Add solution #808

Author: JoshCrozier

README.md

@@ -616,6 +616,7 @@
 804|[Unique Morse Code Words](./0804-unique-morse-code-words.js)|Easy|
 805|[Split Array With Same Average](./0805-split-array-with-same-average.js)|Hard|
 806|[Number of Lines To Write String](./0806-number-of-lines-to-write-string.js)|Easy|
+808|[Soup Servings](./0808-soup-servings.js)|Medium|
 819|[Most Common Word](./0819-most-common-word.js)|Easy|
 821|[Shortest Distance to a Character](./0821-shortest-distance-to-a-character.js)|Easy|
 824|[Goat Latin](./0824-goat-latin.js)|Easy|

solutions/0808-soup-servings.js

@@ -0,0 +1,52 @@
+/**
+ * 808. Soup Servings
+ * https://leetcode.com/problems/soup-servings/
+ * Difficulty: Medium
+ *
+ * There are two types of soup: type A and type B. Initially, we have n ml of each type of soup.
+ * There are four kinds of operations:
+ * 1. Serve 100 ml of soup A and 0 ml of soup B,
+ * 2. Serve 75 ml of soup A and 25 ml of soup B,
+ * 3. Serve 50 ml of soup A and 50 ml of soup B, and
+ * 4. Serve 25 ml of soup A and 75 ml of soup B.
+ *
+ * When we serve some soup, we give it to someone, and we no longer have it. Each turn, we will
+ * choose from the four operations with an equal probability 0.25. If the remaining volume of
+ * soup is not enough to complete the operation, we will serve as much as possible. We stop once
+ * we no longer have some quantity of both types of soup.
+ *
+ * Note that we do not have an operation where all 100 ml's of soup B are used first.
+ *
+ * Return the probability that soup A will be empty first, plus half the probability that A and B
+ * become empty at the same time. Answers within 10-5 of the actual answer will be accepted.
+ */
+
+/**
+ * @param {number} n
+ * @return {number}
+ */
+var soupServings = function(n) {
+  if (n >= 4800) return 1.0;
+
+  n = Math.ceil(n / 25);
+  const memo = new Map();
+
+  function calculateProbability(a, b) {
+    if (a <= 0 && b <= 0) return 0.5;
+    if (a <= 0) return 1.0;
+    if (b <= 0) return 0.0;
+
+    const key = a * 10000 + b;
+    if (memo.has(key)) return memo.get(key);
+
+    const probability = 0.25 * (
+      calculateProbability(a - 4, b) + calculateProbability(a - 3, b - 1)
+      + calculateProbability(a - 2, b - 2) + calculateProbability(a - 1, b - 3)
+    );
+
+    memo.set(key, probability);
+    return probability;
+  }
+
+  return calculateProbability(n, n);
+};