#808765 (C++17) No.856 増える演算

提出ソース

結果

問題	No.856 増える演算
ユーザー	heno239
提出日時	2022-10-19 05:48:36
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	454 ms / 3,153 ms
コード長	9,015 bytes
コンパイル時間	2,643 ms
コンパイル使用メモリ	170,940 KB
実行使用メモリ	37,656 KB
最終ジャッジ日時	2024-06-29 10:51:15
合計ジャッジ時間	19,286 ms
ジャッジサーバーID （参考情報）	judge1 / judge3

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	23 ms 24,832 KB
testcase_01	AC	25 ms 24,832 KB
testcase_02	AC	24 ms 24,832 KB
testcase_03	AC	24 ms 24,832 KB
testcase_04	AC	24 ms 24,704 KB
testcase_05	AC	24 ms 24,832 KB
testcase_06	AC	23 ms 24,704 KB
testcase_07	AC	24 ms 24,704 KB
testcase_08	AC	24 ms 24,832 KB
testcase_09	AC	24 ms 24,832 KB
testcase_10	AC	24 ms 24,832 KB
testcase_11	AC	24 ms 24,832 KB
testcase_12	AC	24 ms 24,832 KB
testcase_13	AC	26 ms 24,960 KB
testcase_14	AC	26 ms 24,832 KB
testcase_15	AC	26 ms 24,960 KB
testcase_16	AC	26 ms 24,960 KB
testcase_17	AC	27 ms 24,960 KB
testcase_18	AC	25 ms 24,960 KB
testcase_19	AC	25 ms 24,960 KB
testcase_20	AC	26 ms 24,960 KB
testcase_21	AC	26 ms 24,960 KB
testcase_22	AC	26 ms 25,088 KB
testcase_23	AC	25 ms 24,960 KB
testcase_24	AC	26 ms 24,960 KB
testcase_25	AC	24 ms 24,832 KB
testcase_26	AC	24 ms 24,704 KB
testcase_27	AC	24 ms 24,704 KB
testcase_28	AC	25 ms 24,960 KB
testcase_29	AC	25 ms 24,832 KB
testcase_30	AC	24 ms 24,960 KB
testcase_31	AC	24 ms 24,832 KB
testcase_32	AC	25 ms 24,960 KB
testcase_33	AC	29 ms 24,960 KB
testcase_34	AC	32 ms 25,216 KB
testcase_35	AC	29 ms 25,216 KB
testcase_36	AC	32 ms 25,344 KB
testcase_37	AC	31 ms 25,216 KB
testcase_38	AC	27 ms 24,960 KB
testcase_39	AC	27 ms 25,088 KB
testcase_40	AC	28 ms 25,088 KB
testcase_41	AC	28 ms 25,088 KB
testcase_42	AC	33 ms 25,344 KB
testcase_43	AC	28 ms 24,960 KB
testcase_44	AC	26 ms 24,960 KB
testcase_45	AC	27 ms 24,960 KB
testcase_46	AC	28 ms 25,088 KB
testcase_47	AC	28 ms 25,088 KB
testcase_48	AC	30 ms 25,088 KB
testcase_49	AC	28 ms 25,088 KB
testcase_50	AC	30 ms 25,216 KB
testcase_51	AC	31 ms 25,344 KB
testcase_52	AC	33 ms 25,344 KB
testcase_53	AC	435 ms 37,088 KB
testcase_54	AC	421 ms 36,736 KB
testcase_55	AC	435 ms 37,060 KB
testcase_56	AC	416 ms 36,688 KB
testcase_57	AC	435 ms 37,132 KB
testcase_58	AC	432 ms 36,940 KB
testcase_59	AC	447 ms 37,408 KB
testcase_60	AC	424 ms 36,820 KB
testcase_61	AC	446 ms 37,564 KB
testcase_62	AC	445 ms 37,312 KB
testcase_63	AC	378 ms 36,364 KB
testcase_64	AC	441 ms 37,104 KB
testcase_65	AC	411 ms 36,620 KB
testcase_66	AC	422 ms 36,812 KB
testcase_67	AC	430 ms 36,988 KB
testcase_68	AC	445 ms 37,296 KB
testcase_69	AC	442 ms 37,132 KB
testcase_70	AC	450 ms 37,428 KB
testcase_71	AC	442 ms 37,408 KB
testcase_72	AC	436 ms 37,032 KB
testcase_73	AC	454 ms 37,652 KB
testcase_74	AC	450 ms 37,656 KB
testcase_75	AC	452 ms 37,652 KB
testcase_76	AC	454 ms 37,652 KB
testcase_77	AC	452 ms 37,648 KB
testcase_78	AC	453 ms 37,624 KB
testcase_79	AC	449 ms 37,612 KB
testcase_80	AC	453 ms 37,528 KB
testcase_81	AC	452 ms 37,652 KB
testcase_82	AC	261 ms 37,524 KB

