Design & Analysis of Algorithms - Vol 2 | 12. Divide and Conquer: Counting Inversions by Abraham | Learn Smarter
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12. Divide and Conquer: Counting Inversions

The chapter focuses on the divide-and-conquer algorithmic paradigm, using the example of counting inversions in rankings as a case study. By comparing preferences across different rankings, a method for quantifying dissimilarity is developed through an efficient algorithm inspired by merge sort. This algorithm not only counts inversions but does so in a time-efficient manner of O(n log n), making it applicable for recommendation systems.

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Sections

  • 12

    Divide And Conquer: Counting Inversions

    This section discusses the divide and conquer approach to count inversions in lists, highlighting how efficient algorithms can be designed to enhance performance over naive methods.

    Learning Practice

  • 12.1

    Divide And Conquer Paradigm

    The divide and conquer paradigm involves breaking down problems into smaller subproblems, solving them independently, and then efficiently combining results to achieve a final solution.

    Learning Practice

  • 12.2

    Recommendation Systems And Profiles

    This section explores how recommendation systems leverage user profiles and preferences to provide tailored suggestions, using inversion counting as a metric to measure similarity in rankings.

    Learning Practice

  • 12.3

    Measuring Dissimilarity: Inversions

    This section covers the concept of measuring dissimilarity in rankings through the use of inversions, and introduces an efficient way to count them using a divide and conquer algorithm.

    Learning Practice

  • 12.4

    Basic Ranking And Inversions

    This section introduces the concept of ranking and inversions using the divide and conquer approach, particularly focusing on how to measure the dissimilarity of rankings using inversion counts.

    Learning Practice

  • 12.5

    Graphical Representation Of Inversions

    This section explores counting inversions using a divide and conquer approach, particularly through graphical representations.

    Learning Practice

  • 12.6

    Brute Force Approach To Count Inversions

    The section discusses the brute force method for counting inversions in rankings and compares it with a more efficient divide and conquer approach.

    Learning Practice

  • 12.7

    Divide And Conquer For Counting Inversions

    This section explores the divide and conquer technique for counting inversions in sequences, emphasizing its application to recommendation systems and comparing rankings.

    Learning Practice

  • 12.8

    Merging And Counting Inversions

    This section presents the divide and conquer approach for counting inversions in rankings, using an example of movie preferences.

    Learning Practice

  • 12.9

    Implementation Of Merge Procedure With Counting

    This section details how to efficiently count inversions in ranking using the merge procedure within the divide and conquer paradigm.

    Learning Practice

  • 12.10

    Analysis Of Time Complexity

    This section focuses on the divide and conquer strategy for analyzing time complexity through counting inversions in rankings.

    Learning Practice

References

ch37.pdf

Class Notes

Memorization

What we have learnt

  • The divide-and-conquer para...
  • Inversions are a measure of...
  • A more efficient way to cou...

Final Test

Revision Tests