AKS Primality Test cpp

CPP/AKS_Primalitytest.cpp

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+
+// C++ code to check if number is prime. This 
+// program demonstrates concept behind AKS 
+// algorithm and doesn't implement the actual 
+// algorithm (This works only till n = 64) 
+#include <bits/stdc++.h> 
+using namespace std; 
+
+// array used to store coefficients . 
+long long c[100]; 
+
+// function to calculate the coefficients 
+// of (x - 1)^n - (x^n - 1) with the help 
+// of Pascal's triangle . 
+void coef(int n) 
+{ 
+    c[0] = 1; 
+    for (int i = 0; i < n; c[0] = -c[0], i++) { 
+        c[1 + i] = 1; 
+
+        for (int j = i; j > 0; j--) 
+            c[j] = c[j - 1] - c[j]; 
+    } 
+} 
+
+// function to check whether 
+// the number is prime or not 
+bool isPrime(int n) 
+{ 
+    // Calculating all the coefficients by 
+    // the function coef and storing all 
+    // the coefficients in c array . 
+    coef(n); 
+
+    // subtracting c[n] and adding c[0] by 1 
+    // as ( x - 1 )^n - ( x^n - 1), here we 
+    // are subtracting c[n] by 1 and adding 
+    // 1 in expression. 
+    c[0]++, c[n]--; 
+
+    // checking all the coefficients whether 
+    // they are divisible by n or not. 
+    // if n is not prime, then loop breaks 
+    // and (i > 0). 
+    int i = n; 
+    while (i-- && c[i] % n == 0) 
+        ; 
+
+    // Return true if all coefficients are 
+    // divisible by n. 
+    return i < 0; 
+} 
+
+// driver program 
+int main() 
+{ 
+    int n = 37; 
+    if (isPrime(n)) 
+        cout << "Prime" << endl; 
+    else
+        cout << "Not Prime" << endl; 
+    return 0; 
+}