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