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42 lines
1.0 KiB
C++
42 lines
1.0 KiB
C++
/// C++ Program to find Euler Totient Function
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#include<iostream>
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/*
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* Euler Totient Function is also known as phi function.
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* phi(n) = phi(p1^a1).phi(p2^a2)...
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* where p1, p2,... are prime factors of n.
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* 3 Euler's properties:
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* 1. phi(prime_no) = prime_no-1
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* 2. phi(prime_no^k) = (prime_no^k - prime_no^(k-1))
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* 3. phi(a,b) = phi(a). phi(b) where a and b are relative primes.
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* Applying this 3 properties on the first equation.
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* phi(n) = n. (1-1/p1). (1-1/p2). ...
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* where p1,p2... are prime factors.
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* Hence Implementation in O(sqrt(n)).
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* phi(100) = 40
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* phi(1) = 1
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* phi(17501) = 15120
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* phi(1420) = 560
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*/
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// Function to caculate Euler's totient phi
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int phiFunction(int n) {
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int result = n;
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for (int i = 2; i * i <= n; i++) {
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if (n % i == 0) {
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while (n % i == 0) {
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n /= i;
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}
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result -= result / i;
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}
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}
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if (n > 1) result -= result / n;
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return result;
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}
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int main() {
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int n;
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std::cin >> n;
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std::cout << phiFunction(n);
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}
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