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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.
1public class LargestVariance {
2 public static int largestVariance(String s) {
3 int maxVariance = 0;
4 int n = s.length();
5 for (char a = 'a'; a <= 'z'; a++) {
6 for (char b = 'a'; b <= 'z'; b++) {
7 if (a == b) continue;
8 int countA = 0, countB = 0;
9 int maxBal = Integer.MIN_VALUE;
10 for (int i = 0; i < n; i++) {
11 if (s.charAt(i) == a) countA++;
12 if (s.charAt(i) == b) countB++;
13 if (countB > 0) {
14 maxVariance = Math.max(maxVariance, countA - countB);
15 } else {
16 maxVariance = Math.max(maxVariance, countA);
17 }
18 if (countA < countB) {
19 countA = 0; countB = 0;
20 }
21 }
22 }
23 }
24 return maxVariance;
25 }
26
27 public static void main(String[] args) {
28 System.out.println(largestVariance("aababbb")); // Output: 3
29 }
30}The Java solution mirrors the logic of preceding code samples, using nested loops to evaluate each unique character combination. Frequency variances are assessed using a dynamic tracking strategy.
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.