#275672 (C++14) No.719 Coprime

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結果

問題	No.719 Coprime
コンテスト
ユーザー	kurenaif
提出日時	2018-07-29 03:41:54
言語	C++14 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	1,339 ms / 3,000 ms
コード長	12,656 bytes
コンパイル時間	1,690 ms
コンパイル使用メモリ	141,216 KB
実行使用メモリ	31,100 KB
最終ジャッジ日時	2024-07-07 05:51:35
合計ジャッジ時間	9,279 ms
ジャッジサーバーID （参考情報）	judge2 / judge5
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ファイルパターン	結果
other	AC * 61
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ソースコード

raw source code
#include <iostream>
#include <queue>
#include <map>
#include <list>
#include <vector>
#include <string>
#include <stack>
#include <limits>
#include <climits>
#include <cassert>
#include <fstream>
#include <cstring>
#include <cmath>
#include <bitset>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <cstdio>
#include <ciso646>
#include <set>
#include <array>
#include <unordered_map>
#include <unordered_set>
#include <type_traits>

using namespace std;

#define FOR(i,a,b) for (int i=(a);i<(b);i++)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n) for (int i=0;i<(n);i++)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#define VEC2(T, N, M) vector<T>(N, vector<T>(M));
#define inf 0x3f3f3f3f3f3f3f3f
#define PB push_back
#define MP make_pair
#define ALL(a) (a).begin(),(a).end()
#define SET(a,c) memset(a,c,sizeof a)
#define CLR(a) memset(a,0,sizeof a)
#define VS vector<string>
#define VI vector<ll>
#define DEBUG(x) cout<<#x<<": "<<x<<endl
#define MIN(a,b) (a>b?b:a)
#define MAX(a,b) (a>b?a:b)
#define pi 2*acos(0.0)
#define INFILE() freopen("in0.txt","r",stdin)
#define OUTFILE()freopen("out0.txt","w",stdout)
#define ll long long
#define ull unsigned long long
#define pii pair<ll,ll>
#define pcc pair<char,char>
#define pic pair<ll,char>
#define pci pair<char,ll>
#define eps 1e-14
#define FST first
#define SEC second
#define SETUP cin.tie(0), ios::sync_with_stdio(false), cout << setprecision(15) << std::fixed;

template <class T>
using vec2 = std::vector<vector<T>>;

namespace {
	struct input_returnner {
		ll N; input_returnner(ll N_ = 0) :N(N_) {}
		template<typename T> operator vector<T>() const { vector<T> res(N); for (auto &a : res) cin >> a; return std::move(res); }
		template<typename T> operator T() const { T res; cin >> res; return res; }
		template<typename T> T operator - (T right) { return T(input_returnner()) - right; }
		template<typename T> T operator + (T right) { return T(input_returnner()) + right; }
		template<typename T> T operator * (T right) { return T(input_returnner()) * right; }
		template<typename T> T operator / (T right) { return T(input_returnner()) / right; }
		template<typename T> T operator << (T right) { return T(input_returnner()) << right; }
		template<typename T> T operator >> (T right) { return T(input_returnner()) >> right; }
	};
	template<typename T> input_returnner in() { return in<T>(); }
	input_returnner in() { return input_returnner(); }
	input_returnner in(ll N) { return std::move(input_returnner(N)); }
}

template<typename T>
istream& operator >> (istream& is, vector<T>& vec) {
	for (T& x : vec) is >> x;
	return is;
}

template < typename T >
struct is_vector : std::false_type {};

template < typename T >
struct is_vector<std::vector<T>> : std::true_type {};

template < typename T >
constexpr bool is_vector_v = is_vector<T>::value;

template <typename T>
std::ostream& operator<< (std::ostream& out, const std::vector<T>& v) {
	if (!v.empty()) {
		for (int i = 0; i < v.size(); ++i) {
			out << v[i] << (i == v.size() - 1 ? "\n" : (is_vector_v<T> ? "" : ", "));
		}
	}
	return out;
}

namespace std {
	// ref: https://stackoverflow.com/questions/7110301/generic-hash-for-tuples-in-unordered-map-unordered-set
	template <class T>
	inline void hash_combine(std::size_t& seed, T const& v)
	{
		seed ^= std::hash<T>()(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
	}

