結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー snrnsidysnrnsidy
提出日時 2021-04-06 04:25:16
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 22 ms / 5,000 ms
コード長 4,887 bytes
コンパイル時間 1,980 ms
コンパイル使用メモリ 144,988 KB
最終ジャッジ日時 2025-01-20 12:09:56
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 37
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘std::vector<int> berlekamp_massey(std::vector<int>)’:
main.cpp:55:33: warning: ‘lf’ may be used uninitialized [-Wmaybe-uninitialized]
   55 |                 vector<int> c(i - lf - 1);
      |                               ~~^~~~
main.cpp:41:13: note: ‘lf’ was declared here
   41 |         int lf, ld;
      |             ^~
main.cpp:54:44: warning: ‘ld’ may be used uninitialized [-Wmaybe-uninitialized]
   54 |                 lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod;
      |                                        ~~~~^~~~~~~~~~~~~
main.cpp:41:17: note: ‘ld’ was declared here
   41 |         int lf, ld;
      |                 ^~

ソースコード

diff # 

#include <map>
#include <set>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <cstdio>
#include <limits>
#include <vector>
#include <cstdlib>
#include <numeric>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <functional> 
#include <iomanip>
#include <unordered_map>
#include <memory.h>
#include <unordered_set>
#include <fstream>
#include <random>

using namespace std;
const long long int mod = 1e9 + 7;

using lint = long long;
lint ipow(lint x, lint p) {
	lint ret = 1, piv = x;
	while (p) {
		if (p & 1) ret = ret * piv % mod;
		piv = piv * piv % mod;
		p >>= 1;
	}
	return ret;
}
vector<int> berlekamp_massey(vector<int> x) {
	vector<int> ls, cur;
	int lf, ld;
	for (int i = 0; i < x.size(); i++) {
		lint t = 0;
		for (int j = 0; j < cur.size(); j++) {
			t = (t + 1ll * x[i - j - 1] * cur[j]) % mod;
		}
		if ((t - x[i]) % mod == 0) continue;
		if (cur.empty()) {
			cur.resize(i + 1);
			lf = i;
			ld = (t - x[i]) % mod;
			continue;
		}
		lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod;
		vector<int> c(i - lf - 1);
		c.push_back(k);
		for (auto& j : ls) c.push_back(-j * k % mod);
		if (c.size() < cur.size()) c.resize(cur.size());
		for (int j = 0; j < cur.size(); j++) {
			c[j] = (c[j] + cur[j]) % mod;
		}
		if (i - lf + (int)ls.size() >= (int)cur.size()) {
			tie(ls, lf, ld) = make_tuple(cur, i, (t - x[i]) % mod);
		}
		cur = c;
	}
	for (auto& i : cur) i = (i % mod + mod) % mod;
	return cur;
}
int get_nth(vector<int> rec, vector<int> dp, lint n) {
	int m = rec.size();
	vector<int> s(m), t(m);
	s[0] = 1;
	if (m != 1) t[1] = 1;
	else t[0] = rec[0];
	auto mul = [&rec](vector<int> v, vector<int> w) {
		int m = v.size();
		vector<int> t(2 * m);
		for (int j = 0; j < m; j++) {
			for (int k = 0; k < m; k++) {
				t[j + k] += 1ll * v[j] * w[k] % mod;
				if (t[j + k] >= mod) t[j + k] -= mod;
			}
		}
		for (int j = 2 * m - 1; j >= m; j--) {
			for (int k = 1; k <= m; k++) {
				t[j - k] += 1ll * t[j] * rec[k - 1] % mod;
				if (t[j - k] >= mod) t[j - k] -= mod;
			}
		}
		t.resize(m);
		return t;
	};
	while (n) {
		if (n & 1) s = mul(s, t);
		t = mul(t, t);
		n >>= 1;
	}
	lint ret = 0;
	for (int i = 0; i < m; i++) ret += 1ll * s[i] * dp[i] % mod;
	return ret % mod;
}
int guess_nth_term(vector<int> x, lint n) {
	if (n < x.size()) return x[n];
	vector<int> v = berlekamp_massey(x);
	if (v.empty()) return 0;
	return get_nth(v, x, n);
}
struct elem { int x, y, v; }; // A_(x, y) <- v, 0-based. no duplicate please..
vector<int> get_min_poly(int n, vector<elem> M) {
	// smallest poly P such that A^i = sum_{j < i} {A^j \times P_j}
	vector<int> rnd1, rnd2;
	mt19937 rng(0x14004);
	auto randint = [&rng](int lb, int ub) {
		return uniform_int_distribution<int>(lb, ub)(rng);
	};
	for (int i = 0; i < n; i++) {
		rnd1.push_back(randint(1, mod - 1));
		rnd2.push_back(randint(1, mod - 1));
	}
	vector<int> gobs;
	for (int i = 0; i < 2 * n + 2; i++) {
		int tmp = 0;
		for (int j = 0; j < n; j++) {
			tmp += 1ll * rnd2[j] * rnd1[j] % mod;
			if (tmp >= mod) tmp -= mod;
		}
		gobs.push_back(tmp);
		vector<int> nxt(n);
		for (auto& i : M) {
			nxt[i.x] += 1ll * i.v * rnd1[i.y] % mod;
			if (nxt[i.x] >= mod) nxt[i.x] -= mod;
		}
		rnd1 = nxt;
	}
	auto sol = berlekamp_massey(gobs);
	reverse(sol.begin(), sol.end());
	return sol;
}
lint det(int n, vector<elem> M) {
	vector<int> rnd;
	mt19937 rng(0x14004);
	auto randint = [&rng](int lb, int ub) {
		return uniform_int_distribution<int>(lb, ub)(rng);
	};
	for (int i = 0; i < n; i++) rnd.push_back(randint(1, mod - 1));
	for (auto& i : M) {
		i.v = 1ll * i.v * rnd[i.y] % mod;
	}
	auto sol = get_min_poly(n, M)[0];
	if (n % 2 == 0) sol = mod - sol;
	for (auto& i : rnd) sol = 1ll * sol * ipow(i, mod - 2) % mod;
	return sol;
}

