#287368 (C++11) No.206 数の積集合を求めるクエリ

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結果

問題	No.206 数の積集合を求めるクエリ
ユーザー	mdj982
提出日時	2018-09-27 06:13:15
言語	C++11 (gcc 11.4.0)
結果	AC
実行時間	776 ms / 7,000 ms
コード長	8,855 bytes
コンパイル時間	1,764 ms
コンパイル使用メモリ	123,840 KB
実行使用メモリ	17,648 KB
最終ジャッジ日時	2024-10-12 04:24:50
合計ジャッジ時間	13,228 ms
ジャッジサーバーID （参考情報）	judge2 / judge3

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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 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	3 ms 6,816 KB
testcase_03	AC	1 ms 6,820 KB
testcase_04	AC	2 ms 6,816 KB
testcase_05	AC	2 ms 6,816 KB
testcase_06	AC	16 ms 6,816 KB
testcase_07	AC	16 ms 6,820 KB
testcase_08	AC	16 ms 6,820 KB
testcase_09	AC	16 ms 6,816 KB
testcase_10	AC	2 ms 6,816 KB
testcase_11	AC	3 ms 6,816 KB
testcase_12	AC	20 ms 6,816 KB
testcase_13	AC	19 ms 6,816 KB
testcase_14	AC	19 ms 6,820 KB
testcase_15	AC	19 ms 6,820 KB
testcase_16	AC	19 ms 6,816 KB
testcase_17	AC	656 ms 17,520 KB
testcase_18	AC	650 ms 17,648 KB
testcase_19	AC	666 ms 17,520 KB
testcase_20	AC	615 ms 17,516 KB
testcase_21	AC	646 ms 17,648 KB
testcase_22	AC	641 ms 17,644 KB
testcase_23	AC	663 ms 17,516 KB
testcase_24	AC	759 ms 17,524 KB
testcase_25	AC	766 ms 17,524 KB
testcase_26	AC	776 ms 17,648 KB
testcase_27	AC	716 ms 17,520 KB
testcase_28	AC	764 ms 17,520 KB
testcase_29	AC	772 ms 17,648 KB
testcase_30	AC	747 ms 17,648 KB

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ソースコード

raw source code

#include <iostream>
#include <fstream>
#include <iomanip>
#include <climits>
#include <limits>
#include <algorithm>
#include <array>
#include <vector>
#include <deque>
#include <queue>
#include <list>
#include <stack>
#include <string>
#include <functional>
#include <numeric>
#include <map>
#include <set>
#include <cstdlib>
#include <bitset>
#include <unordered_map>
#include <random>
#include <cmath>
#include <complex>
// #include "utiltime.hpp"

using namespace std;

typedef long long int ll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef pair<int, int> P;
typedef pair<ll, ll> Pll;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef complex<double> cdouble;

const int INFL = (int)1e9;
const ll INFLL = (ll)1e18;
const double INFD = numeric_limits<double>::infinity();
const double PI = 3.14159265358979323846;
#define Loop(i, n) for(int i = 0; i < (int)n; i++)
#define Loopll(i, n) for(ll i = 0; i < (ll)n; i++)
#define Loop1(i, n) for(int i = 1; i <= (int)n; i++)
#define Loopll1(i, n) for(ll i = 1; i <= (ll)n; i++)
#define Loopr(i, n) for(int i = (int)n - 1; i >= 0; i--)
#define Looprll(i, n) for(ll i = (ll)n - 1; i >= 0; i--)
#define Loopr1(i, n) for(int i = (int)n; i >= 1; i--)
#define Looprll1(i, n) for(ll i = (ll)n; i >= 1; i--)
#define Loopitr(itr, container) for(auto itr = container.begin(); itr != container.end(); itr++)
#define printv(vector) Loop(i, vector.size()) { cout << vector[i] << " "; } cout << endl;
#define printmx(matrix) Loop(i, matrix.size()) { Loop(j, matrix[i].size()) { cout << matrix[i][j] << " "; } cout << endl; }
#define quickio() ios::sync_with_stdio(false); cin.tie(0);
#define readfile(filename) ifstream in(filename); cin.rdbuf(in.rdbuf());
#define bitmanip(m,val) static_cast<bitset<(int)m>>(val)
ll rndf(double x) { return (ll)(x + (x >= 0 ? 0.5 : -0.5)); }
ll floorsqrt(double x) { ll m = (ll)sqrt(x); return m + (m * m <= (ll)(x) ? 0 : -1); }
ll ceilsqrt(double x) { ll m = (ll)sqrt(x); return m + ((ll)x <= m * m ? 0 : 1); }
ll rnddiv(ll a, ll b) { return (a / b + (a % b * 2 >= b ? 1 : 0)); }
ll ceildiv(ll a, ll b) { return (a / b + (a % b == 0 ? 0 : 1)); }
ll gcd(ll m, ll n) { if (n == 0) return m; else return gcd(n, m % n); }

