結果

問題 No.1760 Setwise Coprime
ユーザー heno239heno239
提出日時 2021-11-20 16:19:18
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 508 ms / 2,000 ms
コード長 6,921 bytes
コンパイル時間 2,193 ms
コンパイル使用メモリ 158,976 KB
実行使用メモリ 42,592 KB
最終ジャッジ日時 2023-09-02 11:07:55
合計ジャッジ時間 12,917 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge13
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 125 ms
36,764 KB
testcase_01 AC 116 ms
36,756 KB
testcase_02 AC 117 ms
36,884 KB
testcase_03 AC 122 ms
36,812 KB
testcase_04 AC 115 ms
36,948 KB
testcase_05 AC 116 ms
37,044 KB
testcase_06 AC 114 ms
36,828 KB
testcase_07 AC 107 ms
36,864 KB
testcase_08 AC 106 ms
36,872 KB
testcase_09 AC 109 ms
36,820 KB
testcase_10 AC 112 ms
36,796 KB
testcase_11 AC 122 ms
36,924 KB
testcase_12 AC 114 ms
36,820 KB
testcase_13 AC 105 ms
36,840 KB
testcase_14 AC 126 ms
36,832 KB
testcase_15 AC 114 ms
36,796 KB
testcase_16 AC 126 ms
36,896 KB
testcase_17 AC 125 ms
36,964 KB
testcase_18 AC 113 ms
36,972 KB
testcase_19 AC 111 ms
36,800 KB
testcase_20 AC 110 ms
36,844 KB
testcase_21 AC 407 ms
41,216 KB
testcase_22 AC 360 ms
40,808 KB
testcase_23 AC 447 ms
42,068 KB
testcase_24 AC 237 ms
38,888 KB
testcase_25 AC 414 ms
41,260 KB
testcase_26 AC 348 ms
40,220 KB
testcase_27 AC 191 ms
38,040 KB
testcase_28 AC 149 ms
37,260 KB
testcase_29 AC 454 ms
42,368 KB
testcase_30 AC 458 ms
42,368 KB
testcase_31 AC 215 ms
38,364 KB
testcase_32 AC 428 ms
41,756 KB
testcase_33 AC 313 ms
39,996 KB
testcase_34 AC 469 ms
42,484 KB
testcase_35 AC 394 ms
41,012 KB
testcase_36 AC 492 ms
42,580 KB
testcase_37 AC 491 ms
42,592 KB
testcase_38 AC 508 ms
42,516 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
const ll mod = 998244353;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-4;
const ld pi = acosl(-1.0);

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}


int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };

ll gcd(ll a, ll b) {
	a = abs(a);
	b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}

template <typename T>
void fwt(vector<T>& f) {
	int n = f.size();
	for (int i = 1; i < n; i <<= 1) {
		for (int j = 0; j < n; j++) {
			if ((j & i) == 0) {
				T x = f[j], y = f[j | i];
				f[j] = x + y, f[j | i] = x - y;
			}
		}
	}
}
template <typename T>
void ifwt(vector<T>& f) {
	int n = f.size();
	for (int i = 1; i < n; i <<= 1) {
		for (int j = 0; j < n; j++) {
			if ((j & i) == 0) {
				T x = f[j], y = f[j | i];
				f[j] = (x + y) / 2, f[j | i] = (x - y) / 2;
			}
		}
	}
}

typedef vector<vector<modint>> mat;
typedef vector<modint> vec;
mat mtmul(mat& A, mat& B) {
	mat C(A.size(), vec(B[0].size()));
	rep(i, (int)A.size()) {
		rep(k, (int)B.size()) {
			rep(j, (int)B[0].size()) {
				C[i][j] += A[i][k] * B[k][j];
			}
		}
	}
	return C;
}
mat mtpow(mat A, ll n) {
	mat B(A.size(), vec(A.size()));
	rep(i, (int)A.size()) {
		B[i][i] = 1;
	}
	while (n > 0) {
		if (n & (ll)1)B = mtmul(B, A);
		A = mtmul(A, A);
		n >>= 1;
	}
	return B;
}

