#733075 (C++17) No.1821 LEQ-GEQ Permutations

提出ソース

結果

問題	No.1821 LEQ-GEQ Permutations
ユーザー	heno239
提出日時	2022-01-21 22:45:34
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	647 ms / 2,500 ms
コード長	5,085 bytes
コンパイル時間	2,033 ms
コンパイル使用メモリ	152,128 KB
実行使用メモリ	11,776 KB
最終ジャッジ日時	2024-05-04 13:59:37
合計ジャッジ時間	4,796 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

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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	15 ms 11,648 KB
testcase_01	AC	16 ms 11,520 KB
testcase_02	AC	15 ms 11,776 KB
testcase_03	AC	16 ms 11,520 KB
testcase_04	AC	15 ms 11,520 KB
testcase_05	AC	17 ms 11,648 KB
testcase_06	AC	16 ms 11,520 KB
testcase_07	AC	17 ms 11,520 KB
testcase_08	AC	23 ms 11,520 KB
testcase_09	AC	125 ms 11,520 KB
testcase_10	AC	16 ms 11,584 KB
testcase_11	AC	24 ms 11,520 KB
testcase_12	AC	24 ms 11,520 KB
testcase_13	AC	34 ms 11,520 KB
testcase_14	AC	62 ms 11,584 KB
testcase_15	AC	121 ms 11,520 KB
testcase_16	AC	114 ms 11,520 KB
testcase_17	AC	58 ms 11,648 KB
testcase_18	AC	166 ms 11,648 KB
testcase_19	AC	183 ms 11,648 KB
testcase_20	AC	171 ms 11,520 KB
testcase_21	AC	180 ms 11,716 KB
testcase_22	AC	172 ms 11,584 KB
testcase_23	AC	647 ms 11,520 KB
testcase_24	AC	17 ms 11,716 KB

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ソースコード

raw source code

#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;
constexpr 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;

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);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
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;
	if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	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];
}

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;
}
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-8;
const ld pi = acosl(-1.0);
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
template<typename T>
void addv(vector<T>& v,int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
//-----------------------------------------

int calc(int a,int b) {
	if (a == 0 && b == 0)return 1;
	int res = 0;
	int n = a + b;
	vector<int> v(n);
	rep(i, n)v[i] = i;
	do {
		vector<int> v2(n);
		rep(i, n)v2[i] = i;
		do {
			bool valid = true;
			rep(j, a)if (v[j] > v2[j])valid = false;
			Rep(j, a, n)if (v[j] < v2[j])valid = false;
			if (valid)res++;
		} while (next_permutation(all(v2)));
	} while (next_permutation(all(v)));
	rep1(i, a)res /= i;
	rep1(i, b)res /= i;
	return res;
}
void expr() {
	for (int a = 0; a <= 7; a++) {
		for (int b = 0; b <= 7; b++) {
			if (a + b > 7)break;
			cout << calc(a, b) << " ";
		}
		cout << "\n";
	}
}

modint calce1(int n, int k) {
	modint res = 0;
	for (int j = 0; j <= k; j++) {
		modint val = 1;
		if (j % 2)val *= -1;
		val *= comb(n + 1, j);
		val *= mod_pow(k + 1 - j, n);
		res += val;
	}
	return res;
}
modint calcans(int n, int k) {
	modint res = 0;
	for (int j = k; j <= n; j++) {
		modint val = comb(n, j) * calce1(j, j - k);
		res += val;
	}
	return res;
}

//https://oeis.org/A046802 に(0の個数)!と(1の個数)!をかけたやつ
void solve() {
	int n; cin >> n;
	string s; cin >> s;
	int k = 0;
	rep(i, s.size()) {
		if (s[i] == '1')k++;
	}
	modint ans = calcans(n, k);
	ans *= fact[k];
	ans *= fact[n - k];
	cout << ans << "\n";
}


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

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結果

テストケース

ソースコード