Math/tests/aizu_ntl_1_d_euler_phi.test.cpp

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Last update: 2022-12-19 21:18:52+08:00
Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=NTL_1_D

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=NTL_1_D"

#include "../../template.h"
#include "../Prime/EulerPhi.h"

using ll = long long;
void solve() {
    ll n; cin >> n;
    if (n < N) {
        assert(eulerPhi(n) == eulerPhi_lookup(n));
    }
    cout << eulerPhi(n) << endl;
}

#line 1 "Math/tests/aizu_ntl_1_d_euler_phi.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=NTL_1_D"

#line 1 "template.h"
#include <bits/stdc++.h>
using namespace std;

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

#define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; }
#define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; }
#define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))

// For printing pair, container, etc.
// Copied from https://quangloc99.github.io/2021/07/30/my-CP-debugging-template.html
template<class U, class V> ostream& operator << (ostream& out, const pair<U, V>& p) {
    return out << '(' << p.first << ", " << p.second << ')';
}

template<class Con, class = decltype(begin(declval<Con>()))>
typename enable_if<!is_same<Con, string>::value, ostream&>::type
operator << (ostream& out, const Con& con) {
    out << '{';
    for (auto beg = con.begin(), it = beg; it != con.end(); it++) {
        out << (it == beg ? "" : ", ") << *it;
    }
    return out << '}';
}
template<size_t i, class T> ostream& print_tuple_utils(ostream& out, const T& tup) {
    if constexpr(i == tuple_size<T>::value) return out << ")"; 
    else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); 
}
template<class ...U> ostream& operator << (ostream& out, const tuple<U...>& t) {
    return print_tuple_utils<0, tuple<U...>>(out, t);
}

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long get_rand(long long r) {
    return uniform_int_distribution<long long> (0, r-1)(rng);
}

template<typename T>
vector<T> read_vector(int n) {
    vector<T> res(n);
    for (int& x : res) cin >> x;
    return res;
}

void solve();

int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    solve();
    return 0;
}
#line 1 "Math/Prime/EulerPhi.h"
long long eulerPhi(long long n) { // = n (1-1/p1) ... (1-1/pn)
    if (n == 0) return 0;
    long long ans = n;
    for (int x = 2; x*x <= n; ++x) {
        if (n % x == 0) {
            ans -= ans / x;
            while (n % x == 0) n /= x;
        }
    }
    if (n > 1) ans -= ans / n;
    return ans;
}
// LookUp Version
const int N = 1000000;
int eulerPhi_lookup(int n) {
    static int lookup = 0, p[N], f[N];
    if (!lookup) {
        REP(i,N) p[i] = 1, f[i] = i;
        for (int i = 2; i < N; ++i) {
            if (p[i]) {
            f[i] -= f[i] / i;
                for (int j = i+i; j < N; j+=i)
                    p[j] = 0, f[j] -= f[j] / i;
            }
        }
        lookup = 1;
    }
    return f[n];
}

// Segmented sieve version, compute phi(i) for i in [l, r]
// Tested: https://www.spoj.com/problems/ETFS/
namespace EulerPhiSegmented {
vector<int> primes;    // NOTE: must initialize this
const int N = 100111;  // >= r - l + 1

long long phi[N], val[N];  // phi[i-l] = euler_phi(i)
void eulerPhi_segmentedSieve(long long l, long long r) {
    assert(!primes.empty());  // must precompute primes upto sqrt(r)

    for (auto i = l; i <= r; ++i) {
        phi[i-l] = i;
        val[i-l] = i;
    }
    
    for (auto p : primes) {
        if (p > r) break;
        long long first = (l / p) * p;
        if (first < l) first += p;

        while (first <= r) {
            phi[first - l] -= phi[first - l] / p;
            while (val[first - l] % p == 0) val[first - l] /= p;
            first += p;
        }
    }

    for (auto i = l; i <= r; ++i) {
        if (val[i-l] > 1) {
            phi[i-l] -= phi[i-l] / val[i-l];
        }
    }
}
}
#line 5 "Math/tests/aizu_ntl_1_d_euler_phi.test.cpp"

using ll = long long;
void solve() {
    ll n; cin >> n;
    if (n < N) {
        assert(eulerPhi(n) == eulerPhi_lookup(n));
    }
    cout << eulerPhi(n) << endl;
}