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ソースコード

raw source code

//分母について、候補となる(i,j)の組は高々2つに絞り込めるので、多倍長整数を用いれば一応log1つで比較することが可能
































#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;
constexpr ll mod = 1000000007;
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;
}
//mod should be <2^31
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; }
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 -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)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 << 21;
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;
}
using ld = long double;
//typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
	return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
	a = a + b; return a;
}
mP operator-(mP a, mP b) {
	return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
	a = a - b; return a;
}
LP operator+(LP a, LP b) {
	return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
	a = a + b; return a;
}
LP operator-(LP a, LP b) {
	return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
	a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------

int get_premitive_root(const ll& p) {
	int primitive_root = 0;
	if (!primitive_root) {
		primitive_root = [&]() {
			set<int> fac;
			int v = p - 1;
			for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
			if (v > 1) fac.insert(v);
			for (int g = 1; g < p; g++) {
				bool ok = true;
				for (auto i : fac) if (mod_pow(g, (p - 1) / i, p) == 1) { ok = false; break; }
				if (ok) return g;
			}
			return -1;
		}();
	}
	return primitive_root;
}

typedef vector <ll> poly;
void dft(poly& f, const ll& p, const int& proot, bool inverse = false) {
	int n = f.size(); if (n == 1)return;

	poly w{ 1 }, iw{ 1 };
	for (int m = w.size(); m < n / 2; m *= 2) {
		ll dw = mod_pow(proot, (p - 1) / (4 * m), p), dwinv = mod_pow(dw, p - 2, p);
		w.resize(m * 2); iw.resize(m * 2);
		for (int i = 0; i < m; i++)w[m + i] = w[i] * dw % p, iw[m + i] = iw[i] * dwinv % p;
	}
	if (!inverse) {
		for (int m = n; m >>= 1;) {
			for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
				for (int i = s; i < s + m; i++) {
					ll x = f[i], y = f[i + m] * w[k] % p;
					f[i] = x + y, f[i + m] = x - y;
					if (f[i] >= p)f[i] -= p;
					if (f[i + m] < 0)f[i + m] += p;
				}
			}
		}
	}
	else {
		for (int m = 1; m < n; m *= 2) {
			for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
				for (int i = s; i < s + m; i++) {
					ll x = f[i], y = f[i + m];
					f[i] = x + y, f[i + m] = (x - y) * iw[k] % p;
					if (f[i] >= p)f[i] -= p;
					if (f[i + m] < 0)f[i + m] += p;
				}
			}
		}
		ll n_inv = mod_pow(n, p - 2, p);
		for (ll& v : f)(v *= n_inv) %= p;
	}
}

poly multi(poly g, poly h, const ll& p, int n) {
	const int proot = get_premitive_root(p);
	dft(g, p, proot, false);
	dft(h, p, proot, false);
	poly f(n);
	rep(i, n) {
		f[i] = g[i] * h[i] % p;
	}
	dft(f, p, proot, true);
	return f;
}

constexpr ll m0 = 1107296257;
constexpr ll m1 = 1224736769;
const ll inv01 = mod_pow(m0, m1 - 2, m1);

ll calc(ll& a, ll& b) {
	ll res = 0;
	ll x1 = a;
	ll x2 = (b - x1) * inv01;
	x2 %= m1; if (x2 < 0)x2 += m1;
	res = x1 + x2 * m0;
	return res;
}
poly multiply(poly g, poly h) {

	int resz = g.size() + h.size() - 1;

	int n = 1;
	int pi = 0, qi = 0;
	rep(i, g.size())if (g[i])pi = i;
	rep(i, h.size())if (h[i])qi = i;
	int sz = pi + qi + 2;
	while (n < sz)n *= 2;
	g.resize(n); h.resize(n);

	poly vp[2];
	vp[0] = multi(g, h, m0, n);
	vp[1] = multi(g, h, m1, n);
	poly res(resz);
	rep(i, res.size()) {
		ll a, b, c;
		if (i < vp[0].size())a = vp[0][i];
		else a = 0;
		if (i < vp[1].size())b = vp[1][i];
		else b = 0;
		res[i] = calc(a, b);
	}
	return res;
}

void solve(){
	int n; cin >> n;
	vector<int> a(n);
	rep(i, n)cin >> a[i];
	modint ans = 1;
	vector<ll> ra(n + 1);
	rep(i, n)ra[i + 1] = ra[i] + a[i];
	rep(i, n) {
		ll num = ra[n] - ra[i + 1];
		ans *= mod_pow(a[i], num);
	}
	poly p(1 << 17);
	rep(i, n)p[a[i]]++;
	p = multiply(p, p);
	rep(i, n) {
		p[a[i] + a[i]]--;
	}
	rep(i, p.size()) {
		ll num = p[i] / 2;
		if (num)ans *= mod_pow(i, num);
	}
	int mi = mod;
	rep(i, n)chmin(mi, a[i]);
	vector<int> vloc;
	rep(i, n)if (mi == a[i]) {
		vloc.push_back(i);
	}
	if (vloc.size() >= 2) {
		ans /= 2 * mi;
		ans /= mod_pow(mi, mi);
	}
	else {
		int vl = mod, vr = mod;
		rep(i, vloc[0]) {
			chmin(vl, a[i]);
		}
		Rep(i, vloc[0] + 1, n) {
			chmin(vr, a[i]);
		}
		if (vr == mod) {
			ans /= vl + mi;
			ans /= mod_pow(vl, mi);
		}
		else if (vl == mod) {
			ans /= mi + vr;
			ans /= mod_pow(mi, vr);
		}
		else {
			ld cl = log(vl + mi) + mi * log(vl);
			ld cr = log(mi + vr) + vr * log(mi);
			if (cl < cr) {
				ans /= vl + mi;
				ans /= mod_pow(vl, mi);
			}
			else {
				ans /= mi + vr;
				ans /= mod_pow(mi, vr);
			}
		}
	}
	cout << ans << "\n";
}





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

yukicoder

結果

テストケース

ソースコード