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Grokking the Coding Interview Patterns

Solution: Freedom Trail

Explore a dynamic programming approach to solve the Freedom Trail problem by minimizing the number of rotation steps and button presses needed to spell a key on a circular ring. Learn how memoization helps optimize the process by caching intermediate results, ensuring efficient handling of overlapping subproblems for optimal solutions.

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Statement

You are given a circular ring represented by a string ring, and a keyword represented by a string key that you need to spell out.

Initially, the first character of ring (index 00) is aligned at the "12:00" position. To spell each character in key sequentially, you must:

  1. Rotate the ring clockwise or anticlockwise. Each rotation by one position counts as one step. Rotate until a character in ring that matches the current target character key[i] is aligned at the "12:00" position.

  2. Press the center button to confirm the character, which counts as one additional step.

After pressing, you move on to spell the next character in key. The ring is circular, meaning its last character wraps around to its first character.

Return the minimum total number of steps required to spell all characters in key.

Note: Each button press counts as one step in addition to the rotation steps.

Constraints:

  • ...