Ackermann Function

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/COCUBES-PREPARATION/data-structures/stack/toh-classic-apps/asset-ackermann-function after enrolling

Inside: a video lesson and guided study material.

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 detailed explanation of the Ackerman function, a classic example of a recursive function in computer science. The instructor begins by defining the function A(m, n) through three specific recursive cases based on the values of m and n. He then demonstrates the complexity of the function by manually expanding the calculation for A(3, 4). The lecture progresses to a tabular representation of the function's values, illustrating how the output grows rapidly with small increases in input, particularly for higher values of m.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the Ackerman function A(m, n) and writes its formal definition on the screen. The definition includes three conditions: if m=0, A(m, n) = n+1; if m!=0 and n=0, A(m, n) = A(m-1, 1); and if both m and n are non-zero, A(m, n) = A(m-1, A(m, n-1)). He begins a worked example by writing A(3, 4) in red ink. He applies the third rule to expand this into A(2, A(3, 3)). He continues to expand the inner term A(3, 3) into A(2, A(3, 2)), drawing a branching diagram to visualize the recursive calls. This section establishes the recursive structure and begins the step-by-step evaluation process, showing how the function calls itself with modified parameters.

  2. 2:00 – 4:14 02:00-04:14

    The instructor continues the manual expansion of A(3, 4), writing out the nested recursive calls: A(2, A(2, A(3, 2))), then A(2, A(2, A(2, A(3, 1)))), and finally reaching the base case A(2, A(2, A(2, A(2, 1)))). After showing the expansion, he transitions to a table titled "Values of A(m, n)". The table displays a grid with m values (0 to 4) as rows and n values (0 to 4) as columns. He points out specific values, circling 125 for A(3, 4). The table also includes general formulas for the rows, such as n+1 for m=0, n+2 for m=1, 2n+3 for m=2, and 2^(n+3)-3 for m=3. For m=4, the values are shown as massive powers of 2, demonstrating the function's explosive growth rate.

The lecture effectively bridges the gap between the abstract recursive definition of the Ackerman function and its concrete computational behavior. By manually expanding A(3, 4), the instructor highlights the deep nesting required for calculation, which is characteristic of the function. The subsequent table reinforces this by showing how quickly the values escalate, moving from simple addition to exponentiation and tetration. This progression helps students understand why the Ackerman function is significant in computability theory, serving as a benchmark for non-primitive recursive functions. The visual aids, including the handwritten expansion and the data table, provide a comprehensive view of the function's properties.

Loading lesson…