solves prime arrangements

Author: anishLearnsToCode

README.md

@@ -309,7 +309,7 @@
 | 1160 | [Find Words That Can Be Formed By Characters](https://leetcode.com/problems/find-words-that-can-be-formed-by-characters)                             |                                                                                                                                                                             |                                                                                                                                   |
 | 1165 | [Single Row Keyboard](https://leetcode.com/problems/single-row-keyboard)                                                                             |                                                  [![Java](assets/java.png)](src/FindWordsThatCanBeFormedByCharacters.java)                                                  |                                                                                                                                   |
 | 1170 | [Compare Strings By Frequency of the Smallest Character](https://leetcode.com/problems/compare-strings-by-frequency-of-the-smallest-character)       |                                                                                                                                                                             |                                                                                                                                   |
-| 1175 | [Prime Arrangements](https://leetcode.com/problems/prime-arrangements)                                                                               |                                                                                                                                                                             |                                                                                                                                   |
+| 1175 | [Prime Arrangements](https://leetcode.com/problems/prime-arrangements)                                                                               |                                                           [![Java](assets/java.png)](src/PrimeArrangements.java)                                                            |                                                                                                                                   |
 | 1176 | [Diet Plan Performance](https://leetcode.com/problems/diet-plan-performance)                                                                         |                                                                                                                                                                             |                                                                                                                                   |
 | 1180 | [Count Substrings with only one Distinct Letter](https://leetcode.com/problems/count-substrings-with-only-one-distinct-letter)                       |                                                                                                                                                                             |                                                                                                                                   |
 | 1184 | [Distance Between Bus Stops](https://leetcode.com/problems/distance-between-bus-stops)                                                               |                                                                                                                                                                             |                                                                                                                                   |

src/PrimeArrangements.java

@@ -0,0 +1,36 @@
+public class PrimeArrangements {
+    private static final int[] PRIME_DENSITY = {
+            0, 1, 2, 2, 3, 3, 4, 4, 4, 4,
+            5, 5, 6, 6, 6, 6, 7, 7, 8, 8,
+            8, 8, 9, 9, 9, 9, 9, 9, 10, 10,
+            11, 11, 11, 11, 11, 11, 12, 12,
+            12, 12, 13, 13, 14, 14, 14, 14,
+            15, 15, 15, 15, 15, 15, 16, 16,
+            16, 16, 16, 16, 17, 17, 18, 18,
+            18, 18, 18, 18, 19, 19, 19, 19,
+            20, 20, 21, 21, 21, 21, 21, 21,
+            22, 22, 22, 22, 23, 23, 23, 23,
+            23, 23, 24, 24, 24, 24, 24, 24,
+            24, 24, 25, 25, 25, 25
+    };
+
+    private static final int MOD = 1000_000_007;
+
+    public int numPrimeArrangements(int n) {
+        final int primeNumbers = PRIME_DENSITY[n - 1];
+        return factorialMod(primeNumbers, factorialMod(n - primeNumbers))  % MOD;
+    }
+
+    private int factorialMod(long number, final long start) {
+        long result = start;
+        while (number > 1) {
+            result = (result * number) % MOD;
+            number--;
+        }
+        return (int) result;
+    }
+
+    private int factorialMod(int number) {
+        return factorialMod(number, 1);
+    }
+}