#536014 (C++17) No.1181 Product Sum for All Subsets

提出ソース

結果

問題	No.1181 Product Sum for All Subsets
ユーザー	FF256grhy
提出日時	2020-08-22 00:44:23
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	57 ms / 2,000 ms
コード長	6,245 bytes
コンパイル時間	2,200 ms
コンパイル使用メモリ	211,232 KB
実行使用メモリ	6,528 KB
最終ジャッジ日時	2024-10-15 06:35:26
合計ジャッジ時間	3,645 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

このコードへのチャレンジ
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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 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	3 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	2 ms 5,248 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	2 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	2 ms 5,248 KB
testcase_09	AC	2 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	2 ms 5,248 KB
testcase_12	AC	48 ms 5,888 KB
testcase_13	AC	11 ms 5,248 KB
testcase_14	AC	44 ms 5,632 KB
testcase_15	AC	35 ms 5,248 KB
testcase_16	AC	49 ms 6,016 KB
testcase_17	AC	22 ms 5,248 KB
testcase_18	AC	43 ms 5,632 KB
testcase_19	AC	40 ms 5,376 KB
testcase_20	AC	48 ms 5,888 KB
testcase_21	AC	27 ms 5,248 KB
testcase_22	AC	17 ms 5,248 KB
testcase_23	AC	8 ms 5,248 KB
testcase_24	AC	14 ms 5,248 KB
testcase_25	AC	26 ms 5,248 KB
testcase_26	AC	3 ms 5,248 KB
testcase_27	AC	2 ms 5,248 KB
testcase_28	AC	57 ms 6,528 KB
testcase_29	AC	53 ms 6,528 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
using LL = long long int;
#define incID(i, l, r) for(int i = (l)    ; i <  (r); i++)
#define decID(i, l, r) for(int i = (r) - 1; i >= (l); i--)
#define incII(i, l, r) for(int i = (l)    ; i <= (r); i++)
#define decII(i, l, r) for(int i = (r)    ; i >= (l); i--)
#define inc(i, n)  incID(i, 0, n)
#define dec(i, n)  decID(i, 0, n)
#define inc1(i, n) incII(i, 1, n)
#define dec1(i, n) decII(i, 1, n)
#define inID(v, l, r) ((l) <= (v) && (v) <  (r))
#define inII(v, l, r) ((l) <= (v) && (v) <= (r))
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define MT make_tuple
#define FI first
#define SE second
#define FR front()
#define BA back()
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
auto setmin   = [](auto & a, auto b) { return (b <  a ? a = b, true : false); };
auto setmax   = [](auto & a, auto b) { return (b >  a ? a = b, true : false); };
auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); };
auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); };
#define SI(v) static_cast<int>(v.size())
#define RF(e, v) for(auto & e: v)
#define until(e) while(! (e))
#define if_not(e) if(! (e))
#define ef else if
#define UR assert(false)
// 以下、入出力関係のテンプレ案のテスト
auto * IS = & cin;
// input elements (as a tuple)
template<typename U, int I> void in_(U & t) { }
template<typename U, int I, typename A, typename ... B> void in_(U & t) { (* IS) >> get<I>(t); in_<U, I + 1, B ...>(t); }
template<typename ... T> auto in() { tuple<T ...> t; in_<tuple<T ...>, 0, T ...>(t); return t; }
// input an array
template<typename T, int N> auto ain() { array<T, N> a; inc(i, N) { (* IS) >> a[i]; } return a; }
// input a (multi-dimensional) vector
template<typename T> T vin() { return * istream_iterator<T>(* IS); }
template<typename T, typename N, typename ... M> auto vin(N n, M ... m) {
	vector<decltype(vin<T, M ...>(m ...))> v(n); inc(i, n) { v[i] = vin<T, M ...>(m ...); } return v;
}
// input multi-column (as a tuple of vector)
template<typename U, int I> void colin_(U & t) { }
template<typename U, int I, typename A, typename ... B> void colin_(U & t) {
	get<I>(t).emplace_back(* istream_iterator<A>(* IS)); colin_<U, I + 1, B ...>(t);
}
template<typename ... T> auto colin(int n) {
	tuple<vector<T> ...> t; inc(i, n) { colin_<tuple<vector<T> ...>, 0, T ...>(t); } return t;
}
auto * OS = & cout;
string SP = " ", LN = "\n";
// output elements
void out() { (* OS) << LN << flush; }
template<typename A                > void out(A && a            ) { (* OS) << a      ; out(     ); }
template<typename A, typename ... B> void out(A && a, B && ... b) { (* OS) << a << SP; out(b ...); }
// output a (multi-dimensional) vector
template<typename T> ostream & operator<<(ostream & os, vector<T> const & v) {
	inc(i, v.size()) { os << (i == 0 ? "" : SP) << v[i]; } return os << flush;
}
template<typename T> void vout_(T && v) { (* OS) << v; }
template<typename T, typename A, typename ... B> void vout_(T && v, A a, B ... b) {
	for(auto && w: v) { vout_(w, b ...); (* OS) << a; }
}
template<typename T, typename ... A> void vout(T && v, A ... a) { vout_(v, a ...); out(); }

