0514-freedom-trail.js

/**
 * 514. Freedom Trail
 * https://leetcode.com/problems/freedom-trail/
 * Difficulty: Hard
 *
 * In the video game Fallout 4, the quest "Road to Freedom" requires players to reach a metal dial
 * called the "Freedom Trail Ring" and use the dial to spell a specific keyword to open the door.
 *
 * Given a string ring that represents the code engraved on the outer ring and another string key
 * that represents the keyword that needs to be spelled, return the minimum number of steps to spell
 * all the characters in the keyword.
 *
 * Initially, the first character of the ring is aligned at the "12:00" direction. You should spell
 * all the characters in key one by one by rotating ring clockwise or anticlockwise to make each
 * character of the string key aligned at the "12:00" direction and then by pressing the center
 * button.
 *
 * At the stage of rotating the ring to spell the key character key[i]:
 * - You can rotate the ring clockwise or anticlockwise by one place, which counts as one step.
 *   The final purpose of the rotation is to align one of ring's characters at the "12:00"
 *   direction, where this character must equal key[i].
 * - If the character key[i] has been aligned at the "12:00" direction, press the center button
 *   to spell, which also counts as one step. After the pressing, you could begin to spell the
 *   next character in the key (next stage). Otherwise, you have finished all the spelling.
 */

/**
 * @param {string} ring
 * @param {string} key
 * @return {number}
 */
var findRotateSteps = function(ring, key) {
  const map = new Map();
  return dp(0, 0);

  function dp(ringIndex, keyIndex) {
    if (keyIndex === key.length) return 0;
    const state = `${ringIndex},${keyIndex}`;
    if (map.has(state)) return map.get(state);
    let minSteps = Infinity;
    for (let i = 0; i < ring.length; i++) {
      if (ring[i] === key[keyIndex]) {
        const distance = Math.abs(i - ringIndex);
        const steps = Math.min(distance, ring.length - distance);
        minSteps = Math.min(minSteps, steps + 1 + dp(i, keyIndex + 1));
      }
    }
    map.set(state, minSteps);
    return minSteps;
  }
};