Double Hashing

Duration: 2 min

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Module outline

  1. Quantitative Aptitude: Number System, Divisibility Rules, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Partnership, Age Problems, Time and Work, Pipe and Cistern, Speed Time and Distance, Algebra, Arithmetic, Data Interpretation, Sequence and Series (Series), Logarithm, Powers and Exponents (Surds and Indices), Permutation and Combination, Probability, Speed Mathematics and Basic Mathematics, Trigonometry
  2. Logical Reasoning: Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Syllogisms, Inequality, Data Sufficiency, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Venn Diagram, Logical Sequence Of Words, Calendar, Clock, Cubes & Dices, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Noun, Pronoun, Adjectives, Verb, Adverb, Tenses, Subject Verb Agreement (Verb Noun Agreement), Articles, Preposition, Conjunction, Modals, Determiner, Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Construction
  4. Data Structures (Domain Test): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  5. Algorithms (Domain Test): Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms
  6. OOPs (Domain Test): Object Oriented Programming (OOPS)
  7. DBMS (Domain Test): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  8. SQL (Domain Test): SQL
  9. Operating Systems (Domain Test): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  10. Computer Networks (Domain Test): 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, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  11. Coding: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  12. Written English Test: English Writing Ability
  13. Psychometric Test: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
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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