結果

問題 No.719 Coprime
コンテスト
ユーザー snrnsidy
提出日時 2021-07-15 15:23:01
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 4,161 bytes
コンパイル時間 2,910 ms
コンパイル使用メモリ 213,884 KB
最終ジャッジ日時 2025-01-23 01:07:22
ジャッジサーバーID
（参考情報） 		judge3 / judge3
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ファイルパターン 結果
other AC * 44 WA * 17
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コンパイルメッセージ
main.cpp: In function ‘std::vector<int> berlekamp_massey(std::vector<int>)’:
main.cpp:34:32: warning: ‘lf’ may be used uninitialized [-Wmaybe-uninitialized]
   34 |                 vector<int> c(i-lf-1);
      |                               ~^~~
main.cpp:20:13: note: ‘lf’ was declared here
   20 |         int lf, ld;
      |             ^~
main.cpp:33:44: warning: ‘ld’ may be used uninitialized [-Wmaybe-uninitialized]
   33 |                 lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod;
      |                                        ~~~~^~~~~~~~~~~~~
main.cpp:20:17: note: ‘ld’ was declared here
   20 |         int lf, ld;
      |                 ^~

ソースコード

diff # 

#include <bits/stdc++.h>

using namespace std;

vector <int> prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71};
int dp[2][1<<20];
const int mod = 998244353;
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;
}

int main() 
{
	cin.tie(0);
	ios::sync_with_stdio(false);
	
	int N;
	vector <int> v = {0,0};
	cin >> N;
	
	for(int i=0;i<2;i++)
	{
		for(int j=0;j<(1<<20);j++)
		{
			dp[i][j] = -1e9;
		}
	}
	
	dp[1][0] = 0;
	
	for(int i=1;i<100;i++)
	{
		memcpy(dp[0],dp[1],sizeof(dp[1]));
		fill(dp[1],dp[1]+(1<<20),-1e9);
		int bitmask = 0;
		for(int j=0;j<20;j++)
		{
			if(((i+1)%prime[j])==0)
			{
				bitmask += (1<<j);
			}
		}
		//cout << i+1 << ' ' << bitmask << '\n';
		for(int j=0;j<(1<<20);j++)
		{
			if(dp[0][j]<=-1e9) continue;
			dp[1][j] = max(dp[1][j],dp[0][j]);
			if((j&bitmask)) continue;
			dp[1][bitmask + j] = max(dp[1][bitmask + j],dp[0][j] + (i+1));
		}
		int res = 0;
	
		for(int j=0;j<(1<<20);j++)
		{
			res = max(res,dp[1][j]);
		}
		v.push_back(res);
	}
	
	cout << guess_nth_term(v,N) << '\n';
	
	return 0;
}
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