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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 <iostream>
2#include <string>
3#include <climits>
4
5using namespace std;
6
7int largestVariance(string s) {
8 int maxVariance = 0;
9 int n = s.length();
10 for (char a = 'a'; a <= 'z'; a++) {
11 for (char b = 'a'; b <= 'z'; b++) {
12 if (a == b) continue;
13 int countA = 0, countB = 0;
14 int maxBal = INT_MIN;
15 for (int i = 0; i < n; i++) {
16 if (s[i] == a) countA++;
17 if (s[i] == b) countB++;
18 if (countB > 0) {
19 maxVariance = max(maxVariance, countA - countB);
20 } else {
21 maxVariance = max(maxVariance, countA);
22 }
23 if (countA < countB) {
24 countA = 0; countB = 0;
25 }
26 }
27 }
28 }
29 return maxVariance;
30}
31
32int main() {
33 cout << largestVariance("aababbb") << endl; // Output: 3
34 return 0;
35}This C++ solution follows the same logic as the C solution. We iterate over each character pair and use a difference tracking approach from Kadane's algorithm to compute the maximum variance for each pair of characters. Reset occurs to manage balance dynamics.
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
Java code uses a sliding window to actively compute variance, stretching over sections of the string based on active character comparisons and frequency adjustments.