Double Hashing

Duration: 2 min

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Module outline

  1. English Comprehension/Verbal Ability: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Vocabulary, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Subject Verb Agreement (Verb Noun Agreement), Tenses, Verb, Articles, Preposition, Conjunction, Pronoun, Noun, Adjectives, Adverb, Modals, Cloze Test (Cloze Passage), Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Construction
  2. Logical Ability: Coding Decoding, Directions (Direction Test), Analogy, Inequality, Data Sufficiency, Series (Number and Letter Series) (Numerical Relations and Reasoning), Syllogisms, Seating Arrangements, Puzzle Solving (Puzzles), Blood Relations, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Data Arrangement, Venn Diagram, Calendar, Clock
  3. Quantitative Ability: Logarithm, Permutation and Combination, Probability, Profit and Loss, Speed Time and Distance, Mixture and Alligation, Partnership, Simple Interest and Compound Interest, Percentage, Ratio and Proportion (Ratios), Average, Time and Work, Pipe and Cistern, Number System, Divisibility Rules, HCF LCM, Algebra, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Age Problems, Data Interpretation, Sequence and Series (Series)
  4. Basic Analytical Ability: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Cubes & Dices, Selection Decision Table (Decision Making)
  5. Computer Programming: Pseudo Codes, Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  6. DBMS (Computer Science): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Transaction Management, Concurrency Control, Database Security & Authorization
  7. SQL (Computer Science): SQL
  8. OS (Computer Science): Introduction to OS, Process Management, CPU Scheduling, Deadlock, Process Synchronization, Threads & Process Creation, Memory Management, Virtual Memory, File Management
  9. Computer Networks (Computer Science): Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  10. Data Structures (Computer Science): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. OOPs (Computer Science): Object Oriented Programming (OOPS)
  12. Software Engineering (Computer Science): Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. SVAR Conversational - Spoken English: Communication Assessment
  14. HR Interview: MR & HR Interview Preparation
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture provides a comprehensive introduction to Double Hashing, a collision resolution technique used in hash tables with open-addressing. The instructor, Sanchit Jain Sir, explains that double hashing uses a secondary hash of the key as an offset when a collision occurs. He contrasts this with linear and quadratic probing, noting that in double hashing, the interval depends on the data, which minimizes repeated collisions and clustering. The instructor writes the probe sequence formula $h_i(k) = (h_1(k) + i \cdot h_2(k)) \pmod m$ on the screen. He defines $h_1(k)$ as the primary hash function and $h_2(k)$ as the secondary hash function. He specifies that $h_1$ maps to $[0, |T|-1]$ and $h_2$ maps to $[1, |T|-1]$. The variable $i$ represents the probe number, starting from 0. The lecture emphasizes that $h_1$ and $h_2$ should be independent and uniform to approximate a random distribution. The slide text further explains that pair-wise independent hash functions yield a probability of $(h_1/|T|)^2$ that any pair of keys will follow the same bucket sequence.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces Double Hashing, writing the formula $h_i(k) = (h_1(k) + i \cdot h_2(k)) \pmod m$ on the screen. He explains that unlike linear probing, the step size is determined by a second hash function $h_2(k)$. He writes $i=0, 1, 2$ to demonstrate the iteration. The slide text defines the technique and mentions minimizing repeated collisions. He details the ranges for $h_1$ and $h_2$ as $[0, |T|-1]$ and $[1, |T|-1]$ respectively. He also mentions that $h_1$ and $h_2$ are selected from a set of universal hash functions.

  2. 2:00 – 2:10 02:00-02:10

    The instructor concludes the explanation of the formula's components. He highlights the independence of the hash functions to ensure a random distribution. He mentions that pair-wise independent hash functions yield a probability of $(h_1/|T|)^2$ that any pair of keys will follow the same bucket sequence, ensuring minimal clustering. He reiterates that this method approximates a random distribution effectively.

The lesson progresses from a high-level definition of double hashing to a detailed breakdown of its probe sequence formula. By writing the equation $h_i(k) = (h_1(k) + i \cdot h_2(k)) \pmod m$, the instructor clarifies how the secondary hash function determines the step size, effectively solving the primary clustering issues found in linear probing. The constraints on the ranges of $h_1$ and $h_2$ are crucial for ensuring that the entire table is probed.

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