Create prime-arrangements.py

Author: kamyu104

Python/prime-arrangements.py

@@ -0,0 +1,35 @@
+# Time:  O(n)
+# Space: O(n)
+
+class Solution(object):
+    def numPrimeArrangements(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        def count_primes(n):
+            if n <= 1:
+                return 0
+            is_prime = [True]*((n+1)//2)
+            cnt = len(is_prime)
+            for i in xrange(3, n+1, 2):
+                if i*i > n:
+                    break
+                if not is_prime[i//2]:
+                    continue
+                for j in xrange(i*i, n+1, 2*i):
+                    if not is_prime[j//2]:
+                        continue
+                    cnt -= 1
+                    is_prime[j//2] = False
+            return cnt
+        
+        def factorial(n):
+            result = 1
+            for i in xrange(2, n+1):
+                result = (result*i)%MOD
+            return result
+
+        MOD = 10**9+7
+        cnt = count_primes(n)
+        return factorial(cnt) * factorial(n-cnt) % MOD