long long int S[1000001];
long long int F[1000001];
int main(void)
{
	cin.tie(0);
	ios::sync_with_stdio(false);
	
	long long int n, k, t;
	vector <int> v,v2;
	v.push_back(0);
	cin >> n >> k;
	for (int i = 0; i < n; i++)
	{
		cin >> t;
		v.push_back(t);
	}

	if (k <= 1e6)
	{
		S[0] = 0;
		F[0] = 0;
		for (int i = 1; i <= n; i++)
		{
			F[i] = v[i];
			S[i] = (S[i-1] + v[i]%mod);
			F[i] %= mod;
			S[i] %= mod;
		}
		for (int i = n + 1; i <= k; i++)
		{
			long long int val = S[i - 1];
			val -= S[i - n - 1];
			val %= mod;
			if (val < 0)
			{
				val += mod;
			}
			F[i] = val;
			S[i] = ((S[i - 1] % mod) + (val % mod) % mod);
			S[i] %= mod;
		}
		cout << F[k] << ' ' << S[k] << '\n';
	}
	else
	{
		for (int i = n + 1; i <= 300; i++)
		{
			long long int sum = 0;
			for (int j = 1; j <= n; j++)
			{
				sum += v[i - j];
				sum %= mod;
			}
			v.push_back(sum);
		}

		long long int sum = 0;
		for (int i = 0; i <= 300; i++)
		{
			sum += v[i];
			sum %= mod;
			v2.push_back(sum);
		}

		cout << guess_nth_term(v, k) << ' ' << guess_nth_term(v2, k) << '\n';
	}
	return 0;
}
0