From e8e60ed18eb2faf881f85023de84bd7d9b11d65a Mon Sep 17 00:00:00 2001
From: Priyansh Kumar <71462800+Kpriyansh@users.noreply.github.com>
Date: Fri, 22 Oct 2021 23:59:50 +0530
Subject: [PATCH] chore(CPlusPlus): add totient function (#549)

Co-authored-by: Arsenic <54987647+Arsenic-ATG@users.noreply.github.com>
---
 algorithms/CPlusPlus/Maths/totient.cpp | 58 ++++++++++++++++++++++++++
 algorithms/CPlusPlus/README.md         |  1 +
 2 files changed, 59 insertions(+)
 create mode 100644 algorithms/CPlusPlus/Maths/totient.cpp

diff --git a/algorithms/CPlusPlus/Maths/totient.cpp b/algorithms/CPlusPlus/Maths/totient.cpp
new file mode 100644
index 00000000..0c51e96f
--- /dev/null
+++ b/algorithms/CPlusPlus/Maths/totient.cpp
@@ -0,0 +1,58 @@
+/*
+Program Description:
+Euler's totient function (also called the Phi function) counts the number of positive integers less than n that 
+are coprime to n. That is, totient(n) is the number of m∈N such that 1≤m<n and gcd(m,n)=1.
+You are given an integer N and are supposed to find the value of Euler toient function for N.
+
+Constraints:
+1 <= N <= 10^9
+
+Approach:
+totient(N) = N*(1 - 1/p1)*(1 - 1/p2)...*(1 - 1/pn).
+where, p1,p2...pn are prime factors of n.
+So, we can write the above function as,
+totient(N) = N*[(p1-1)(p2-1)...(pn-1)/(p1*p2*p3...*pn)]
+1)Calculate all the primefactors of N.
+2)Calculate the numerator and denominator i.e N*(p1-1)(p2-1)...(pn-1) and (p1*p2*p3...*pn)
+3)Divide numerator by denominator.
+
+Time Complexity: O(NloglogN)
+*/
+
+#include<iostream>
+#include<vector>
+using namespace std;
+
+
+vector<int>getPrimeFactors(int n) {
+    vector<int>factors;
+    if (n % 2 == 0) {
+        factors.push_back(2);
+        while (n % 2 == 0)n /= 2;
+    }
+    for (int i = 3; i * i <= n; i += 2) {
+        if (n % i == 0) {
+            factors.push_back(i);
+            while (n % i == 0)n /= i;
+        }
+    }
+    if (n > 1)factors.push_back(n);
+    return factors;
+}
+long long totient(int n) {
+    vector<int>primefactors = getPrimeFactors(n);
+    long long numerator = 1, denominator = 1;
+    for (auto p : primefactors) {
+        numerator *= (long long)(p - 1);
+        denominator *= (long long)p;
+    }
+    return ((long long)n * numerator) / denominator;
+}
+int main() {
+
+    int n;
+    cout << "Enter a number: ";
+    cin >> n;
+    cout << "Number of coprime integers are: " << totient(n) << "\n";
+    return 0;
+}
diff --git a/algorithms/CPlusPlus/README.md b/algorithms/CPlusPlus/README.md
index 128c6aae..baa07a9c 100644
--- a/algorithms/CPlusPlus/README.md
+++ b/algorithms/CPlusPlus/README.md
@@ -147,6 +147,7 @@
 - [Missing number](Maths/missing-number.cpp)
 - [Factorial of a number](Maths/factorial.cpp)
 - [Prime-number](Maths/prime-number.cpp)
+- [Totient-function](Maths/totient.cpp)
 - [Even number of digits](Maths/even-no-of-digits.cpp)
 - [Power of two](Maths/power-of-two.cpp)
 - [Small numbers](Maths/small-numbers.cpp)