Design & Analysis of Algorithms - Vol 2 | 23. Dynamic Programming by Abraham | Learn Smarter
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23. Dynamic Programming

Dynamic programming is introduced as a powerful architectural technique for designing algorithms, built on a foundation of inductive definitions. It allows for the systematic solving of problems by defining them in terms of smaller subproblems, leveraging properties like optimal substructure and overlapping subproblems. The chapter explores various examples including factorial computation and scheduling algorithms, culminating in strategies to optimize problem-solving through memoization and direct enumeration.

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Sections

  • 23

    Dynamic Programming

    Dynamic programming is a powerful algorithm design technique that involves breaking down problems into simpler subproblems, leveraging optimal substructure and overlapping subproblems.

    Learning Practice

  • 23.1

    Inductive Definitions

    This section introduces inductive definitions, emphasizing their role in dynamic programming and algorithm design.

    Learning Practice

  • 23.2

    Insertion Sort Example

    This section discusses the insertion sort algorithm, outlining its recursive nature and inductive definition.

    Learning Practice

  • 23.3

    Optimal Substructure Property

    The Optimal Substructure Property is fundamental to dynamic programming, indicating that optimal solutions to a problem can be constructed from optimal solutions to its subproblems.

    Learning Practice

  • 23.4

    Interval Scheduling Problem

    The Interval Scheduling Problem focuses on maximizing the number of non-overlapping bookings within a given time period by applying both greedy methods and dynamic programming.

    Learning Practice

  • 23.5

    Greedy Strategy In Interval Scheduling

    The section discusses the greedy strategy for solving the interval scheduling problem, focusing on maximizing bookings while addressing overlapping requests.

    Learning Practice

  • 23.6

    Weight Associated With Requests

    This section discusses dynamic programming as a powerful technique for algorithm design, emphasizing the use of inductive definitions and optimal substructure properties.

    Learning Practice

  • 23.7

    Inductive Solution Approach

    The inductive solution approach in dynamic programming relies on inductive definitions that help derive solutions to complex problems using smaller subproblems.

    Learning Practice

  • 23.8

    Computational Challenges

    This section introduces dynamic programming and its significance in solving computational challenges through optimal substructure and inductive definitions.

    Learning Practice

  • 23.9

    Memoization And Dynamic Programming

    This section introduces dynamic programming and memoization as techniques to solve optimization problems efficiently by breaking down problems into subproblems.

    Learning Practice

References

ch44.pdf

Class Notes

Memorization

What we have learnt

  • Dynamic programming involve...
  • Inductive definitions natur...
  • Optimal substructure allows...

Final Test

Revision Tests