	// Recursive template code derived from Matthieu M.
	template <class Tuple, size_t Index = std::tuple_size<Tuple>::value - 1>
	struct HashValueImpl
	{
		static void apply(size_t& seed, Tuple const& tuple)
		{
			HashValueImpl<Tuple, Index - 1>::apply(seed, tuple);
			hash_combine(seed, std::get<Index>(tuple));
		}
	};

	template <class Tuple>
	struct HashValueImpl<Tuple, 0>
	{
		static void apply(size_t& seed, Tuple const& tuple)
		{
			hash_combine(seed, std::get<0>(tuple));
		}
	};
	template <typename ... TT>
	struct hash<std::tuple<TT...>>
	{
		size_t operator()(std::tuple<TT...> const& tt) const
		{
			size_t seed = 0;
			HashValueImpl<std::tuple<TT...> >::apply(seed, tt);
			return seed;
		}
	};

	template <class T, class U>
	class hash<std::pair<T, U>> {
	public:
		size_t operator()(const std::pair<T, U>& x) const {
			return hash<std::tuple<T, U>>()(std::tie(x.first, x.second));
		}
	};
}

// ref: https://stackoverflow.com/questions/6245735/pretty-print-stdtuple
namespace aux {
	template<std::size_t...> struct seq {};

	template<std::size_t N, std::size_t... Is>
	struct gen_seq : gen_seq<N - 1, N - 1, Is...> {};

	template<std::size_t... Is>
	struct gen_seq<0, Is...> : seq<Is...> {};

	template<class Ch, class Tr, class Tuple, std::size_t... Is>
	void print_tuple(std::basic_ostream<Ch, Tr>& os, Tuple const& t, seq<Is...>) {
		using swallow = int[];
		(void)swallow {
			0, (void(os << (Is == 0 ? "" : ", ") << std::get<Is>(t)), 0)...
		};
	}
} // aux::

template<class Ch, class Tr, class... Args>
auto operator<<(std::basic_ostream<Ch, Tr>& os, std::tuple<Args...> const& t)
-> std::basic_ostream<Ch, Tr>&
{
	os << "(";
	aux::print_tuple(os, t, aux::gen_seq<sizeof...(Args)>());
	return os << ")";
}

template<class S, class T>
std::ostream & operator<<(std::ostream & os, const std::pair<S, T> & p)
{
	return os << "(" << p.first << ", " << p.second << ")";
}

// ref: https://stackoverflow.com/questions/8542591/c11-reverse-range-based-for-loo�Fp
template <typename T>
struct reversion_wrapper { T& iterable; };

template <typename T>
auto begin(reversion_wrapper<T> w) { return std::rbegin(w.iterable); }

template <typename T>
auto end(reversion_wrapper<T> w) { return std::rend(w.iterable); }

template <typename T>
reversion_wrapper<T> REV(T&& iterable) { return { iterable }; }

ll MOD = 1e9 + 7;

class prime;

void solve();

signed main() {
	SETUP;
	solve();
#ifdef _DEBUG
	system("pause");
#endif
	return 0;
}

#define int ll

// template

template<class T>
struct fkvector {
public:
	vector<T> v;
	fkvector(size_t size) :v(size) {}
	size_t size() const { return v.size(); }

	T& operator [] (const int index) {
		return v[index];
	}

	T dot(const fkvector<T>& right) {
		assert(v.size() == right.size());
		T res = 0;
		for (int i = 0; i < right.size(); ++i) {
			res += v[i] * right.v[i];
		}
		return res;
	}

	void operator = (const fkvector<T>& right) {
		v.clear();
		v.resize(right.size());
		copy(right.v.begin(), right.v.end(), v.begin());
	}

	fkvector<T> operator + (const fkvector<T>& right) {
		assert(v.size() == right.size());
		fkvector<T> res(v.size());
		for (size_t i = 0; i < v.size(); ++i) {
			res[i] = v[i] + right.v[i];
		}
		return res;
	}

