New Problem Solution -"1819. Number of Different Subsequences GCDs"

Author: haoel

README.md

@@ -9,6 +9,7 @@ LeetCode
 
 | # | Title | Solution | Difficulty |
 |---| ----- | -------- | ---------- |
+|1819|[Number of Different Subsequences GCDs](https://leetcode.com/problems/number-of-different-subsequences-gcds/) | [C++](./algorithms/cpp/numberOfDifferentSubsequencesGcds/NumberOfDifferentSubsequencesGcds.cpp)|Hard|
 |1818|[Minimum Absolute Sum Difference](https://leetcode.com/problems/minimum-absolute-sum-difference/) | [C++](./algorithms/cpp/minimumAbsoluteSumDifference/MinimumAbsoluteSumDifference.cpp)|Medium|
 |1817|[Finding the Users Active Minutes](https://leetcode.com/problems/finding-the-users-active-minutes/) | [C++](./algorithms/cpp/findingTheUsersActiveMinutes/FindingTheUsersActiveMinutes.cpp)|Medium|
 |1816|[Truncate Sentence](https://leetcode.com/problems/truncate-sentence/) | [C++](./algorithms/cpp/truncateSentence/TruncateSentence.cpp)|Easy|

algorithms/cpp/numberOfDifferentSubsequencesGcds/NumberOfDifferentSubsequencesGcds.cpp

@@ -0,0 +1,78 @@
+// Source : https://leetcode.com/problems/number-of-different-subsequences-gcds/
+// Author : Hao Chen
+// Date   : 2021-04-05
+
+/***************************************************************************************************** 
+ *
+ * You are given an array nums that consists of positive integers.
+ * 
+ * The GCD of a sequence of numbers is defined as the greatest integer that divides all the numbers in 
+ * the sequence evenly.
+ * 
+ * 	For example, the GCD of the sequence [4,6,16] is 2.
+ * 
+ * A subsequence of an array is a sequence that can be formed by removing some elements (possibly 
+ * none) of the array.
+ * 
+ * 	For example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].
+ * 
+ * Return the number of different GCDs among all non-empty subsequences of nums.
+ * 
+ * Example 1:
+ * 
+ * Input: nums = [6,10,3]
+ * Output: 5
+ * Explanation: The figure shows all the non-empty subsequences and their GCDs.
+ * The different GCDs are 6, 10, 3, 2, and 1.
+ * 
+ * Example 2:
+ * 
+ * Input: nums = [5,15,40,5,6]
+ * Output: 7
+ * 
+ * Constraints:
+ * 
+ * 	1 <= nums.length <= 10^5
+ * 	1 <= nums[i] <= 2 * 10^5
+ ******************************************************************************************************/
+
+class Solution {
+private:
+    // Euclidean algorithm
+    // https://en.wikipedia.org/wiki/Euclidean_algorithm
+    int gcd(int a, int b) {
+        while ( b != 0 ) {
+            int t = b;
+            b = a % b;
+            a = t;
+        }
+        return a;
+    }
+
+public:
+    int countDifferentSubsequenceGCDs(vector<int>& nums) {
+        int len = nums.size();
+        vector<int> gcds(200001, 0);
+        
+        for(int i=0; i<len; i++) {
+            int n = nums[i];
+            int m = sqrt(n);
+            for(int g=1; g<=m; g++){
+                if (n % g != 0) continue;
+                int x = g, y = n/g;
+                if (x != y ){
+                    gcds[x] = gcd(n, gcds[x]);
+                    gcds[y] = gcd(n, gcds[y]);
+                }else {
+                    gcds[x] = gcd(n, gcds[x]);
+                }
+            }
+        }
+        
+        int cnt = 0;
+        for(int i=1; i<gcds.size(); i++){
+            if (gcds[i]==i) cnt++;
+        }
+        return cnt;
+    }
+};