Balanced Package Sequence ā Problem Statement & Solution Guide
Problem Description
Given a sequence of characters, where 'L' represents a large package and 'S' represents a small package, find the length of the longest contiguous subsequence that contains an equal number of 'L' and 'S' packages and starts and ends with the same character.
Examples
Input
LSL
Output
3
Explanation: Step-by-step: with input 'LSL', we first initialize two pointers, one at the start and one at the end of the string. We then move the pointers towards each other, counting the number of 'L' and 'S' packages. When the counts are equal, we check if the start and end characters are the same. If they are, we update the maximum length of the subsequence. Finally, we return the maximum length.
Input
SSLS
Output
0
Explanation: Step-by-step: with input 'SSLS', we first initialize two pointers, one at the start and one at the end of the string. We then move the pointers towards each other, counting the number of 'L' and 'S' packages. However, since the counts are never equal, we return 0 as there is no subsequence that meets the conditions.
Constraints
- 1 <= length of the input string <= 1000
- The input string only contains 'L' and 'S' characters.
Optimal Approach & Strategy
The optimal approach uses two pointers, one at the start and one at the end of the subsequence, and expands or contracts the subsequence as needed to maintain an equal number of 'L' and 'S' packages. This approach has a time complexity of O(n).
Brute Force Approach
A naive approach would involve checking all possible subsequences of the input string to see if they have an equal number of 'L' and 'S' packages and start and end with the same package size. This approach has a time complexity of O(nĀ²) due to the nested loops. It's inefficient for large inputs.
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