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This is the modifications made to the original code:
1. Create Doctest Instructions: Python "doctest" can be executed by running the following command: python -m doctest -v equilibrium_index.py.
2. Deleted Argument {size}: Deleted the `size` argument because `len(arr)} allows the array's length to be determined inside the function, simplifying and improving the readability of the function signature.
3. Used {enumerate}: To improve code readability and indicate that we're working with element-index pairs, we iterated through the array using both elements and their indices using the `enumerate` function.
4. Optimized the Loop: To prevent pointless additions, the loop was improved by initializing {left_sum} with the value of the first element (arr[0]). Furthermore, since the beginning and last items (0 and size - 1) cannot be equilibrium indices, there is no need to check them, saving further computations.
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* Made binary tree memory-friendly using generators based travels. Fixes
#8725
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#8725
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Consider a word, and a copy of that word, but with the last letter repeating twice. (e.g., ["ABC", "ABCC"])
When adding the second word's last letter, it only compares the previous word's prefix—the last letter of the word already in the Radix Tree: 'C'—and the letter to be added—the last letter of the word we're currently adding: 'C'. So it wrongly passes the "Case 1" check, marks the current node as a leaf node when it already was, then returns when there's still one more letter to add.
The issue arises because `prefix` includes the letter of the node itself. (e.g., `nodes: {'C' : RadixNode()}, is_leaf: True, prefix: 'C'`) It can be easily fixed by simply adding the `is_leaf` check, asking if there are more letters to be added.
- Test Case: `"A AA AAA AAAA"`
- Fixed correct output:
```
Words: ['A', 'AA', 'AAA', 'AAAA']
Tree:
- A (leaf)
-- A (leaf)
--- A (leaf)
---- A (leaf)
```
- Current incorrect output:
```
Words: ['A', 'AA', 'AAA', 'AAAA']
Tree:
- A (leaf)
-- AA (leaf)
--- A (leaf)
```
*N.B.* This passed test cases for [Croatian Open Competition in Informatics 2012/2013 Contest #3 Task 5 HERKABE](https://hsin.hr/coci/archive/2012_2013/)
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