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Fundamentals of Python: From First Programs Through Data Structures

Learn about the array-based representation of binary trees, its practicality, efficiency, and implementation for complete binary trees and heaps. Discover how heaps are implemented using arrays.

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Fundamentals of Python: From First Programs Through Data Structures

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  1. Fundamentals of Python:From First Programs Through Data Structures Chapter 18 Hierarchical Collections: Trees

  2. An Array Implementation of Binary Trees • An array-based implementation of a binary tree is difficult to define and practical only in some cases • For complete binary trees, there is an elegant and efficient array-based representation • Elements are stored by level • The array representation of a binary tree is pretty rare and is used mainly to implement a heap Fundamentals of Python: From First Programs Through Data Structures

  3. An Array Implementation of Binary Trees (continued) Fundamentals of Python: From First Programs Through Data Structures

  4. An Array Implementation of Binary Trees (continued) Fundamentals of Python: From First Programs Through Data Structures

  5. An Array Implementation of Binary Trees (continued) Fundamentals of Python: From First Programs Through Data Structures

  6. Implementing Heaps Fundamentals of Python: From First Programs Through Data Structures

  7. Implementing Heaps (continued) • At most, log2n comparisons must be made to walk up the tree from the bottom, so add is O(log n) • Method may trigger a doubling in the array size • O(n), but amortized over all additions, it is O(1) Fundamentals of Python: From First Programs Through Data Structures

  8. Using a Heap to Implement a Priority Queue • In Ch15, we implemented a priority queue with a sorted linked list; alternatively, we can use a heap Fundamentals of Python: From First Programs Through Data Structures

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