1+ /**
2+ * Author : joney_000 [developer.jaswant@gmail.com]
3+ * Algorithm : Miller Rabin
4+ * Platform : Codejam
5+ * Ref : https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test#Testing_against_small_sets_of_bases
6+ */
7+ 8+ class MillerRabin {
9+ 10+ /* @input: `number` for which we need to check weather it is prime or not
11+ * @description: this is the deterministic varient of the miller ribbin
12+ */
13+ boolean isPrime (long number ){
14+ if (number < 2 ){
15+ return false ;
16+ }
17+ int smallPrimes [] = {2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 };
18+ for (int prime : smallPrimes ){
19+ if (number % prime == 0 ){
20+ return number == prime ;
21+ }
22+ }
23+ int trailingZeros = Long .numberOfTrailingZeros (number - 1 );
24+ long power = (number - 1 ) >> trailingZeros ;
25+ long bases [] = {2 , 7 , 61 };
26+ // sufficient for number < 4,759,123,141
27+ // we dont need to test all the base a < 2(ln number)2
28+ for (long base : bases ){
29+ long exp = pow (base % number , power , number );
30+ if (exp <= 1 || exp != number - 1 ){
31+ continue ;
32+ }
33+ for (int i = 0 ; i < trailingZeros - 1 && exp != number - 1 ; i ++){
34+ exp = (exp * exp ) % number ; // warning: integer overflow, use mulMod in case of int\long overflow
35+ }
36+ if (exp != number - 1 ){
37+ return false ;
38+ }
39+ }
40+ return true ;
41+ }
42+ 43+ long pow (long a , long b , long mod ){
44+ if (b == 0 )
45+ return 1 ;
46+ if (b == 1 )
47+ return a % mod ;
48+ long ans = pow (a , b /2 , mod );
49+ ans = (ans * ans ) % mod ;
50+ // mulMod(ans, ans, mod); use when ans^2 does int or long overflow.
51+ // this will perform multiplication using divide and conquer
52+ if (b % 2 == 1 )
53+ ans = (a * ans ) % mod ; // warning: integer overflow
54+ return ans ;
55+ }
56+ }
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