Create SrcCode.cpp

Author: Priyangshuyogi

Competitive Coding/Math/Primality Test/Fermat Method/SrcCode.cpp

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+
+#include <bits/stdc++.h>
+using namespace std;
+ 
+/* Iterative Function to calculate (a^n)%p in O(logy) */
+int power(int a, unsigned int n, int p)
+{
+ int res = 1; // Initialize result
+ a = a % p; // Update 'a' if 'a' >= p
+ 
+ while (n > 0)
+ {
+ // If n is odd, multiply 'a' with result
+ if (n & 1)
+ res = (res*a) % p;
+ 
+ // n must be even now
+ n = n>>1; // n = n/2
+ a = (a*a) % p;
+ }
+ return res;
+}
+ 
+// If n is prime, then always returns true, If n is
+// composite than returns false with high probability
+// Higher value of k increases probability of correct result.
+
+bool isPrime(unsigned int n, int k)
+{
+ // Corner cases
+ if (n <= 1 || n == 4) return false;
+ if (n <= 3) return true;
+ 
+ // Try k times
+ while (k>0)
+ {
+ // Pick a random number in [2..n-2] 
+ // Above corner cases make sure that n > 4
+ int a = 2 + rand()%(n-4); 
+ 
+ // Fermat's little theorem
+ if (power(a, n-1, n) != 1)
+ return false;
+ 
+ k--;
+ }
+ 
+ return true;
+}
+ 
+// Driver Program
+int main()
+{
+ int k = 3;
+ isPrime(11, k)? cout << " true\n": cout << " false\n";
+ isPrime(15, k)? cout << " true\n": cout << " false\n";
+ return 0;
+}
+
+
+Output:
+
+true
+false