Probability of a Two Boxes Having the Same Number of Distinct Balls solved

Author: hasibulislam999

Probability and Statistics/1467_probability-of-a-two-boxes-having-the-same-number-of-distinct-balls.js

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+/**
+ * Title: Probability of a Two Boxes Having the Same Number of Distinct Balls
+ * Description: 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.
+ * Author: Hasibul Islam
+ * Date: 04/04/2023
+ */
+
+/**
+ * @param {number[]} balls
+ * @return {number}
+ */
+var getProbability = function (balls) {
+  var k = balls.length;
+  var halfUsed = balls.reduce((acc, val) => acc + val, 0) / 2;
+  var startArray = new Array(k);
+  startArray.fill(0);
+
+  const perm = function (b1, b2) {
+    var p1, p2, s1, s2;
+
+    s1 = b1.reduce((acc, val) => acc + val, 0);
+    s2 = b2.reduce((acc, val) => acc + val, 0);
+
+    const fact = function (n) {
+      var f = 1;
+      for (let i = 2; i <= n; i++) f *= i;
+      return f;
+    };
+
+    p1 = fact(s1);
+    p2 = fact(s2);
+
+    b1.forEach((val) => {
+      if (val > 1) p1 /= fact(val);
+    });
+    b2.forEach((val) => {
+      if (val > 1) p2 /= fact(val);
+    });
+
+    return p1 * p2;
+  };
+
+  const getValidCombos = function (ballsUsed, colorNum = 0) {
+    var box1Used = ballsUsed.reduce((acc, val) => acc + val, 0);
+    var matches = { good: 0, total: 0 },
+      thisColorMax = halfUsed - box1Used;
+
+    if (colorNum === k - 1) {
+      /* 
+                               Last ball color - adjust # of balls of this color to equal half
+                               (if possible).  Then count # of different balls in each box.
+                       */
+      if (thisColorMax > balls[colorNum]) return { good: 0, total: 0 };
+
+      ballsUsed[colorNum] = thisColorMax;
+      let ballsLeft = [];
+      let colorsUsed = [0, 0];
+      for (let i = 0; i < k; i++) {
+        ballsLeft[i] = balls[i] - ballsUsed[i];
+        if (ballsUsed[i] > 0) colorsUsed[0]++;
+        if (ballsLeft[i] > 0) colorsUsed[1]++;
+      }
+
+      /* Count the # of permutations for the boxes represented by this 1 combination. */
+      let permutations = perm(ballsUsed, ballsLeft, k);
+      return {
+        good: colorsUsed[1] === colorsUsed[0] ? permutations : 0,
+        total: permutations,
+      };
+    }
+
+    thisColorMax = Math.min(thisColorMax, balls[colorNum]);
+    for (let i = 0; i <= thisColorMax; i++) {
+      let match = getValidCombos([...ballsUsed], colorNum + 1);
+      matches = {
+        good: matches.good + match.good,
+        total: matches.total + match.total,
+      };
+      ballsUsed[colorNum]++;
+    }
+    return matches;
+  };
+
+  /* Probability = (total # of permutations with equal # of balls) / (permutations with same # of unique balls) */
+  let res = getValidCombos(startArray);
+  return res.good / res.total;
+};
+
+console.log(getProbability([1, 2, 3, 4, 5]));