/*******************************************************/

namespace mod_op {

	ll MOD = (ll)1e9 + 7;

	class modll {
	private:
		ll val;
		inline ll modify(ll x) { ll ret = x % MOD; if (ret < 0) ret += MOD; return ret; }
		inline ll inv(ll x) {
			if (x == 0) return 1 / x;
			else if (x == 1) return 1;
			else return modify(inv(MOD % x) * modify(-MOD / x));
		}
	public:
		modll(ll init = 0) { val = modify(init); return; }
		modll(const modll& another) { val = another.val; return; }
		inline modll& operator=(const modll &another) { val = another.val; return *this; }
		inline modll operator+(const modll &x) { return modify(val + x.val); }
		inline modll operator-(const modll &x) { return modify(val - x.val); }
		inline modll operator*(const modll &x) { return modify(val * x.val); }
		inline modll operator/(const modll &x) { return modify(val * inv(x.val)); }
		inline modll& operator+=(const modll &x) { val = modify(val + x.val); return *this; }
		inline modll& operator-=(const modll &x) { val = modify(val - x.val); return *this; }
		inline modll& operator*=(const modll &x) { val = modify(val * x.val); return *this; }
		inline modll& operator/=(const modll &x) { val = modify(val * inv(x.val)); return *this; }
		inline bool operator==(const modll &x) { return val == x.val; }
		inline bool operator!=(const modll &x) { return val != x.val; }
		friend inline istream& operator >> (istream &is, modll& x) { is >> x.val; return is; }
		friend inline ostream& operator << (ostream &os, const modll& x) { os << x.val; return os; }
		ll get_val() { return val; }
	};

	modll pow(modll n, ll p) {
		modll ret;
		if (p == 0) ret = 1;
		else if (p == 1) ret = n;
		else {
			ret = pow(n, p / 2);
			ret *= ret;
			if (p % 2 == 1) ret *= n;
		}
		return ret;
	}

	vector<modll> facts;

	inline void make_facts(int n) {
		if (facts.empty()) facts.push_back(modll(1));
		for (int i = (int)facts.size(); i <= n; ++i) facts.push_back(modll(facts.back() * (ll)i));
		return;
	}

	vector<modll> ifacts;
	vector<modll> invs;

	inline void make_invs(int n) {
		if (invs.empty()) {
			invs.push_back(modll(0));
			invs.push_back(modll(1));
		}
		for (int i = (int)invs.size(); i <= n; ++i) {
			// because 0 = MOD = kq + r, 1/k = -q/r
			invs.push_back(invs[(int)MOD % i] * ((int)MOD - (int)MOD / i));
		}
		return;
	}

	inline void make_ifacts(int n) {
		make_invs(n);
		if (ifacts.empty()) ifacts.push_back(modll(1));
		for (int i = (int)ifacts.size(); i <= n; ++i) ifacts.push_back(modll(ifacts.back() * invs[i]));
		return;
	}

	//nCr
	modll combination(ll n, ll r) {
		if (n >= r && r >= 0) {
			modll ret;
			make_facts((int)n);
			make_ifacts((int)n);
			ret = facts[(unsigned)n] * ifacts[(unsigned)r] * ifacts[(unsigned)(n - r)];
			return ret;
		}
		else return 0;
	}

	modll get_fact(ll n) {
		make_facts((int)n);
		return facts[(int)n];
	}

	modll get_ifact(ll n) {
		make_ifacts((int)n);
		return ifacts[(int)n];
	}

	//log_a(b), if x does not exist, return -1
	ll disc_log(modll a, modll b) {
		ll ret = -1;
		ll m = ceilsqrt(MOD);
		unordered_map<ll, ll> mp;
		modll x = 1;
		Loop(i, m) {
			mp[x.get_val()] = i;
			x *= a;
		}
		x = modll(1) / pow(a, m);
		modll k = b;
		Loop(i, m) {
			if (mp.find(k.get_val()) == mp.end()) k *= x;
			else {
				ret = i * m + mp[k.get_val()];
				break;
			}
		}
		return ret;
	}
}

using namespace mod_op;
typedef vector<modll> vmodll;
typedef vector<vector<modll>> vvmodll;

