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Grokking the Coding Interview Patterns

Solution: Freedom Trail

Explore how to apply dynamic programming to the Freedom Trail problem by using memoization and recursion. Understand how to minimize rotations and button presses on a circular ring to spell out a given key. This lesson helps you grasp optimal substructure and overlapping subproblems within an algorithmic context.

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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:

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