const int mn = 200005;
bool isp[mn];
vector<int> ch[mn];
int meb[mn];
void init() {
	fill(isp + 2, isp + mn, true);
	fill(meb + 1, meb + mn, 1);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		meb[i] *= -1;
		for (int j = 2 * i; j < mn; j+=i) {
			isp[j] = false;
			meb[j] *= -1;
			if ((j / i) % i == 0)meb[j] = 0;
		}
	}
	//rep(i, 20)cout << i << " " << meb[i] << "\n";
	for (int i = 1; i < mn; i++) {
		if (meb[i] != 0) {
			for (int j = i; j < mn; j += i) {
				ch[j].push_back(i);
			}
		}
	}
}
void solve() {
	int n; cin >> n;
	vector<modint> t2(n + 1), t3(n + 1);
	t2[0] = 1;
	t3[0] = 1;
	rep(i, n) {
		t2[i + 1] = t2[i] + t2[i];
		t3[i + 1] = (modint)3 * t3[i];
	}
	modint presum = 0;
	vector<modint> mem(n + 1);
	rep1(i, n)mem[i]= (modint)meb[i] * t2[n / i];
	rep1(i, n)presum += mem[i];
	vector<modint> sum(n + 1,presum);
	/*int premebsum = 0;
	rep1(i, n)premebsum += meb[i];
	vector<int> mebsum(n + 1,premebsum);*/
	int cnt[2] = {};
	rep1(i, n) {
		if (meb[i] == 1)cnt[1]++;
		else if (meb[i] == -1)cnt[0]++;
	}

	modint ans = 0;
	/*rep1(i, n)rep1(j, n) {
		int g = gcd(i, j);
		int l = i / g * j;
		modint val = meb[i] * meb[j];
		modint num= t3[n / l] * t2[n / i - n / l] * t2[n / j - n / l];
		//num -= t2[n / i];
		//num -= t2[n / j];
		//num += 1;
		val *= num;
		ans += val;
	}*/
	//cout << ans << "\n"; ans = 0;
	for (int l = 1; l <= n; l++) {
		rep(i, ch[l].size()) {
			Rep(j, i, ch[l].size()) {
				int c1 = ch[l][i];
				int c2 = ch[l][j];
				int g = gcd(c1, c2);
				if ((ll)(c1/g)*c2== l) {
					sum[c1] -= mem[c2]; //mebsum[c1] -= meb[c2];
					if (c1 != c2)sum[c2] -= mem[c1]; //mebsum[c2] -= meb[c1];
					modint val = meb[c1] * meb[c2];
					if (c1 != c2)val = val + val;
					val *= t3[n / l] * t2[n / c1 - n / l] * t2[n / c2 - n / l];
					ans += val;
					//cout << "? " << l << " " << c1 << " " << c2 << " " << val << "\n";
				}
			}
		}
	}
	//cout << cnt[1] - cnt[0] << "\n";
	for (int i = 1; i <= n; i++) {
		if (meb[i] == 0)continue;
		//cout << i << " " << sum[i] << "\n";
		modint val = mem[i] * sum[i];
		//cout << "? " << i << " " << val << "\n";
		ans += val;
		val = mem[i];
		modint coef = cnt[1] - cnt[0];
		ans -= val * coef;
		ans -= (modint)meb[i] * presum;
		/*rep1(j, n) {
			val =(modint)( meb[i] * meb[j]) * t2[n / i];
			ans -= val;
			ans += meb[i] * meb[j];
		}*/
	}
	ll c1 = (ll)cnt[1] * cnt[1] + (ll)cnt[0] * cnt[0];
	ll c2 = (ll)2 * cnt[0] * cnt[1];
	ans += c1 - c2;
	/*cout << c1 - c2 << "\n";
	int r = 0;
	rep1(i, n)rep1(j, n) {
		r += meb[i] * meb[j];
	}
	cout << r << "\n";*/

	cout << ans << "\n";
}



signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init_f();
	init();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
0