesday, December 12, 2023
Perm Missing Element (A problem of time complexity)
Perm Missing Element Find the missing element in a given permutation.
Problem
An array A consisting of N different integers is given. The array contains integers in the range [1..(N + 1)], which means that exactly one element is missing.
Your goal is to find that missing element.
Write a function:
def solution(A)
that, given an array A, returns the value of the missing element.
Write an efficient algorithm for the following assumptions:
N is an integer within the range [0..100,000];
the elements of A are all distinct;
each element of array A is an integer within the range [1..(N + 1)].
Example
For example, given array A such that:
A[0] = 2
A[1] = 3
A[2] = 1
A[3] = 5
the function should return 4, as it is the missing element.
Hint
Concept 1: Arithmetic Progression
General case of Arithmetic Progression.
An arithmetic progression (AP) is a sequence of numbers in which the difference of any two successive members is a constant. This constant difference is often denoted by "d." The general form of an arithmetic progression is:
a, a+d, a+2d, a+3d, …
Here:
a is the first term (initial term) of the sequence.
d is the common difference between consecutive terms.
For example, consider the arithmetic progression with a first term (a) of 3 and a common difference (d) of 2:
3, 5, 7, 9, 11,…
Sum of an A.P. is: [2a+(n−1)d] * n / 2
Concept 2: Triangular Numbers
Which is a specific case of Arithmetic Progression.
Triangular numbers are a sequence of numbers that represent the number of objects that can be arranged in the shape of an equilateral triangle. The n-th triangular number is the sum of the first n natural numbers. The formula for the n-th triangular number, often denoted as Tn, is given by:
Tn=1+2+3+…+n = n⋅(n+1) / 2
The sequence of triangular numbers begins with:
1, 3, 6, 10, 15, 21,…
Code
We will use the idea of N’th Triangular number to find our missing number using the following steps:
1. We find the ideal sum if the missing number were also there.
This is given by the formula for the sum of an A.P. or formula for N’th Triangular number.
2. We find the sum of input we have.
3. Missing number = result_from_step_1 - result_from_step_2
def solution(A): # Implement your solution here sum_of_series = (len(A) + 1) * (len(A) + 2) / 2 sum_of_input = sum(A) missing_element = int(sum_of_series - sum_of_input) return missing_element
Detected Time Complexity
- O(N) or O(N * log(N))
Test Cases
Correctness tests
empty_and_single
empty list and single element
missing_first_or_last
the first or the last element is missing
single
single element
double
two elements
simple
simple test
Performance tests
medium1
medium test, length = ~10,000
medium2
medium test, length = ~10,000
large_range
range sequence, length = ~100,000
large1
large test, length = ~100,000
large2
large test, length = ~100,000