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The two pointers approach uses two indices to represent the start and end of the string. The idea is to check for matching characters from both ends and shrink the string until the characters differ. Loop through the string, adjusting these pointers to remove any prefixes and suffixes with matching characters. This method is efficient as it only requires a single pass through the string.
Time Complexity: O(n), where n is the length of the string, because each character is visited at most twice.
Space Complexity: O(1), as no additional space is used apart from variables.
1function minimumLength(s) {
2 let left = 0, right = s.length - 1;
3 while (left < right && s[left] === s[right]) {
4 const currentChar = s[left];
5 while (left <= right && s[left] === currentChar) {
6 left++;
7 }
8 while (left <= right && s[right] === currentChar) {
9 right--;
10 }
11 }
12 return right - left + 1;
13}
14
15console.log(minimumLength('aabccabba')); // Output: 3The JavaScript implementation follows the two-pointer technique, removing matching prefix and suffixes iteratively to achieve a minimal string length.
This recursive approach tries to minimize the string length by removing valid prefixes and suffixes. The base case is when no more valid removals are possible, and the remaining string length is minimal. Each recursive call attempts to strip away the symmetric ends and proceeds with the interior until the results match.
Time Complexity: O(n), since it navigates through the string at minimal overhead.
Space Complexity: O(n) due to recursion depth management.
This Python recursive approach continuously analyzes characters at the string's periphery, peeling symmetrical areas iteratively upon matches. The recursion simplifies the problem and calculates the minimal feasible length.