Solution Explanation:

This problem involves performing left and right shifts on a string based on a given shift matrix. The most efficient approach avoids repeatedly shifting the string for each operation in the matrix. Instead, it calculates the net shift and applies it once.

Algorithm:

1. Calculate Net Shift: Iterate through the shift matrix. For each operation:

   • If direction is 0 (left shift), subtract the amount from a running total x.
   • If direction is 1 (right shift), add the amount to x.

2. Handle Modular Arithmetic: The net shift x might be greater than the string length or negative. We use the modulo operator (%) to wrap around. The expression (x % n + n) % n ensures that x is always a positive number within the range [0, n) where n is the string length. This correctly handles both positive and negative shifts beyond the string length.

3. Apply the Shift: After obtaining the effective shift x, we can efficiently apply the shift by extracting substrings:

   • The substring s[-x:] takes the last x characters (right shift).
   • The substring s[:-x] takes the characters from the beginning to the index -x (all but the last x characters). These two substrings are concatenated to get the result.

Time Complexity Analysis:

• Calculating the net shift takes O(m) time, where m is the number of shifts in the shift matrix.
• Extracting and concatenating substrings takes O(n) time, where n is the length of the string s.
• Therefore, the overall time complexity is O(m + n).

Space Complexity Analysis:

• We only use a few integer variables to store the running total and string length.
• The space used is constant regardless of the input size.
• Therefore, the space complexity is O(1).

Code in Different Languages:

The solutions provided earlier demonstrate the algorithm in Python, Java, C++, Go, and TypeScript. Each solution follows the same algorithm, differing only in syntax. The core steps—calculating the net shift, handling modular arithmetic, and applying the shift using substring manipulation—remain consistent across all languages. Refer to the code examples in the previous response for detailed implementation.