Shifting Letters II

Problem Description

You are given a string s of lowercase English letters and a 2D integer array shifts where shifts[i] = [start_i, end_i, direction_i]. For every i, shift the characters in s from the index start_i to the index end_i (inclusive) forward if direction_i = 1, or shift the characters backward if direction_i = 0. Shifting a character forward means replacing it with the next letter in the alphabet (wrapping around so that 'z' becomes 'a'). Similarly, shifting a character backward means replacing it with the previous letter in the alphabet (wrapping around so that 'a' becomes 'z'). Return the final string after all such shifts to s are applied.

Key Insights

• Each shift operation can affect overlapping ranges in the string.
• Directly applying shifts one by one can lead to inefficiencies, especially with large input sizes.
• Using a frequency array to track the net effect of shifts allows for a more efficient application.
• The shifting logic can be efficiently handled by calculating the cumulative effect of shifts in a single pass.

Space and Time Complexity

Time Complexity: O(n + m), where n is the length of the string and m is the number of shifts. Space Complexity: O(n), for the frequency array used to accumulate shift effects.

Solution

To solve the problem, we can use the following approach:

1. Frequency Array: Create a frequency array to keep track of the net shifts for each character in the string.
2. Apply Shifts: For each shift instruction, we update the start and end indices in the frequency array to indicate the direction and magnitude of the shifts.
3. Cumulative Changes: Traverse the frequency array to calculate the cumulative shifts for each character in the string.
4. Final Adjustments: Adjust each character in the string based on the cumulative shifts calculated in the previous step, making sure to wrap around the alphabet as necessary.

Code Solutions