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
  • B-Tree Data Structure: Search, Insertion, and Deletion

    B-Tree Data Structure: Search, Insertion, and Deletion
    Feb 9 2025
    Jump in and discover the B-tree data structure, a fundamental tool for processing queries on one-dimensional data stored on disk. We explain how B-trees efficiently support range reporting, successor/predecessor searches, insertion, and deletion operations.
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    18 mins
  • Tries: Data Structures for String Processing

    Tries: Data Structures for String Processing
    Jan 25 2025
    A Trie, also known as a prefix tree, is a specialized tree-based data structure primarily used for efficiently storing and retrieving strings. Unlike traditional search trees where a node stores the entire key, each node in a trie represents a prefix shared by all its descendants. This unique structure facilitates fast search, insertion, and deletion operations based on string prefixes.
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    16 mins
  • Topological Sort and Strongly Connected Components

    Topological Sort and Strongly Connected Components
    Jan 19 2025
    This podcast reviews key concepts related to Depth First Search (DFS) algorithm and its application in topological sorting and finding strongly connected components in graphs.
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    14 mins
  • QuickSort and Order Selection

    QuickSort and Order Selection
    Dec 20 2024
    This episode focuses on QuickSort, a divide-and-conquer sorting algorithm, comparing it to MergeSort, and analyzing its average and worst-case time complexities. It then explains the order selection problem, which involves finding the kth smallest element in a dataset, presenting several algorithms with varying time complexities and practical considerations, including a linear worst-case algorithm and an approximate heuristic. The analysis includes recurrence relations and their solutions to determine the algorithm's efficiency. Finally, it contrasts the different approaches for solving the order selection problem based on their performance characteristics.
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    14 mins
  • Recurrence Equations and Asymptotic Notation

    Recurrence Equations and Asymptotic Notation
    Dec 15 2024
    This episodes presents methods for solving recurrence equations, which are crucial for analyzing the time complexity of recursive algorithms. It introduces asymptotic notations (Big O, Big Omega, Big Theta, little o, little omega) to describe the growth of functions. The lecture then explores several techniques for solving recurrences, including the substitution method, iteration method (and recursion trees), the Master Theorem, and solving homogeneous and non-homogeneous linear recurrences. Specific examples such as merge sort, binary search, and the Towers of Hanoi are used to illustrate these techniques. Finally, the limitations of the Master Theorem are discussed, along with strategies for handling cases where it is not applicable.
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    20 mins