Add solution #1467

Author: JoshCrozier

README.md

@@ -1,4 +1,4 @@
-# 1,316 LeetCode solutions in JavaScript
+# 1,317 LeetCode solutions in JavaScript
 
 [https://leetcodejavascript.com](https://leetcodejavascript.com)
 
@@ -1122,6 +1122,7 @@
 1464|[Maximum Product of Two Elements in an Array](./solutions/1464-maximum-product-of-two-elements-in-an-array.js)|Easy|
 1465|[Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts](./solutions/1465-maximum-area-of-a-piece-of-cake-after-horizontal-and-vertical-cuts.js)|Medium|
 1466|[Reorder Routes to Make All Paths Lead to the City Zero](./solutions/1466-reorder-routes-to-make-all-paths-lead-to-the-city-zero.js)|Medium|
+1467|[Probability of a Two Boxes Having The Same Number of Distinct Balls](./solutions/1467-probability-of-a-two-boxes-having-the-same-number-of-distinct-balls.js)|Hard|
 1470|[Shuffle the Array](./solutions/1470-shuffle-the-array.js)|Easy|
 1472|[Design Browser History](./solutions/1472-design-browser-history.js)|Medium|
 1475|[Final Prices With a Special Discount in a Shop](./solutions/1475-final-prices-with-a-special-discount-in-a-shop.js)|Easy|

solutions/1467-probability-of-a-two-boxes-having-the-same-number-of-distinct-balls.js

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+/**
+ * 1467. Probability of a Two Boxes Having The Same Number of Distinct Balls
+ * https://leetcode.com/problems/probability-of-a-two-boxes-having-the-same-number-of-distinct-balls/
+ * Difficulty: Hard
+ *
+ * Given 2n balls of k distinct colors. You will be given an integer array balls of size k where
+ * balls[i] is the number of balls of color i.
+ *
+ * All the balls will be shuffled uniformly at random, then we will distribute the first n balls to
+ * the first box and the remaining n balls to the other box (Please read the explanation of the
+ * second example carefully).
+ *
+ * Please note that the two boxes are considered different. For example, if we have two balls of
+ * colors a and b, and two boxes [] and (), then the distribution [a] (b) is considered different
+ * than the distribution [b] (a) (Please read the explanation of the first example carefully).
+ *
+ * Return the probability that the two boxes have the same number of distinct balls. Answers
+ * within 10-5 of the actual value will be accepted as correct.
+ */
+
+/**
+ * @param {number[]} balls
+ * @return {number}
+ */
+var getProbability = function(balls) {
+  const totalBalls = balls.reduce((sum, count) => sum + count, 0);
+  const halfBalls = totalBalls / 2;
+  let validCombinations = 0;
+  let totalCombinations = 0;
+
+  calculateCombinations(0, new Array(balls.length).fill(0), halfBalls, 0);
+  return validCombinations / totalCombinations;
+
+  function countDistinct(config) {
+    return config.filter(count => count > 0).length;
+  }
+
+  function calculateCombinations(index, config, remaining, firstBoxCount) {
+    if (index === balls.length) {
+      if (firstBoxCount === halfBalls) {
+        const secondBox = balls.map((count, i) => count - config[i]);
+        if (countDistinct(config) === countDistinct(secondBox)) {
+          validCombinations += combinatorialProduct(config) * combinatorialProduct(secondBox);
+        }
+        totalCombinations += combinatorialProduct(config) * combinatorialProduct(secondBox);
+      }
+      return;
+    }
+
+    for (let i = 0; i <= balls[index] && firstBoxCount + i <= halfBalls; i++) {
+      if (remaining >= i) {
+        config[index] = i;
+        calculateCombinations(index + 1, config, remaining - i, firstBoxCount + i);
+        config[index] = 0;
+      }
+    }
+  }
+
+  function combinatorialProduct(config) {
+    const numerator = factorial(halfBalls);
+    let denominator = 1;
+    for (const count of config) {
+      denominator *= factorial(count);
+    }
+    return numerator / denominator;
+  }
+
+  function factorial(n) {
+    let result = 1;
+    for (let i = 2; i <= n; i++) {
+      result *= i;
+    }
+    return result;
+  }
+};