Design & Analysis of Algorithms - Vol 2 | 7. Union-Find Data Structure Using Pointers by Abraham | Learn Smarter
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7. Union-Find Data Structure Using Pointers

The chapter introduces the union-find data structure and its implementation using pointers. It describes operations including make-union-find, find, and union, highlighting the differences between an array-based and a pointer-based implementation. The chapter underscores the efficiency improvements achieved through the use of path compression, ultimately reducing the complexity of find operations from logarithmic to nearly constant time.

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Sections

  • 7

    Union-Find Data Structure Using Pointers

    This section discusses the advanced implementation of the Union-Find data structure using nodes with pointers, which improves the efficiency of union and find operations.

    Learning Practice

  • 7.1

    Operations Of Union-Find Data Structure

    This section explores the Union-Find data structure, emphasizing operations such as 'make', 'find', and 'union' with pointer-based implementations to enhance efficiency.

    Learning Practice

  • 7.2

    Array Based Implementation

    This section investigates the array-based implementation details of the union-find data structure, emphasizing operational complexities.

    Learning Practice

  • 7.3

    Node Representation With Pointers

    This section introduces the node-based implementation of the union-find data structure, emphasizing pointer representation and the efficiency of operations.

    Learning Practice

  • 7.4

    Make Union Find Initialization

    This section introduces the union-find data structure's initialization phase using nodes and pointers, detailing its operations and complexities.

    Learning Practice

  • 7.5

    Merging Components

    This section elaborates on the union-find data structure using pointers, improving upon the array-based implementation by enhancing operation efficiency.

    Learning Practice

  • 7.6

    Maintaining Component Information

    This section discusses the union-find data structure using pointers, detailing its operations and efficiencies.

    Learning Practice

  • 7.7

    Union Operation Complexity

    This section addresses the efficiency of the union operation in the union-find data structure, particularly focusing on a pointer-based implementation.

    Learning Practice

  • 7.8

    Find Operation Complexity

    This section covers the complexity of the find operation in the union-find data structure, highlighting the efficiencies gained through path compression.

    Learning Practice

  • 7.9

    Path Compression Technique

    The path compression technique optimizes the union-find data structure by reducing the time complexity of the find operation, enhancing overall efficiency when managing component merged structures.

    Learning Practice

  • 7.10

    Effect Of Path Compression On Complexity

    This section discusses the impact of path compression on the complexity of operations in the union-find data structure, highlighting improvements in efficiency.

    Learning Practice

  • 7.11

    Summary Of Union-Find Implementation

    This section explores the Union-Find data structure's pointer-based implementation, detailing its efficiency improvements over an array-based system.

    Learning Practice

References

ch33.pdf

Class Notes

Memorization

What we have learnt

  • The union-find data structu...
  • Using pointers for implemen...
  • The amortized complexity fo...

Final Test

Revision Tests