Shifting Letters II

Shifting Letters II

What is this problem about?

The Shifting Letters II interview question extends the first version by replacing individual shift values with range shift operations. Each operation [l, r, direction] shifts all characters in the range [l, r] forward (direction=1) or backward (direction=0) by 1 step. After applying all operations, return the resulting string. With up to 10^5 operations and a 10^5 character string, this requires a difference array to handle range updates efficiently.

Why is this asked in interviews?

Meta, Amazon, and Google ask this problem because it tests the difference array technique — the canonical tool for batch range updates in O(1) per operation and O(n) final reconstruction. Range updates are fundamental in time-series analytics, segment tree applications, and event scheduling. The ability to avoid O(n × q) brute force in favor of O(n + q) difference arrays distinguishes strong candidates from beginners.

Algorithmic pattern used

The pattern is difference array for range updates. Create a difference array diff of size n+1, initialized to 0. For each operation [l, r, direction]: add +1 to diff[l] and -1 to diff[r+1] if direction=1 (forward); add -1 to diff[l] and +1 to diff[r+1] if direction=0 (backward). Compute prefix sum of diff to get the net shift at each position. Apply (net_shift % 26 + 26) % 26 to each character (double modulo handles negative shifts).

Example explanation

s = "dzz", shifts = [[0,0,0],[1,1,1]].

Operation [0,0,0]: diff[0] -= 1, diff[1] += 1. diff = [-1, 1, 0, 0]. Operation [1,1,1]: diff[1] += 1, diff[2] -= 1. diff = [-1, 2, -1, 0].

Prefix sum → net shifts: [-1, 1, 0].

Apply:

• 'd' + (-1) = 'c'. (3-1=2 → 'c').
• 'z' + 1 = 'a'. (25+1=26 % 26 = 0 → 'a').
• 'z' + 0 = 'z'.

Result: "caz".

Common mistakes candidates make

• Not handling negative shifts — (shift % 26 + 26) % 26 is required since Python/Java/C++ modulo can return negative values for negative inputs.
• Using O(n) per operation to update each position in range — defeats the purpose; use difference array for O(1) updates.
• Applying diff[r+1] -= 1 out of bounds when r = n-1 — ensure the difference array has size n+1 to handle boundary updates.
• Confusing this with Shifting Letters I (which uses suffix sums, not difference arrays).

Interview preparation tip

For the Shifting Letters II coding problem, the array prefix sum difference array interview pattern is essential. The difference array trick converts range-update problems from O(n × q) to O(n + q). Meta and Amazon interviewers test this exact pattern — practice implementing it from scratch. Key formula: (accumulated_shift % 26 + 26) % 26 handles both forward and backward shifts correctly. The difference array technique also applies to range paint problems, event scheduling, and the classic "add 1 to a range" operation.