mmrz's library

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:heavy_check_mark: verify/aoj/id/1642.test.cpp

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1642"

#include "./../../../template/template.hpp"
#include "./../../../math/factor.hpp"
#include "./../../../math/enumerate_divisors.hpp"

using namespace mmrz;

bool SOLVE(){
	ll n;
	cin >> n;
	if(n == 0)return 1;
	ll ans = 2+n;
	auto fs = enumerate_divisors(n);
	for(int i = 0;i < len(fs) && fs[i] <= n/fs[i] && fs[i]*fs[i] <= n/fs[i];i++){
		for(int j = i;j < len(fs) && fs[j] <= n/fs[j] && fs[i]*fs[j] <= n/fs[j];j++){
			if(n%(fs[i]*fs[j]))continue;
			chmin(ans, fs[i]+fs[j]+n/(fs[i]*fs[j]));
		}
	}
	cout << ans << '\n';
	return 0;
}

void mmrz::solve(){
	while(!SOLVE());
}
#line 1 "verify/aoj/id/1642.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1642"

#line 1 "template/template.hpp"
# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
const double pi = acos(-1);
template<class T>constexpr T inf() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T hinf() { return inf<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(ll n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(ll n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); };
ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g*b; };
ll MOD(ll x, ll m){return (x%m+m)%m; }
ll FLOOR(ll x, ll m) {ll r = (x%m+m)%m; return (x-r)/m; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define all(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        (wpwpw).erase(unique(all((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(all((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(all((rprpr)),(rprpr).begin(),TU<char>)
# define rep(i,upupu)         for(ll i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define reps(i,opopo)        for(ll i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((ll)(x).size())
# define bit(n)               (1LL << (n))
# define pb push_back
# define eb emplace_back
# define exists(c, e)         ((c).find(e) != (c).end())

struct INIT{
	INIT(){
		std::ios::sync_with_stdio(false);
		std::cin.tie(0);
		cout << fixed << setprecision(20);
	}
}INIT;

namespace mmrz {
	void solve();
}

int main(){
	mmrz::solve();
}
#line 2 "math/factor.hpp"

#line 2 "math/is_prime.hpp"

#line 4 "math/is_prime.hpp"

__int128_t __power(__int128_t n, __int128_t k, __int128_t m) {
	n %= m;
	__int128_t ret = 1;
	while(k > 0){
		if(k & 1)ret = ret * n % m;
		n = __int128_t(n) * n % m;
		k >>= 1;
	}
	return ret % m;
}

bool is_prime(long long n){
	if(n <= 1)return false;
	if(n == 2 || n == 3 || n == 5)return true;
	if(n % 2 == 0)return false;
	if(n % 3 == 0)return false;
	if(n % 5 == 0)return false;

	std::vector<long long> A = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};

	long long s = 0, d = n - 1;
	while(d % 2 == 0){
		s++;
		d >>= 1;
	}

	for (auto a : A){
		if(a % n == 0)return true;
		long long t, x = __power(a, d, n);
		if(x != 1){
			for(t = 0;t < s;t++){
				if(x == n - 1)break;
				x = __int128_t(x) * x % n;
			}
			if(t == s)return false;
		}
	}
	return true;
}
#line 4 "math/factor.hpp"

#line 8 "math/factor.hpp"

long long rho(long long n){
	if(n % 2 == 0)return 2;
	if(is_prime(n))return n;

	auto f = [&](long long x) -> long long {
		return (__int128_t(x) * x + 13) % n;
	};

	long long step = 0;
	while (true) {
		++step;
		long long x = step, y = f(x);
		while (true) {
			long long p = std::gcd(y - x + n, n);
			if (p == 0 || p == n) break;
			if (p != 1) return p;
			x = f(x);
			y = f(f(y));
		}
	}
}

std::vector<long long> factor(long long x){
	if(x == 1)return {};
	long long p = rho(x);
	if(p == x) return {p};
		
	std::vector<long long> l = factor(p);
	std::vector<long long> r = factor(x / p);

	l.insert(l.end(), r.begin(), r.end());
	std::sort(l.begin(), l.end());

	return l;
}
#line 2 "math/enumerate_divisors.hpp"

#line 4 "math/enumerate_divisors.hpp"

#line 7 "math/enumerate_divisors.hpp"

template<typename T>
std::vector<T> enumerate_divisors(T n) {
	std::vector<T> ret = {1};

	long long mul = -1;
	long long pre = -1;
	int size_before = 1;

	for(auto p : factor(n)){
		mul = (p == pre ? mul*p : p);
		int sz = (p == pre ? size_before : std::ssize(ret));
		for(int i = 0;i < sz;i++){
			ret.emplace_back(ret[i] * mul);
		}
		pre = p;
		size_before = sz;
	}
	std::sort(ret.begin(), ret.end());
	return ret;
}
#line 6 "verify/aoj/id/1642.test.cpp"

using namespace mmrz;

bool SOLVE(){
	ll n;
	cin >> n;
	if(n == 0)return 1;
	ll ans = 2+n;
	auto fs = enumerate_divisors(n);
	for(int i = 0;i < len(fs) && fs[i] <= n/fs[i] && fs[i]*fs[i] <= n/fs[i];i++){
		for(int j = i;j < len(fs) && fs[j] <= n/fs[j] && fs[i]*fs[j] <= n/fs[j];j++){
			if(n%(fs[i]*fs[j]))continue;
			chmin(ans, fs[i]+fs[j]+n/(fs[i]*fs[j]));
		}
	}
	cout << ans << '\n';
	return 0;
}

void mmrz::solve(){
	while(!SOLVE());
}
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