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Format Euler's Totient

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John Law 2020-03-31 23:26:32 +02:00 committed by GitHub
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math/eulers_totient_function.cpp
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/// C++ Program to find Euler Totient Function
#include<iostream>
/**
/*
* Euler Totient Function is also known as phi function.
* phi(n) = phi(p1^a1).phi(p2^a2)...
* where p1, p2,... are prime factors of n.
* 3 Euler's properties:
* 1. phi(prime_no) = prime_no-1
* 2. phi(prime_no^k) = (prime_no^k - prime_no^(k-1))
* 3. phi(a,b) = phi(a). phi(b) where a and b are relative primes.
* Applying this 3 properties on the first equation.
* phi(n) = n. (1-1/p1). (1-1/p2). ...
* where p1,p2... are prime factors.
* Hence Implementation in O(sqrt(n)).
* phi(100) = 40
* phi(1) = 1
* phi(17501) = 15120
* phi(1420) = 560
*/
Euler Totient Function also know as phi function.
phi(n) = phi(p1^a1).phi(p2^a2)...
where p1, p2,... are prime factor of n.
3 Euler's Property:
1. phi(prime_no) = prime_no-1
2. phi(prime_no^k) = (prime_no^k - prime_no^(k-1))
3. phi(a,b) = phi(a). phi(b) where a and b are relative primes.
Applying this 3 property on the first equation.
phi(n) = n. (1-1/p1). (1-1/p2). ...
where p1,p2... are prime factors.
Hence Implementation in O(sqrt(n)).
*/
/// Function to caculate euler totient function
// Function to caculate Euler's totient phi
int phiFunction(int n) {
int result = n;
for (int i=2; i*i <= n; i++) {
if (n%i == 0) {
while (n%i == 0) {
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) {
while (n % i == 0) {
n /= i;
}
result -= result/i;
result -= result / i;
}
}
if (n > 1) result -= result/n;
if (n > 1) result -= result / n;
return result;
}