Math/tests/smallest_prime_factor_stress.test.cpp

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Last update: 2023-01-16 13:01:49+07:00
Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"

#include "../../template.h"
#include "../multiplicative_functions_linear.h"
using namespace linear_sieve;

void solve() {
    const int N = 10000;
    linear_sieve_smallest_prime_factor(N + 1);
    assert(smallest_p[1] == 0);
    for (int n = 2; n <= N; ++n) {
        bool is_prime = true;
        for (int i = 2; i*i <= n; ++i) {
            if (n % i == 0) {
                is_prime = false;
                assert(smallest_p[n] == i);
                break;
            }
        }
        if (is_prime) assert(smallest_p[n] == 0);
    }
    cout << "Hello World\n";
}

#line 1 "Math/tests/smallest_prime_factor_stress.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"

#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/multiplicative_functions_linear.h"
// This is only for calculating multiplicative functions
// If we need a fast sieve, see SieveFast.h
// From https://codeforces.com/blog/entry/54090
namespace linear_sieve {
const int MN = 2e7;
vector<int> primes;

int smallest_p[MN];  // smallest_p[n] = smallest prime factor of n
void linear_sieve_smallest_prime_factor(int n) {
    primes.clear();
    memset(smallest_p, 0, sizeof smallest_p);

    for (int i = 2; i < n; ++i) {
        if (!smallest_p[i]) primes.push_back(i);
        for (int j = 0; j < int(primes.size()) && i * primes[j] < n; ++j) {
            smallest_p[i * primes[j]] = primes[j];
            if (i % primes[j] == 0) break;
        }
    }
}

// Euler Phi {{{
bool is_composite[MN];
int phi[MN];

void linear_sieve_phi(int n) {
    memset(is_composite, false, sizeof is_composite);
    primes.clear();
 
    phi[1] = 1;
    for (int i = 2; i < n; ++i) {
        if (!is_composite[i]) {
            primes.push_back(i);
            phi[i] = i - 1; // i is prime
        }
        for (int j = 0; j < (int) primes.size() && i * primes[j] < n; ++j) {
            is_composite[i * primes[j]] = true;
            if (i % primes[j] == 0) {
                phi[i * primes[j]] = phi[i] * primes[j]; //primes[j] divides i
                break;
            } else {
                phi[i * primes[j]] = phi[i] * phi[primes[j]]; //primes[j] does not divide i
            }
        }
    }
}
// }}}

// Number of divisors {{{
int cnt_divisors[MN + 11];  // call linear_sieve_divisors(n+1) to init
int cnt[MN + 11];           // power of smallest prime factor of i
void linear_sieve_divisors(int n) {  // init range [1, n-1]
    memset(is_composite, false, sizeof is_composite);
    primes.clear();

    cnt_divisors[1] = 1;
    for (int i = 2; i < n; ++i) {
        if (!is_composite[i]) {
            primes.push_back(i);
            cnt[i] = 1;
            cnt_divisors[i] = 2;
        }
        for (int j = 0; j < (int) primes.size() && i * primes[j] < n; ++j) {
            int ip = i * primes[j];
            is_composite[ip] = true;
            if (i % primes[j] == 0) {
                cnt[ip] = cnt[i] + 1;
                cnt_divisors[ip] = cnt_divisors[i] / (cnt[i] + 1) * (cnt[i] + 2);
            } else {
                cnt[ip] = 1;
                cnt_divisors[ip] = 2 * cnt_divisors[i];
            }
        }
    }
}
// }}}

}
#line 5 "Math/tests/smallest_prime_factor_stress.test.cpp"
using namespace linear_sieve;

void solve() {
    const int N = 10000;
    linear_sieve_smallest_prime_factor(N + 1);
    assert(smallest_p[1] == 0);
    for (int n = 2; n <= N; ++n) {
        bool is_prime = true;
        for (int i = 2; i*i <= n; ++i) {
            if (n % i == 0) {
                is_prime = false;
                assert(smallest_p[n] == i);
                break;
            }
        }
        if (is_prime) assert(smallest_p[n] == 0);
    }
    cout << "Hello World\n";
}