Linear Probing

Duration: 6 min

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Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
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  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
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  13. Full Length Mock Tests:
  14. Sectional Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture segment provides a comprehensive overview of Linear Probing within hash table implementations. The instructor details the sequential search mechanism, emphasizing that operations like insertion, search, and deletion generally achieve constant expected time complexity, provided the load factor remains strictly below one. A significant portion of the lesson is dedicated to the nuances of the deletion operation, explaining why simple removal is insufficient and how special markers are used to preserve search integrity. Finally, the lecture transitions to the disadvantages of this method, specifically focusing on the phenomenon of primary clustering and its detrimental impact on performance as the table fills up.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by defining linear probing as a method that searches the table sequentially starting from the position given by the hash function. He draws a vertical rectangle to represent the hash table structure and writes i, i+1, i+2, and i+3 alongside it to illustrate the probing sequence. The on-screen text highlights that dictionary operations can be implemented in O(1) as long as the load factor is a constant strictly less than one. He explains that for insertion, the algorithm keeps probing until an empty slot is found, while search continues until a matching key is found or an empty slot is reached. He notes that this constant expected time holds when implemented using a random hash function.

  2. 2:00 – 5:00 02:00-05:00

    The discussion moves to the Delete(k) operation, which the instructor marks as interesting in red text. He explains that if a key is simply deleted, subsequent searches for keys that collided and were placed later in the sequence may fail. To solve this, he demonstrates marking slots of deleted keys specially as deleted rather than empty. He writes O(m) next to the table to indicate worst-case time complexity. The instructor then transitions to a new slide titled Disadvantage, preparing to discuss the limitations of this collision resolution scheme. He emphasizes that insert can insert an item in a deleted slot, but search doesn't stop at a deleted slot.

  3. 5:00 – 5:32 05:00-05:32

    The lecturer outlines the disadvantages, specifically underlining primary clustering on the slide. He draws a hash table with a dense cluster of filled slots to visualize how one collision causes more nearby collisions. He writes 1/10 to represent a load factor and circles the cluster, explaining that performance degrades more quickly at high load factors because basic operations take more time. The slide also notes that achieving good performance requires a higher-quality hash function than other schemes. He explains that this is a tendency for one collision to cause more nearby collisions.

The video effectively bridges the gap between theoretical complexity and practical implementation issues. It establishes that while linear probing is efficient on average, the deletion logic is non-trivial and requires special state management. The lesson concludes by identifying primary clustering as a critical flaw, demonstrating through diagrams how collisions propagate and degrade performance, thereby necessitating strict load factor controls and high-quality hash functions for optimal results.

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