# 5 Best Ways to Find the Length of the Longest Substring with Even Vowel Counts in Python

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π‘ Problem Formulation: This article focuses on the Python programming challenge of determining the length of the longest substring in a given string where the counts of all vowels (‘a’, ‘e’, ‘i’, ‘o’, ‘u’) are even. For example, given the input string “leetminers”, one possible longest substring with even vowel counts is “eetmi” with a length of 5.

## Method 1: Brute Force

The brute force approach involves checking every possible substring of the input string and recording the length of the substring if it contains even counts of all vowels. This is done in a nested loop structure, which will ultimately yield the longest such substring length encountered.

Here’s an example:

```def longest_even_vowel_substring(s):
max_length = 0
for i in range(len(s)):
for j in range(i+1, len(s)+1):
substr = s[i:j]
vowels = {'a': 0, 'e': 0,'i': 0,'o': 0,'u': 0}
for char in substr:
if char in vowels:
vowels[char] += 1
if all(v % 2 == 0 for v in vowels.values()):
max_length = max(max_length, j-i)
return max_length

print(longest_even_vowel_substring("leetminers")) # Output: 5
```

The code defines a function `longest_even_vowel_substring(s)` that iterates over all possible substrings of the input string `s` and uses a dictionary to count the occurrence of each vowel. If all counts are even, the length of the substring is considered for the maximum length.

## Method 2: Sliding Window

The sliding window approach optimizes the brute force method by moving a window across the input string while keeping track of the vowels’ counts. This approach significantly reduces the time complexity by not re-checking the entire substring every time.

Here’s an example:

```def even_vowels_count(vowels):
return all(count % 2 == 0 for count in vowels.values())

def longest_even_vowel_substring(s):
vowels = {'a': 0, 'e': 0, 'i': 0, 'o': 0, 'u': 0}
start = max_length = 0

for end in range(len(s)):
char = s[end]
if char in vowels:
vowels[char] += 1
while not even_vowels_count(vowels):
if s[start] in vowels:
vowels[s[start]] -= 1
start += 1
max_length = max(max_length, end - start + 1)
return max_length

print(longest_even_vowel_substring("leetminers")) # Output: 5
```

The function `longest_even_vowel_substring(s)` uses two pointers to define the sliding window, and maintains a dictionary of vowels’ counts. It only updates the count for the current characters and adjusts the window to the smallest size that keeps even counts of vowels, finding the maximum length as it progresses.

## Method 3: Prefix Sum and Hash Map

This method utilizes the concept of prefix sums combined with hash maps to keep track of the counts of vowels at any point in the string. When we encounter a set of vowel counts we’ve seen before, we know we have a substring with even vowel counts.

Here’s an example:

```def longest_even_vowel_substring(s):
vowel_indices = {'a':0, 'e':1, 'i':2, 'o':3, 'u':4}
seen = {0: -1}
state = 0
max_length = 0

for index, char in enumerate(s):
if char in vowel_indices:
state ^= 1 << vowel_indices[char]
if state in seen:
max_length = max(max_length, index - seen[state])
else:
seen[state] = index
return max_length

print(longest_even_vowel_substring("leetminers")) # Output: 5
```

The code defines a function `longest_even_vowel_substring(s)` that uses bit manipulation with a prefix sum technique to efficiently track changes in the vowel count. Each vowel corresponds to a bit in an integer `state` that flips whenever that vowel’s count change between even and odd, allowing for quick lookups to detect if a substring with even vowel counts has been found before.

## Method 4: Optimized Space Usage with Bit Masks

This method is an enhancement over the previous method. Instead of using a dictionary to map vowel characters to their counts, we employ bit masks to represent the counts, thus optimizing the space usage and possibly improving performance.

Here’s an example:

```def vowel_to_bit_index(vowel):
return 'aeiou'.find(vowel)

def longest_even_vowel_substring(s):
seen = {0: -1}
max_length = 0

for index, char in enumerate(s):
bit_index = vowel_to_bit_index(char)
if bit_index != -1:
max_length = max(max_length, index - seen[bit_mask])
else:
return max_length

print(longest_even_vowel_substring("leetminers")) # Output: 5
```

This function `longest_even_vowel_substring(s)` utilizes the same prefix sum and hash map approach as before but simplifies it by directly converting the vowel to a bit index and manipulating a single integer bit mask accordingly, making it more space-efficient.

## Bonus One-Liner Method 5: Functional Approach with itertools

A functional one-liner approach can leverage Python’s itertools and functional programming capabilities to solve the problem in a concise manner, though with less consideration for efficiency.

Here’s an example:

```from itertools import accumulate

def longest_even_vowel_substring(s):
vowels = 'aeiou'
vowel_indices = {v: i for i, v in enumerate(vowels)}
acc = list(accumulate((1 << vowel_indices[char]) if char in vowels else 0 for char in s, lambda x, y: x ^ y, initial=0))
seen = {}
return max(seen.setdefault(state, index) - index for index, state in enumerate(acc))

print(longest_even_vowel_substring("leetminers")) # Output: 5
```

This clever one-liner function `longest_even_vowel_substring(s)` makes use of `itertools.accumulate` to generate a prefix sum list using XOR, along with a dictionary comprehension for the seen states, neatly wrapped in a generator expression to find the maximum length.

## Summary/Discussion

• Method 1: Brute Force. This method is simple to understand and implement but has a high time complexity that makes it inefficient for long strings.
• Method 2: Sliding Window. Offers a performance boost over brute force by avoiding redundant operations, making it more suitable for medium-sized strings.
• Method 3: Prefix Sum and Hash Map. This method is very effective and efficient for varying string lengths due to lower time complexity, but it requires a good understanding of bitwise operations.
• Method 4: Optimized Space Usage with Bit Masks. Builds upon Method 3 with even better space efficiency, although the improvements might be negligible unless dealing with very large data.
• Bonus One-Liner Method 5: Functional Approach with itertools. While very concise, this method trades off readability and may not be the most efficient due to its functional nature, which might not be optimized for all use cases.