	fkvector<T> operator - (const fkvector<T>& right) {
		assert(v.size() == right.size());
		fkvector<T> res(v.size());
		for (size_t i = 0; i < v.size(); ++i) {
			res[i] = v[i] - right.v[i];
		}
		return res;
	}

	void operator += (const fkvector<T>& right) {
		assert(v.size() == right.size());
		*this = *this + right;
	}

	void operator -= (const fkvector<T>& right) {
		assert(v.size() == right.size());
		*this = *this - right;
	}

	void print() {
		cout << "{";
		for (int i = 0; i < v.size()-1; ++i) {
			cout << v[i] << ", ";
		}
		cout << v.back();
		cout << "}" << endl;
	}
};

template<class T>
struct fkmat {
	vector<vector<T> > mat;

	size_t getRowCount() const { return mat.size(); }
	size_t getColomnCount() const { return mat[0].size(); }
	size_t size() const { return mat.size(); }

	fkmat(size_t size_row,size_t size_colomn):mat(size_row, vector<T>(size_colomn)) {}

	vector<T>& operator [] (const int index) { return mat[index]; }

	//Identity matrix
	fkmat<T> Identity() {
		for (int i = 0; i < mat.size(); ++i) {
			mat[i][i] = 1;
		}
		return *this;
	}

	void operator = (const fkmat<T>& right) {
		mat.clear();
		mat.resize(right.size());
		for (int i = 0; i < right.size(); ++i) {
			mat[i] = right.mat[i];
		}
	}

	fkmat<T> operator + (const fkmat<T>& right) {
		fkmat<T> res(getRowCount(), getColomnCount());

		for (int i = 0; i < mat.size(); ++i) {
			for (int j = 0; j < mat[i].size(); ++j) {
				res[i][j] = mat[i][j] + right.mat[i][j];
			}
		}
		
		return res;
	}

	fkmat<T> operator - (const fkmat<T>& right) {
		fkmat<T> res(getRowCount(), getColomnCount());

		for (int i = 0; i < mat.size(); ++i) {
			for (int j = 0; j < mat[i].size(); ++j) {
				res[i][j] = mat[i][j] - right.mat[i][j];
			}
		}
		
		return res;
	}

	fkmat<T> operator * (const fkmat<T>& right) {
		fkmat<T> res(getRowCount(), getColomnCount());
		assert(getColomnCount() == right.getRowCount());

		for (int r = 0; r < getRowCount(); ++r) {
			for (int c = 0; c < right.getColomnCount(); ++c) {
				for (int k = 0; k < getColomnCount(); ++k) {
					res[r][c] += mat[r][k] * right.mat[k][c];
					res[r][c] %= MOD;
				}
			}
		}

		return res;
	}

	void operator += (const fkmat<T>& right) {
		for (int i = 0; i < mat.size(); ++i) {
			for (int j = 0; j < mat[i].size(); ++j) {
				mat[i][j] += right.mat[i][j];
			}
		}
	}
	
	void operator -= (const fkmat<T>& right) {
		for (int i = 0; i < mat.size(); ++i) {
			for (int j = 0; j < mat[i].size(); ++j) {
				mat[i][j] -= right.mat[i][j];
			}
		}
	}

	void operator *= (const fkmat<T>& right) {
		*this = *this * right;
	}

	//power n
	void pow(long long n, fkmat<T>* dst) {
		dst->Identity();
		fkmat<T> x(getRowCount(), getColomnCount());
		x.mat = mat;
		while (n > 0) {
			if (n & 1) *dst = *dst * x;
			x *= x;
			x %= MOD;
			n >>= 1;
		}
	}

