Add solution #1406

Author: JoshCrozier

README.md

@@ -1,4 +1,4 @@
-# 1,285 LeetCode solutions in JavaScript
+# 1,286 LeetCode solutions in JavaScript
 
 [https://leetcodejavascript.com](https://leetcodejavascript.com)
 
@@ -1074,6 +1074,7 @@
 1403|[Minimum Subsequence in Non-Increasing Order](./solutions/1403-minimum-subsequence-in-non-increasing-order.js)|Easy|
 1404|[Number of Steps to Reduce a Number in Binary Representation to One](./solutions/1404-number-of-steps-to-reduce-a-number-in-binary-representation-to-one.js)|Medium|
 1405|[Longest Happy String](./solutions/1405-longest-happy-string.js)|Medium|
+1406|[Stone Game III](./solutions/1406-stone-game-iii.js)|Hard|
 1408|[String Matching in an Array](./solutions/1408-string-matching-in-an-array.js)|Easy|
 1410|[HTML Entity Parser](./solutions/1410-html-entity-parser.js)|Medium|
 1415|[The k-th Lexicographical String of All Happy Strings of Length n](./solutions/1415-the-k-th-lexicographical-string-of-all-happy-strings-of-length-n.js)|Medium|

solutions/1406-stone-game-iii.js

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+/**
+ * 1406. Stone Game III
+ * https://leetcode.com/problems/stone-game-iii/
+ * Difficulty: Hard
+ *
+ * Alice and Bob continue their games with piles of stones. There are several stones arranged
+ * in a row, and each stone has an associated value which is an integer given in the array
+ * stoneValue.
+ *
+ * Alice and Bob take turns, with Alice starting first. On each player's turn, that player can
+ * take 1, 2, or 3 stones from the first remaining stones in the row.
+ *
+ * The score of each player is the sum of the values of the stones taken. The score of each
+ * player is 0 initially.
+ *
+ * The objective of the game is to end with the highest score, and the winner is the player
+ * with the highest score and there could be a tie. The game continues until all the stones
+ * have been taken.
+ *
+ * Assume Alice and Bob play optimally.
+ *
+ * Return "Alice" if Alice will win, "Bob" if Bob will win, or "Tie" if they will end the game
+ * with the same score.
+ */
+
+/**
+ * @param {number[]} stoneValue
+ * @return {string}
+ */
+var stoneGameIII = function(stoneValue) {
+  const n = stoneValue.length;
+  const cache = new Array(n + 1).fill(null);
+
+  function findOptimalScore(index) {
+    if (index >= n) return 0;
+    if (cache[index] !== null) return cache[index];
+
+    let maxScore = -Infinity;
+    let currentSum = 0;
+
+    for (let stones = 1; stones <= 3 && index + stones - 1 < n; stones++) {
+      currentSum += stoneValue[index + stones - 1];
+      const opponentScore = findOptimalScore(index + stones);
+      maxScore = Math.max(maxScore, currentSum + (index + stones < n ? -opponentScore : 0));
+    }
+
+    cache[index] = maxScore;
+    return maxScore;
+  }
+
+  const aliceScore = findOptimalScore(0);
+  if (aliceScore > 0) return 'Alice';
+  if (aliceScore < 0) return 'Bob';
+  return 'Tie';
+};