Create prime-arrangements.cpp

Author: kamyu104

C++/prime-arrangements.cpp

@@ -0,0 +1,42 @@
+// Time:  O(n)
+// Space: O(n)
+
+class Solution {
+public:    
+    int numPrimeArrangements(int n) {
+        int cnt = count_primes(n);
+        return static_cast<uint64_t>(factorial(cnt)) * factorial(n - cnt) % MOD;
+    }
+
+private:
+    int count_primes(int n) {
+        if (n <= 1) {
+            return 0;
+        }
+        vector<bool> is_primes((n + 1) / 2, true);
+        int cnt = is_primes.size();
+        for (int i = 3; i * i <= n; i += 2) {
+            if (!is_primes[i / 2]) {
+                continue;
+            }
+            for (int j = i * i; j <= n; j += 2 * i) {
+                if (!is_primes[j / 2]) {
+                    continue;
+                }
+                --cnt;
+                is_primes[j / 2] = false;
+            }
+        }
+        return cnt;
+    }
+
+    int factorial(int n) {
+        int result = 1ull;
+        for (int i = 2; i <= n; ++i) {
+            result = (static_cast<uint64_t>(result) * i) % MOD;
+        }
+        return result;
+    }
+
+    static const int MOD = 1e9 + 7;
+};