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Merge pull request TheAlgorithms#344 from c-utkarsh/add-eulers-totient
Added EulersTotient
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Maths/EulersTotient.js

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/*
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Source:
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https://en.wikipedia.org/wiki/Euler%27s_totient_function
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EulersTotient(n) = n * product(1 - 1/p for all prime p dividing n)
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Complexity:
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O(sqrt(n))
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*/
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const EulersTotient = (n) => {
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// input: n: int
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// output: phi(n): count of numbers b/w 1 and n that are coprime to n
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let res = n
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for (let 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 = Math.floor(n / i)
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}
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// i is a prime diving n, multiply res by 1 - 1/i
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// res = res * (1 - 1/i) = res - (res / i)
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res = res - Math.floor(res / i)
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}
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}
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if (n > 1) {
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res = res - Math.floor(res / n)
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}
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return res
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}
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const main = () => {
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// EulersTotient(9) = 6 as 1, 2, 4, 5, 7, and 8 are coprime to 9
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// > 6
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console.log(EulersTotient(9))
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// EulersTotient(10) = 4 as 1, 3, 7, 9 are coprime to 10
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// > 4
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console.log(EulersTotient(10))
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}
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main()

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