Data Structures and Algorithms in Python | 42. Grid paths by Abraham | Learn Smarter
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42. Grid paths

This chapter discusses the combinatorial approach to counting grid paths and addressing obstacles in a grid. It explains how to determine the number of paths from the bottom left to the top right corner by using combinatorial mathematics and dynamic programming techniques. The chapter also covers how to adapt these methods when intersections are blocked, employing techniques like memoization and inclusion-exclusion principles for more complex scenarios.

Sections

  • 42.1

    Grid Paths

    This section explores the problem of counting paths on a grid where movement is constrained to only right or up, introducing combinatorial and inductive solutions.

    Learning Practice

  • 42.1.1

    Introduction To Grid Path Problem

    This section introduces the grid path problem, elucidating how to calculate the number of paths from the bottom-left to the top-right corner of a grid while adhering to movement constraints.

    Learning Practice

  • 42.1.2

    Counting Total Grid Paths

    This section discusses the methodology for counting unique grid paths from a starting point to an endpoint on a grid, using combinatorial methods and dynamic programming.

    Learning Practice

  • 42.1.3

    Handling Blocked Intersections

    This section addresses how to calculate grid paths when faced with blocked intersections using combinatorial methods.

    Learning Practice

  • 42.1.4

    Dealing With Multiple Blocked Intersections

    This section discusses grid paths and how to count them, focusing on dealing with blocked intersections using combinatorial techniques and dynamic programming.

    Learning Practice

  • 42.1.5

    Inductive Structure Of The Problem

    This section explores the inductive approach to solving grid path problems using combinatorial methods and dynamic programming.

    Learning Practice

  • 42.1.6

    Implementing With Recursion And Memoization

    This section covers grid path problems, illustrating how to efficiently count paths using recursion and memoization techniques.

    Learning Practice

  • 42.1.7

    Dynamic Programming Approach

    This section discusses the dynamic programming approach to solving grid path problems and how to efficiently count the number of paths from one point to another in a grid.

    Learning Practice

  • 42.1.8

    Comparison Of Memoization And Dynamic Programming

    This section compares memoization and dynamic programming, illustrating their differences through the problem of counting grid paths.

    Learning Practice

  • 42.1.9

    Conclusion: Choosing The Right Approach

    This section provides insights into selecting the appropriate computational approach, focusing on grid path problems and methodologies such as recursion, memoization, and dynamic programming.

    Learning Practice

References

Chapter 42.pdf

Class Notes

Memorization

What we have learnt

  • Grid paths can be counted u...
  • Blocked intersections compl...
  • Dynamic programming offers ...

Final Test

Revision Tests