Phi function implemented

Author: kaidul

README.md

@@ -63,10 +63,11 @@
 + [Prime factorization](algorithms/prime.cpp)
 + [Primality Test(School method)](algorithms/primality_test.cpp)
 + [Miller–Rabin Primality Test](algorithms/primality_test.cpp)
++ [Euler Totient (Phi Function)](algorithms/phi.cpp)
 + [Extended Euclid](algorithms/extended_euclid.cpp)
 + [Linear Diophatine Equation](algorithms/extended_euclid.cpp)
 + [Modular Mutiplicative Inverse(using Extended Euclid)](algorithms/extended_euclid.cpp)
-+ [Matrix Exponenciation](algorithms/matrix_exp.xpp)
++ [Matrix Exponentiation](algorithms/matrix_exp.xpp)
 + [Floyd Cycle Finding Algorithm](algorithms/floyd_cycle_finding.cpp)
 + [Big Integer](algorithms/big_integer.cpp)
 + [Josephus Recurrence](algorithms/Josephus_Recurrence.cpp)

algorithms/phi.cpp

@@ -0,0 +1,48 @@
+// To find positive integers below n that are relatively prime
+// i.e. 36 = 2^3 * 3^2, Phi(36) = 36 * (1 - 1/2)* (1 - 1/3) = 12
+int phi (int n) {
+    if ( n == 1 )
+        return 0;
+    int output = n;
+ 
+    if ( n % 2 == 0 ) {
+        output -= (output / 2);
+        while ( n % 2 == 0 )
+            n /= 2;
+    }
+ 
+    for ( int i = 3; i * i <= n; i += 2 ) { // i <= sqrtN may be ??
+        if ( n % i == 0 ) {
+            output -= (output / i);
+            while ( n % i == 0 )
+                n /= i;
+        }
+    }
+ 
+    if ( n > 1 )
+        output -= (output / n);
+ 
+    return output;
+}
+
+// using prime sieve
+// generate prime numbers upto certain limit using sieve/segmented sieve
+// sieve(sqrt(n));
+int phi (int n) {
+    int phi = n;
+    int sqrtN = sqrt(n);
+    for(int i = 0; i < (int)primes.size() and primes[i] <= sqrtN; i++) {
+        if(n % primes[i] == 0) {
+            phi *= (1 - 1 / (double) primes[i]);
+            while(n % primes[i] == 0) {
+                n /= primes[i];
+            }
+        }
+    }
+
+    if(n > 1) {
+        phi *= (1 - 1 / (double) n);
+    }
+    
+    return phi;
+}

algorithms/prime.cpp

@@ -90,16 +90,4 @@ void primeFactor2(int x, vector<pair<int, int>>& factors) {
             factors.push_back({p, freq});
         }
     }
-}
-
-// primarility test
-bool isPrime(int x) {
-    if(x < 2) return false;
-    int sqrtX = sqrt(x);
-    for(int i = 2; i <= sqrtX; i++) {
-        if(x % i == 0) {
-            return false;
-        }
-    }
-    return true;
 }