feat: add solution 1819. Number of Different Subsequences GCDs

Author: tzuyi0817

solutions/1819. Number of Different Subsequences GCDs/README.md

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+# [1819. Number of Different Subsequences GCDs](https://leetcode.com/problems/number-of-different-subsequences-gcds)
+
+## Description
+
+<div class="elfjS" data-track-load="description_content"><p>You are given an array <code>nums</code> that consists of positive integers.</p>
+
+<p>The <strong>GCD</strong> of a sequence of numbers is defined as the greatest integer that divides <strong>all</strong> the numbers in the sequence evenly.</p>
+
+<ul>
+	<li>For example, the GCD of the sequence <code>[4,6,16]</code> is <code>2</code>.</li>
+</ul>
+
+<p>A <strong>subsequence</strong> of an array is a sequence that can be formed by removing some elements (possibly none) of the array.</p>
+
+<ul>
+	<li>For example, <code>[2,5,10]</code> is a subsequence of <code>[1,2,1,<strong><u>2</u></strong>,4,1,<u><strong>5</strong></u>,<u><strong>10</strong></u>]</code>.</li>
+</ul>
+
+<p>Return <em>the <strong>number</strong> of <strong>different</strong> GCDs among all <strong>non-empty</strong> subsequences of</em> <code>nums</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/03/17/image-1.png" style="width: 149px; height: 309px;">
+<pre><strong>Input:</strong> nums = [6,10,3]
+<strong>Output:</strong> 5
+<strong>Explanation:</strong> The figure shows all the non-empty subsequences and their GCDs.
+The different GCDs are 6, 10, 3, 2, and 1.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre><strong>Input:</strong> nums = [5,15,40,5,6]
+<strong>Output:</strong> 7
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
+	<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>5</sup></code></li>
+</ul>
+</div>
+
+<p>&nbsp;</p>
+
+## Solutions
+
+**Solution: `Math`**
+
+- Time complexity: <em>O(nlogn)</em>
+- Space complexity: <em>O(n)</em>
+
+<p>&nbsp;</p>
+
+### **JavaScript**
+
+```js
+/**
+ * @param {number[]} nums
+ * @return {number}
+ */
+const countDifferentSubsequenceGCDs = function (nums) {
+  const maxNum = Math.max(...nums);
+  const factors = Array.from({ length: maxNum + 1 }, () => 0);
+  let result = 0;
+
+  const gcd = (a, b) => (b ? gcd(b, a % b) : a);
+
+  for (const num of nums) {
+    for (let a = 1; a ** 2 <= num; a++) {
+      if (num % a) continue;
+      const b = num / a;
+
+      factors[a] = gcd(num, factors[a]);
+      factors[b] = gcd(num, factors[b]);
+    }
+  }
+
+  for (let num = 1; num <= maxNum; num++) {
+    if (num === factors[num]) {
+      result += 1;
+    }
+  }
+
+  return result;
+};
+```

solutions/1819. Number of Different Subsequences GCDs/solution.js

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+/**
+ * @param {number[]} nums
+ * @return {number}
+ */
+const countDifferentSubsequenceGCDs = function (nums) {
+  const maxNum = Math.max(...nums);
+  const factors = Array.from({ length: maxNum + 1 }, () => 0);
+  let result = 0;
+
+  const gcd = (a, b) => (b ? gcd(b, a % b) : a);
+
+  for (const num of nums) {
+    for (let a = 1; a ** 2 <= num; a++) {
+      if (num % a) continue;
+      const b = num / a;
+
+      factors[a] = gcd(num, factors[a]);
+      factors[b] = gcd(num, factors[b]);
+    }
+  }
+
+  for (let num = 1; num <= maxNum; num++) {
+    if (num === factors[num]) {
+      result += 1;
+    }
+  }
+
+  return result;
+};