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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.
1#include <stdio.h>
2#include <string.h>
3#include <limits.h>
4
5int largestVariance(char *s) {
6 int maxVariance = 0;
7 int n = strlen(s);
8 for (char a = 'a'; a <= 'z'; a++) {
9 for (char b = 'a'; b <= 'z'; b++) {
10 if (a == b) continue;
11 int countA = 0, countB = 0;
12 int maxBal = INT_MIN;
13 for (int i = 0; i < n; i++) {
14 if (s[i] == a) countA++;
15 if (s[i] == b) countB++;
16 if (countB > 0) {
17 maxVariance = maxVariance > (countA - countB) ?
18 maxVariance : (countA - countB);
19 } else {
20 /* Reset when negative or zero to avoid excessive penalizing */
21 maxVariance = maxVariance > countA ? maxVariance : countA;
22 }
23 if (countA < countB) {
24 countA = 0; countB = 0;
25 }
26 }
27 }
28 }
29 return maxVariance;
30}
31
32int main() {
33 char s[] = "aababbb";
34 printf("%d\n", largestVariance(s)); // Output: 3
35 return 0;
36}The solution involves iterating over all possible pairs of characters (a, b). For each pair, we calculate the difference in frequency counts using a variation of Kadane's algorithm approach to determine the maximum variance for that pair. The balance is reset when frequency of 'b' exceeds 'a', avoiding any negative variance.
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
With JavaScript's leveraging of the sliding window methodology, calculations occur dynamically within a regulated scope, ensuring adaptable and active evaluation.