// ---- ----

template<LL M> class ModInt {
private:
	LL v;
	pair<LL, LL> ext_gcd(LL a, LL b) {
		if(b == 0) { assert(a == 1); return { 1, 0 }; }
		auto p = ext_gcd(b, a % b);
		return { p.SE, p.FI - (a / b) * p.SE };
	}
public:
	ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } }
	LL get_v() { return v; }
	ModInt inv() { return ext_gcd(M, v).SE; }
	ModInt exp(LL b) {
		ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; }
		while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; }
		return p;
	}
	friend bool      operator< (ModInt    a, ModInt   b) { return (a.v <  b.v); }
	friend bool      operator> (ModInt    a, ModInt   b) { return (a.v >  b.v); }
	friend bool      operator<=(ModInt    a, ModInt   b) { return (a.v <= b.v); }
	friend bool      operator>=(ModInt    a, ModInt   b) { return (a.v >= b.v); }
	friend bool      operator==(ModInt    a, ModInt   b) { return (a.v == b.v); }
	friend bool      operator!=(ModInt    a, ModInt   b) { return (a.v != b.v); }
	friend ModInt    operator+ (ModInt    a            ) { return ModInt(+a.v); }
	friend ModInt    operator- (ModInt    a            ) { return ModInt(-a.v); }
	friend ModInt    operator+ (ModInt    a, ModInt   b) { return ModInt(a.v + b.v); }
	friend ModInt    operator- (ModInt    a, ModInt   b) { return ModInt(a.v - b.v); }
	friend ModInt    operator* (ModInt    a, ModInt   b) { return ModInt(a.v * b.v); }
	friend ModInt    operator/ (ModInt    a, ModInt   b) { return a * b.inv(); }
	friend ModInt    operator^ (ModInt    a, LL       b) { return a.exp(b); }
	friend ModInt  & operator+=(ModInt  & a, ModInt   b) { return (a = a + b); }
	friend ModInt  & operator-=(ModInt  & a, ModInt   b) { return (a = a - b); }
	friend ModInt  & operator*=(ModInt  & a, ModInt   b) { return (a = a * b); }
	friend ModInt  & operator/=(ModInt  & a, ModInt   b) { return (a = a / b); }
	friend ModInt  & operator^=(ModInt  & a, LL       b) { return (a = a ^ b); }
	friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; }
	friend ostream & operator<<(ostream & s, ModInt   b) { return (s << b.v); }
};

// ----

template<typename T> struct Combination {
	LL n;
	vector<T> f, r;
	Combination(LL n) : n(n) {
		f = r = vector<T>(n + 1);
		inc(i, n + 1) { f[i] = (i == 0 ? 1          : f[i - 1] *  i     ); }
		dec(i, n + 1) { r[i] = (i == n ? f[n].inv() : r[i + 1] * (i + 1)); }
	}
	T P(LL a, LL b) {
		assert(inII(a, 0, n) && inII(b, 0, n));
		return (a < b ? 0 : f[a] * r[a - b]);
	}
	T C(LL a, LL b) {
		assert(inII(a, 0, n) && inII(b, 0, n));
		return (a < b ? 0 : f[a] * r[a - b] * r[b]);
	}
	T H(LL a, LL b) {
		assert(inII(a, 0, n) && inII(b, 0, n) && inII(a + b - 1, -1, n));
		return (a == 0 ? (b == 0 ? 1 : 0) : f[a + b - 1] * r[a - 1] * r[b]);
	}
};

using MI = ModInt<1'000'000'007>;

int main() {
	auto [n, k] = in<LL, MI>();
	Combination<MI> c(n);
	
	MI s = k * (k + 1) / 2;
	MI ans = 0;
	inc(i, n) {
		LL j = n - i;
		ans += c.C(n, i) * (s ^ i) * (k ^ j);
	}
	out(ans);
}

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結果

テストケース

ソースコード