• Connected Components of Chaos

  • Written by: AmCan Tech
  • Podcast

Connected Components of Chaos

Written by: AmCan Tech
Listen for free

  • Summary

  • A podcast where logic meets lunacy, and graphs guide the way through the madness! Join us as we explore the beautiful intersections of mathematical logic, graph theory, discrete math, computer science, and the quirky chaos of everyday life. From proving theorems to untangling graph traversals, we’ll connect seemingly random dots to create a web of ideas that’s as entertaining as it is enlightening.
    AmCan Tech
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Education Mathematics Science
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Episodes
  • Hash Tables: Theory, Implementation, and Universal Hashing

    Hash Tables: Theory, Implementation, and Universal Hashing
    Feb 16 2025
    In this episode, we explore hash tables, a data structure designed for efficient insertion, deletion, and searching of data using keys. The document contrasts direct addressing with hashing, highlighting the space efficiency of hash tables when dealing with large key universes. It discusses collision resolution techniques like chaining and open addressing, exploring the trade-offs between them. Different hashing methods, including division and multiplication, are analyzed for their suitability in diverse contexts. We also introduce more advanced concepts like universal and adaptive hashing to optimize performance and handle dynamic data sets.


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    16 mins
  • Suffix Trees: Construction, Properties, and Applications

    Suffix Trees: Construction, Properties, and Applications
    Feb 14 2025
    Today, we are exploring suffix trees, a data structure used for solving string problems.We begin with basic definitions related to strings and alphabets, then introduces suffix trees as compressed tries containing all suffixes of a given text. Applications include substring searching, finding repeated substrings, and data compression. The discussion covers the construction of suffix trees using tries and compressed suffix trees, along with the properties that define them, modifications needed for linear time construction, and concludes with problems suffix trees help solve and an overview of Ukkonen's algorithm, which builds suffix trees in linear time by iteratively adding suffixes and leveraging various operational types and an "active position" notation. The active position notation is coupled with suffix links which help to efficiently traverse from one suffix to another, which allows Ukkonen's algorithm to work.
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    10 mins
  • Disjoint Sets: Data Structures and Algorithms

    Disjoint Sets: Data Structures and Algorithms
    Feb 11 2025
    We discuss disjoint sets, also known as union-find data structures. Disjoint sets maintain collections of elements partitioned into non-overlapping sets, each with a representative element. Key operations include Make-Set (creating a new set), Find-Set (locating a set's representative), and Union (merging two sets). Different representations are explored, such as arrays, linked lists, and inverted trees, along with their associated time complexities. Heuristics like weighted union and union by rank are introduced to improve efficiency, and path compression is discussed as a way to optimize the Find-Set operation. The notes culminate in discussing the inverse Ackermann function in the context of the time complexity of the union by rank and path compression methods.
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    12 mins

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