Shifting Letters

Problem Description

You are given a string s of lowercase English letters and an integer array shifts of the same length. Call the shift() of a letter, the next letter in the alphabet, (wrapping around so that 'z' becomes 'a'). For each shifts[i] = x, we want to shift the first i + 1 letters of s, x times. Return the final string after all such shifts to s are applied.

Key Insights

• Each character in the string can be shifted based on the cumulative shifts from the shifts array.
• The shifting is cumulative, meaning that later shifts will affect characters that have already been shifted.
• The shift operation wraps around from 'z' to 'a', which can be handled using modulo arithmetic.
• A reverse traversal of the shifts array can help in accumulating shifts efficiently.

Space and Time Complexity

Time Complexity: O(n) - where n is the length of the string s, as we traverse the string once. Space Complexity: O(1) - since we are modifying the string in place and using a constant amount of additional space.

Solution

To solve the problem, we can use a single pass approach that calculates the cumulative shifts for each character in reverse order (from the last character to the first). This way, each character in the string can be shifted correctly based on the total shifts it needs to undergo.

1. Initialize a variable to keep track of the cumulative shifts.
2. Traverse the shifts array from the end to the beginning.
3. For each character in the string, update the cumulative shifts and calculate the new character by applying the cumulative shifts.
4. Store the result and return the final shifted string.

Code Solutions