	//power n
	void pow(long long n) {
		fkmat<T> res(getRowCount(), getColomnCount());
		res = fkmat<T>(getRowCount(), getColomnCount()).Identity();
		fkmat<T> x(getRowCount(), getColomnCount());
		x = *this;
		while (n > 0) {
			if (n & 1) res = res * x;
			x *= x;
			n >>= 1;
		}
		*this = res;
	}

	void print() {
		for (size_t i = 0; i < mat.size(); ++i) {
			for (size_t j = 0; j < mat[i].size(); ++j) {
				cout << mat[i][j] << " ";
			}
			cout << endl;
		}
	}
};

int gcd(int a, int b) {
  return b != 0 ? gcd(b, a % b) : a;
}

class prime {
private:
public:
	std::vector<int> primes;
	std::vector<bool> isPrime;
	prime(int num = 0) {
		if (num == 0) return;
		isPrime.resize(num + 1);
		fill(isPrime.begin(), isPrime.end(), true);
		int ma = sqrt(num) + 1;
		isPrime[0] = isPrime[1] = false;
		int cnt = 0;
		for (int i = 2; i <= ma; ++i) if (isPrime[i]) {
			for (int j = 2; i*j <= num; ++j) {
				isPrime[i*j] = false;
				cnt++;
			}
		}
		primes.reserve(cnt);
		for (int i = 0; i<isPrime.size(); ++i) if (isPrime[i]) {
			primes.push_back(i);
		}
	}

	bool IsPrime(int num) {
		if (num < isPrime.size()) return isPrime[num];
		for (auto p : primes) {
			if (num%p == 0) return false;
		}
		int ma = sqrt(num) + 1;
		for (int i = primes.back(); i <= ma; i += 2) {
			if (num%i == 0) return false;
		}
		return true;
	}

	std::map<int, int> GetFactor(int num) {
		std::map<int, int> res;
		int ma = sqrt(num) + 1;
		int a = 2;
		auto it = primes.begin();
		while (num >= a*a) {
			if (num%a == 0) {
				res[a]++;
				num /= a;
			}
			else {
				if (it == primes.end()) ++a;
				else {
					++it;
					a = *it;
				}
			}
		}
		res[num]++;
		return res;
	}
};

unordered_map<pair<int, int>, int> memo; // {depth, mask} = res;
int f(vector<vector<int> >& dps, int depth, int mask) {
	if (depth == 0) return dps[0][mask];
	if (memo.find({ depth, mask }) != memo.end()) return memo[{depth, mask}];
	int res = 0;
	for(int i = 0;;i = (i-mask) & mask){ // take out i
		res = max(res, f(dps, depth - 1, mask - i) + dps[depth][i]);
		if (i == mask) break;
	} 
	memo[{depth, mask}] = res;
	return res;
}

void solve() {
	int N; cin >> N;
	if (N == 2) {
		cout << 2 << endl;
		return;
	}
	if (N == 3) {
		cout << 5 << endl;
		return;
	}
	prime primes(N);
	unordered_map<int, int> prime2Num;
	REP(i,primes.primes.size()){
		prime2Num[primes.primes[i]] = i;
	}
	auto rootPrime = upper_bound(ALL(primes.primes), sqrt(N))-1;
	int maxPrime = *rootPrime;
	int M = (rootPrime - primes.primes.begin())+1;

	int res = 0;
	vector<vector<int> > dps(prime2Num.size() - M+1 , vector<int>(1 << M));
	FOR(i, 2, N+1) {
		auto factors = primes.GetFactor(i);
		int bits = 0;
		int maxFactor = 0;
		for (auto &p : factors) {
			maxFactor = max(p.first, maxFactor);
			if (p.first <= maxPrime){
				bits += (1 << prime2Num[p.first]);
			}
		}
		if (maxFactor <= maxPrime) {
			dps[0][bits] = max(dps[0][bits], i);
		}
		else {
			int num = prime2Num[maxFactor] - M;
			dps[num+1][bits] = max(dps[num][bits], i);
		}
	}

	{
		vector<int>& dp = dps[0];
		FOR(tar, 1, dp.size()) {
			for(int i = 0;;i = (i-tar) & tar){
				int invI = tar - i;
				dp[tar] = max(dp[tar], dp[i]+dp[invI]);
				if (i == tar) break;
			}
		}
	}

	cout << f(dps, dps.size() - 1, (1 << M) - 1) << endl;

}
yukicoder

結果

ソースコード
