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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.
1using System;
2
3public class Program
4{
5 public static int LargestVariance(string s)
6 {
7 int maxVariance = 0;
8 int n = s.Length;
9 for (char a = 'a'; a <= 'z'; a++)
10 {
11 for (char b = 'a'; b <= 'z'; b++)
12 {
13 if (a == b) continue;
14 int countA = 0, countB = 0;
15 for (int i = 0; i < n; i++)
16 {
17 if (s[i] == a) countA++;
18 if (s[i] == b) countB++;
19 if (countB > 0)
20 {
21 maxVariance = Math.Max(maxVariance, countA - countB);
22 }
23 else
24 {
25 maxVariance = Math.Max(maxVariance, countA);
26 }
27 if (countA < countB)
28 {
29 countA = 0; countB = 0;
30 }
31 }
32 }
33 }
34 return maxVariance;
35 }
36
37 public static void Main()
38 {
39 Console.WriteLine(LargestVariance("aababbb")); // Output: 3
40 }
41}In this C# solution, nested loops execute over distinct character combinations, employing difference tracking inspired by Kadane's algorithm to find maximum variances within the string's character series.
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
Python's sliding window wraps character evaluations in a way that allows for precise selection of the optimal variance, performing live frequency calculations and window adjustments.