Add solution #837

Author: JoshCrozier

README.md

@@ -644,6 +644,7 @@
 834|[Sum of Distances in Tree](./0834-sum-of-distances-in-tree.js)|Hard|
 835|[Image Overlap](./0835-image-overlap.js)|Medium|
 836|[Rectangle Overlap](./0836-rectangle-overlap.js)|Easy|
+837|[New 21 Game](./0837-new-21-game.js)|Medium|
 841|[Keys and Rooms](./0841-keys-and-rooms.js)|Medium|
 844|[Backspace String Compare](./0844-backspace-string-compare.js)|Easy|
 846|[Hand of Straights](./0846-hand-of-straights.js)|Medium|

solutions/0837-new-21-game.js

@@ -0,0 +1,48 @@
+/**
+ * 837. New 21 Game
+ * https://leetcode.com/problems/new-21-game/
+ * Difficulty: Medium
+ *
+ * Alice plays the following game, loosely based on the card game "21".
+ *
+ * Alice starts with 0 points and draws numbers while she has less than k points. During each draw,
+ * she gains an integer number of points randomly from the range [1, maxPts], where maxPts is an
+ * integer. Each draw is independent and the outcomes have equal probabilities.
+ *
+ * Alice stops drawing numbers when she gets k or more points.
+ *
+ * Return the probability that Alice has n or fewer points.
+ *
+ * Answers within 10-5 of the actual answer are considered accepted.
+ */
+
+/**
+ * @param {number} n
+ * @param {number} k
+ * @param {number} maxPts
+ * @return {number}
+ */
+var new21Game = function(n, k, maxPts) {
+  if (k === 0 || n >= k + maxPts - 1) return 1.0;
+
+  const dp = new Array(n + 1).fill(0);
+  dp[0] = 1.0;
+
+  let sum = 1.0;
+  for (let i = 1; i <= n; i++) {
+    dp[i] = sum / maxPts;
+    if (i < k) {
+      sum += dp[i];
+    }
+    if (i >= maxPts) {
+      sum -= dp[i - maxPts];
+    }
+  }
+
+  let result = 0;
+  for (let i = k; i <= n; i++) {
+    result += dp[i];
+  }
+
+  return result;
+};