namespace number_theoretic_transform {

	ll mod_backup;
	modll min_omega;
	int min_omega_depth;

	void make_base(int mode) {
		mod_backup = MOD;
		switch (mode) {
		case 0:
			MOD = 167772161;
			min_omega = 17;
			min_omega_depth = 25;
			break;
		case 1:
			MOD = 469762049;
			min_omega = 30;
			min_omega_depth = 26;
			break;
		default:
			MOD = 1224736769;
			min_omega = 149;
			min_omega_depth = 24;
		}
	}

	void recover_base() {
		MOD = mod_backup;
	}

	vector<modll> omegas, iomegas;

	inline int bit_reverse(int x, int digit) {
		int ret = digit ? x & 1 : 0;
		Loop(i, digit - 1) { ret <<= 1; x >>= 1; ret |= x & 1; }
		return ret;
	}

	inline void make_omegas(int n) {
		if (omegas.size() != n) {
			omegas.resize(n);
			modll omega = pow(min_omega, (1 << min_omega_depth) / n);
			Loop(i, n) {
				if (i == 0) omegas[i] = 1;
				else omegas[i] = omegas[i - 1] * omega;
			}
		}
	}

	inline void make_iomegas(int n) {
		if (iomegas.size() != n) {
			iomegas.resize(n);
			modll iomega = modll(1) / pow(min_omega, (1 << min_omega_depth) / n);
			Loop(i, n) {
				if (i == 0) iomegas[i] = 1;
				else iomegas[i] = iomegas[i - 1] * iomega;
			}
		}
	}

	// a.size() should be 2^digit
	vector<modll> NTT(const vector<modll> a, int mode = 0) {
		int n = int(a.size());
		int digit = int(rndf(log2(n)));
		vector<modll> ret = a;
		make_omegas(n);
		Loop(i, n) {
			int j = bit_reverse(i, digit);
			if (j > i) swap(ret[i], ret[j]);
		}
		Loop(i, digit) {
			int j = 0, m = 1 << i, mw = (digit - i - 1);
			Loop(group_id, n >> (i + 1)) {
				Loop(k, m) {
					modll x = ret[j] + omegas[k << mw] * ret[j + m];
					modll y = ret[j] - omegas[k << mw] * ret[j + m];
					ret[j] = x; ret[j + m] = y;
					++j;
				}
				j += m;
			}
		}
		return ret;
	}

	// f.size() should be 2^digit
	vector<modll> INTT(const vector<modll>& f, int mode = 0) {
		int n = int(f.size());
		int digit = int(rndf(log2(n)));
		vector<modll> ret = f;
		make_iomegas(n);
		Loopr(i, digit) {
			int j = 0, m = 1 << i, mw = (digit - i - 1);
			Loop(group_id, n >> (i + 1)) {
				Loop(k, m) {
					modll q = (ret[j] + ret[j + m]) / 2;
					modll r = (ret[j] - ret[j + m]) * iomegas[k << mw] / 2;
					ret[j] = q; ret[j + m] = r;
					++j;
				}
				j += m;
			}
		}
		Loop(i, n) {
			int j = bit_reverse(i, digit);
			if (j > i) swap(ret[i], ret[j]);
		}
		return ret;
	}

	// a.size() = b.size() should be 2^digit
	vector<modll> mul_convolution(const vector<modll> &a, const vector<modll> &b) {
		int n = int(a.size());
		vector<modll> ret;
		make_base(0);
		vector<modll> g = NTT(a), h = NTT(b);
		Loop(i, n) g[i] *= h[i];
		ret = INTT(g);
		recover_base();
		return ret;
	}

	int legal_size_of(int n) {
		int ret = 1 << (int)log2(n);
		if (ret < n) ret <<= 1;
		return ret;
	}
}

using namespace number_theoretic_transform;

int main() {
	quickio();
	int L, M, N; cin >> L >> M >> N;
	int n = legal_size_of(N * 2);
	vector<modll> a(n, 0), b(n, 0);
	Loop(i, L) {
		int abuf; cin >> abuf;
		abuf--;
		a[N - 1 - abuf] = 1;
	}
	Loop(i, M) {
		int bbuf; cin >> bbuf;
		bbuf--;
		b[bbuf] = 1;
	}
	vector<modll> c = mul_convolution(a, b);
	int q; cin >> q;
	reverse(c.begin(), c.begin() + N);
	Loop(i, q) {
		cout << c[i] << endl;
	}
}

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結果

テストケース

ソースコード