#619456 (C++17) No.1011 Infinite Stairs

提出ソース

結果

問題	No.1011 Infinite Stairs
ユーザー	tkmst201
提出日時	2021-02-18 23:46:05
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	7 ms / 2,000 ms
コード長	5,224 bytes
コンパイル時間	2,202 ms
コンパイル使用メモリ	207,512 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-07-17 12:16:20
合計ジャッジ時間	3,094 ms
ジャッジサーバーID （参考情報）	judge4 / judge5

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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	2 ms 6,812 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	6 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	7 ms 6,944 KB
testcase_06	AC	2 ms 6,948 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	2 ms 6,940 KB
testcase_11	AC	2 ms 6,940 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	2 ms 6,944 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	2 ms 6,940 KB
testcase_16	AC	4 ms 6,944 KB
testcase_17	AC	2 ms 6,944 KB
testcase_18	AC	4 ms 6,944 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	2 ms 6,940 KB
testcase_21	AC	3 ms 6,940 KB
testcase_22	AC	4 ms 6,940 KB
testcase_23	AC	3 ms 6,944 KB
testcase_24	AC	3 ms 6,944 KB
testcase_25	AC	4 ms 6,940 KB
testcase_26	AC	3 ms 6,944 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) begin(v),end(v)
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 1000000007;
constexpr bool debug = false;
//---------------------------------//

template<int M>
struct ModInt {
	static_assert(M > 0);
	
public:
	using value_type = int;
	using calc_type = std::int_fast64_t;
	
private:
	value_type val_;
	
public:
	constexpr ModInt(calc_type val = 0) : val_(val < 0 ? (val % M + M) % M : val % M) {}
	constexpr const value_type & val() const noexcept { return val_; }
	constexpr static decltype(M) mod() noexcept { return M; }
	
	explicit constexpr operator bool() const noexcept { return val_; }
	constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); }
	constexpr ModInt operator +() const noexcept { return ModInt(*this); }
	constexpr ModInt operator -() const noexcept { return ModInt(-val_); }
	constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; }
	constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; }
	constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; }
	constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; }
	constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; }
	constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; }
	constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; }
	constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); }
	friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; }
	friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; }
	friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; }
	friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; }
	friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; }
	friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); }
	friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; }
	friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; }
	
	constexpr ModInt pow(calc_type n) const noexcept {
		ModInt res = 1, x = val_;
		if (n < 0) { x = x.inv(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	constexpr ModInt inv() const noexcept {
		value_type a = val_, a1 = 1, a2 = 0, b = M, b1 = 0, b2 = 1;
		while (b > 0) {
			value_type q = a / b, r = a % b;
			value_type nb1 = a1 - q * b1, nb2 = a2 - q * b2;
			a = b; b = r;
			a1 = b1; b1 = nb1;
			a2 = b2; b2 = nb2;
		}
		assert(a == 1);
		return a1;
	}
};
using mint = ModInt<MOD>;

template<typename T>
struct Combination {
public:
	using size_type = std::size_t;
	
	Combination(size_type sz = 1) : fact_(1, 1), finv_(1, 1), inv_(1, 1) { build(sz); }
	
	T fact(size_type k) { if (k >= T::mod()) return 0; build(k); return fact_[k]; }
	T finv(size_type k) { assert(k < T::mod()); build(k); return finv_[k]; }
	T inv(size_type k) { assert(k > 0 && k < T::mod()); build(k); return inv_[k]; }
	
	T operator ()(int n, int r) { return c(n, r); }
	T c(int n, int r) {
		if (r < 0 || n < r) return 0;
		return fact(n) * finv(r) * finv(n - r);
	}
	
private:
	std::vector<T> fact_, finv_, inv_;
	static constexpr size_type MAX_LIMIT = 50000000;
	
	void build(size_type k) {
		if (fact_.size() > k) return;
		assert(k < MAX_LIMIT);
		size_type sz = std::min({MAX_LIMIT, static_cast<size_type>(T::mod()), std::max(fact_.size() * 2, k + 1)});
		size_type presz = fact_.size();
		fact_.resize(sz);
		finv_.resize(sz);
		inv_.resize(sz);
		
		for (size_type i = presz; i < sz; ++i) fact_[i] = fact_[i - 1] * i;
		finv_[sz - 1] = T(fact_[sz - 1]).inv();
		for (size_type i = sz - 1; i > presz; --i) {
			finv_[i - 1] = finv_[i] * i;
			inv_[i] = fact_[i - 1] * finv_[i];
		}
		inv_[presz] = fact_[presz - 1] * finv_[presz];
	}
};
using Comb = Combination<mint>;
Comb comb;

int main() {
	int N, D, K;
	cin >> N >> D >> K;
	const int dif = K - N;
	// N 個の箱に dif 個分配, 1 つの箱には D 個以上分配しない場合の数
	mint ans = 0;
	REP(i, N + 1) {
		const int res = dif - i * D;
		if (res < 0) break;
		mint cur = comb(N, i) * comb(N + res - 1, res);
		ans += cur * (i & 1 ? -1 : 1);
	}
	cout << ans << endl;
}

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テストケース

ソースコード