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Add number/get_phi.cc 

Signed-off-by: subcrip <contact@subc.rip>
This commit is contained in:
subcrip 2024-05-20 21:59:12 +08:00
parent 4e7835f6e5
commit 7174c21f8c
1 changed files with 28 additions and 0 deletions
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number/get_phi.cc Normal file
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vector<int> get_phi(int n) {
vector<bool> not_prime(n + 1);
vector<int> res;
vector<int> phi(n + 1);
phi[1] = 1;
for (int i = 2; i <= n; ++i) {
if (not not_prime[i]) {
res.emplace_back(i);
phi[i] = i - 1;
}
for (auto&& x : res) {
if (i * x > n) break;
not_prime[i * x] = 1;
if (i % x == 0) {
// phi(n) = n * prod((p - 1) / p)
// => phi(i * x) = i * x * prod((p - 1) / p) = (i * prod((p - 1) / p)) * x = phi(i) * x,
// since `i` covers all factors of i * x
phi[i * x] = phi[i] * x;
break;
} else {
// i coprimes x
// phi(i * x) = phi(i) * phi(x) = phi(i) * (x - 1)
phi[i * x] = phi[i] * (x - 1);
}
}
}
return phi;
}