Shifting Letters

Shifting Letters

What is this problem about?

The Shifting Letters interview question gives you a string s and an array shifts. For each index i, shift the first i+1 characters of the string forward in the alphabet by shifts[i] positions, wrapping 'z' back to 'a'. After applying all shifts, return the final string. The naive approach applies shifts one by one, but the efficient solution uses suffix prefix sums to compute the cumulative shift for each character.

Why is this asked in interviews?

Microsoft, Meta, Google, and Bloomberg ask this problem because it tests the suffix prefix sum optimization — a core technique for range-update problems. The naive approach is O(n^2); the insight that each character s[i] is shifted by shifts[i] + shifts[i+1] + ... + shifts[n-1] enables an O(n) suffix sum solution. It models batch operations on sequential data — directly applicable to text encoding, Caesar cipher variations, and streaming data transformations.

Algorithmic pattern used

The pattern is suffix prefix sum. Compute the cumulative suffix sum of shifts: suffix[i] = shifts[i] + shifts[i+1] + ... + shifts[n-1]. For each character s[i], the final shifted character is chr((ord(s[i]) - ord('a') + suffix[i]) % 26 + ord('a')). Compute suffix sums in a single right-to-left pass: start from suffix[n-1] = shifts[n-1], then suffix[i] = suffix[i+1] + shifts[i]. Apply modulo 26 at each step to prevent integer overflow.

Example explanation

s = "abc", shifts = [3, 5, 9].

Suffix sums: suffix[2]=9, suffix[1]=5+9=14, suffix[0]=3+14=17.

Apply shifts:

• 'a' + 17 = 'r' (0+17=17 → 'r').
• 'b' + 14 = 'p' (1+14=15 → 'p').
• 'c' + 9 = 'l' (2+9=11 → 'l').

Result: "rpl".

Common mistakes candidates make

• Applying shifts one by one in O(n^2) — this is correct but too slow for large inputs.
• Not applying modulo 26 during suffix sum computation — large accumulated values can overflow; reduce modulo 26 at each step.
• Off-by-one in the suffix sum direction — shift for character i must include shifts[i] through shifts[n-1], not just shifts[i].
• Forgetting to handle wrap-around (z → a) — the modulo 26 formula handles this automatically.

Interview preparation tip

For the Shifting Letters coding problem, the array prefix sum interview pattern applied as a suffix sum is the key optimization. The observation "each character accumulates all subsequent shifts" converts the problem from O(n^2) to O(n) in one insight. Google and Bloomberg interviewers appreciate when you derive the suffix sum formula before writing code. Practice both prefix (left-to-right) and suffix (right-to-left) cumulative sum patterns — they appear in different forms across range-update and batch-operation problems.