Create four-divisors.cpp

Author: kamyu104

C++/four-divisors.cpp

@@ -0,0 +1,65 @@
+// Time:  O(n * sqrt(n))
+// Space: O(sqrt(n))
+
+class Solution {
+public:
+    int sumFourDivisors(vector<int>& nums) {
+        int result = 0;
+        for (const auto& num : nums) {
+            const auto& facs = factorize(num);
+            if (facs.size() == 1 && facs[0].second == 3) {
+                const auto& p = facs[0].first;
+                result += int(pow(p, 4) - 1) / (p - 1);  // p^0 + p^1 +p^2 +p^3
+            } else if (facs.size() == 2 &&
+                       facs[0].second == 1 &&
+                       facs[1].second == 1) {
+                const auto& [p, q] = pair(facs[0].first, facs[1].first);
+                result += (1 + p) * (1 + q);
+            }
+        }
+        return result;
+    }
+
+private:
+    vector<pair<int, int>> factorize(int x) {
+        vector<pair<int, int>> result;
+        for (int d = 2; d * d <= x; d += (d == 2) ? 1: 2) {
+            int e = 0;
+            for (; x % d == 0; ++e) {
+                x /= d;
+            }
+            if (e) {
+                result.emplace_back(d, e);
+            }
+        }
+        if (x > 1) {
+            result.emplace_back(x, 1);
+        }
+        return result;
+    }
+};
+
+// Time:  O(n * sqrt(n))
+// Space: O(sqrt(n))
+class Solution2 {
+public:
+    int sumFourDivisors(vector<int>& nums) {
+        int result = 0;
+        for (const auto& num : nums) {
+            vector<int> facs;
+            for (int i = 1; i * i <= num; ++i) {
+                if (num % i) {
+                    continue;
+                }
+                facs.emplace_back(i);
+                if (i != num / i) {
+                    facs.emplace_back(num / i);
+                }
+            }
+            if (facs.size() == 4) {
+                result += accumulate(cbegin(facs), cend(facs), 0);
+            } 
+        }
+        return result;
+    }
+};