Minimum Time to Type Word Using Special Typewriter

Minimum Time to Type Word Using Special Typewriter

What is this problem about?

The Minimum Time to Type Word Using Special Typewriter problem gives you a circular typewriter with letters 'a' to 'z' arranged in a ring. A pointer starts at 'a'. To type each character, you rotate the pointer clockwise or counterclockwise (1 second per step), then press a key (1 second). Find the minimum total time to type a given word. This Minimum Time to Type Word Using Special Typewriter coding problem is a greedy exercise on circular distance computation.

Why is this asked in interviews?

Thomson Reuters, LinkedIn, IBM, and J.P. Morgan ask this easy-level problem to test clean implementation of circular distance computation and greedy decision-making. It validates that candidates can compute the minimum rotation (clockwise vs counterclockwise) between two characters on a circular alphabet. The string and greedy interview pattern is applied in a precise, concrete way.

Algorithmic pattern used

Greedy character-by-character traversal. For each consecutive pair of characters (current, next), compute the clockwise distance (|next - current|) and counterclockwise distance (26 - |next - current|). Take the minimum of the two. Add 1 for the key press. Sum all times.

Example explanation

Word: "bza". Start at 'a'.

• 'a' → 'b': clockwise = 1, counterclockwise = 25. Min = 1. Press = 1. Cost = 2.
• 'b' → 'z': clockwise = 24, counterclockwise = 2. Min = 2. Press = 1. Cost = 3.
• 'z' → 'a': clockwise = 1, counterclockwise = 25. Min = 1. Press = 1. Cost = 2. Total = 2+3+2 = 7.

Common mistakes candidates make

• Using only clockwise rotation (missing the shorter counterclockwise path).
• Forgetting to add 1 second per key press.
• Computing the distance from 'a' always instead of from the current position.
• Off-by-one in the circular distance formula.

Interview preparation tip

Easy greedy problems test implementation precision, not algorithmic depth. Nail the circular distance formula: min(|a - b|, 26 - |a - b|). Always account for the "press" time separately from the "rotate" time. For interviews, derive this formula from first principles (draw the circle) rather than memorizing it — this helps you adapt it to other circular distance problems (hour hands, ring buffers). Getting easy problems done quickly and correctly builds interview momentum.