Question

Computer Science

Posted 6 months ago

```
Using an array-based representation of a binary tree, the following array represents a binary tree.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
59 39 75 48 70 80 44 68 90
What is the postorder traversal of the binary tree that is created in (i).
What is the parent of 68?
```

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Answer from Sia

Posted 6 months ago

python

python

Explanation

The postorder_traversal function recursively visits the left subtree, then the right subtree, and finally the root node for each subtree. The find_parent function calculates the parent's index and returns its value.

Step-by-step Instruction

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Implement a recursive helper function within postorder_traversal to handle the traversal logic

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Define the find_parent function to find the parent of a given node in the binary tree array

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Use the index of the node to calculate the index of the parent in the array

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Define concrete use cases and testing cases for both functions: postorder_traversal should return the correct postorder sequence, and find_parent should return the correct parent node value

Time Complexity

The time complexity of postorder_traversal is O(n) because it visits each node exactly once. The time complexity of find_parent is O(n) in the worst case due to the use of the index method.

Space Complexity

The space complexity of postorder_traversal is O(n) due to the recursive call stack and the output list. The space complexity of find_parent is O(1) as it only uses a constant amount of extra space.

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