Design & Analysis of Algorithms - Vol 3 | 1. Grid Paths by Abraham | Learn Smarter
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1. Grid Paths

1. Grid Paths

The discussion centers around the problem of counting grid paths in a rectangular grid, focusing on movements from the bottom left corner to the top right corner with specific rules. It explores combinatorial methods to calculate the number of unique paths, including scenarios where certain intersections are blocked. The concepts of inclusion and exclusion are introduced to account for multiple blocked intersections and their effect on path counting.

5 sections

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Sections

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  1. 1

    This section discusses the problem of counting paths on a grid using...

  2. 1.1
    Introduction To Grid Paths

    This section introduces the concept of grid paths, focusing on how to...

  3. 1.2
    Counting Paths Without Blocks

    This section explores the problem of counting distinct grid paths from the...

  4. 1.3
    Paths With A Blocked Intersection

    This section discusses the combinatorial problem of finding grid paths and...

  5. 1.4
    More Complex Blockages

    This section explores the combinatorial problem of computing the number of...

What we have learnt

  • Grid paths can be counted using combinatorial methods.
  • Paths can be calculated based on choosing positions for movements, either right or up.
  • The inclusion-exclusion principle helps to manage blocked paths when multiple intersections are involved.

Key Concepts

-- Grid Path Counting
A method to determine the number of unique paths in a grid under certain movement constraints.
-- Combinatorics
A branch of mathematics dealing with combinations and arrangements of objects.
-- InclusionExclusion Principle
A counting technique used to find the number of elements in the union of multiple sets by including and excluding overlaps.

Additional Learning Materials

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