Add solution #514

Author: JoshCrozier

README.md

@@ -410,6 +410,7 @@
 508|[Most Frequent Subtree Sum](./0508-most-frequent-subtree-sum.js)|Medium|
 509|[Fibonacci Number](./0509-fibonacci-number.js)|Easy|
 513|[Find Bottom Left Tree Value](./0513-find-bottom-left-tree-value.js)|Medium|
+514|[Freedom Trail](./0514-freedom-trail.js)|Hard|
 520|[Detect Capital](./0520-detect-capital.js)|Easy|
 521|[Longest Uncommon Subsequence I](./0521-longest-uncommon-subsequence-i.js)|Easy|
 530|[Minimum Absolute Difference in BST](./0530-minimum-absolute-difference-in-bst.js)|Easy|

solutions/0514-freedom-trail.js

@@ -0,0 +1,51 @@
+/**
+ * 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;
+  }
+};