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This approach leverages a modified version of Kadane's algorithm to find the largest variance by calculating frequency differences for each character pair combination. We'll use a variation of Kadane's approach to track the balance difference in frequencies between two characters across the string.
The time complexity is O(26^2 * n) = O(n), where n is the length of the string, due to iterating over each character pair and traversing the string. The space complexity is O(1) because we use only a fixed amount of extra space.
1def largestVariance(s: str) -> int:
2 maxVariance = 0
3 for a in set(s):
4 for b in set(s):
5 if a == b:
6 continue
7 countA = countB = 0
8 for char in s:
9 if char == a:
10 countA += 1
11 if char == b:
12 countB += 1
13 if countB > 0:
14 maxVariance = max(maxVariance, countA - countB)
15 else:
16 maxVariance = max(maxVariance, countA)
17 if countA < countB:
18 countA = countB = 0
19 return maxVariance
20
21print(largestVariance("aababbb")) # Output: 3This Python solution iterates over each distinct character combination found in the string. The implementation assesses current balance using a frequency count strategy, regulating resets for most effective results.
The second approach is using the sliding window technique, which dynamically adjusts the window as we scan through the string. This helps to efficiently find all possible maximum variances for character combinations by maintaining two counters and extending or shrinking the window as needed.
Time complexity is O(n) due to efficient window management, spanning the string with a single pass, and space complexity veins at O(1) for predictable and limited use.
1
In this C solution using the sliding window technique, we maintain a dynamic window while iterating over the string. The window adjusts dynamically to keep the variance optimal, expanding and contracting based on character balance.