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Added EulersTotient #344

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Merged
raklaptudirm merged 1 commit into from
May 23, 2021
Merged

Added EulersTotient #344

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40 changes: 40 additions & 0 deletions Maths/EulersTotient.js
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Original file line number Diff line number Diff line change
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/*
Source:
https://en.wikipedia.org/wiki/Euler%27s_totient_function

EulersTotient(n) = n * product(1 - 1/p for all prime p dividing n)

Complexity:
O(sqrt(n))
*/

const EulersTotient = (n) => {
// input: n: int
// output: phi(n): count of numbers b/w 1 and n that are coprime to n
let res = n
for (let i = 2; i * i <= n; i++) {
if (n % i === 0) {
while (n % i === 0) {
n = Math.floor(n / i)
}
// i is a prime diving n, multiply res by 1 - 1/i
// res = res * (1 - 1/i) = res - (res / i)
res = res - Math.floor(res / i)
}
}
if (n > 1) {
res = res - Math.floor(res / n)
}
return res
}

const main = () => {
// EulersTotient(9) = 6 as 1, 2, 4, 5, 7, and 8 are coprime to 9
// > 6
console.log(EulersTotient(9))
// EulersTotient(10) = 4 as 1, 3, 7, 9 are coprime to 10
// > 4
console.log(EulersTotient(10))
}

main()