結果

問題 No.980 Fibonacci Convolution Hard
ユーザー snrnsidysnrnsidy
提出日時 2021-09-30 21:44:01
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,555 ms / 2,000 ms
コード長 4,416 bytes
コンパイル時間 2,620 ms
コンパイル使用メモリ 221,868 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-18 02:19:01
合計ジャッジ時間 31,822 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
（要ログイン）

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 1,525 ms
5,248 KB
testcase_01 AC 1,522 ms
5,248 KB
testcase_02 AC 1,538 ms
6,940 KB
testcase_03 AC 1,523 ms
6,944 KB
testcase_04 AC 1,535 ms
6,944 KB
testcase_05 AC 1,524 ms
6,940 KB
testcase_06 AC 1,510 ms
6,940 KB
testcase_07 AC 1,511 ms
6,944 KB
testcase_08 AC 1,534 ms
6,944 KB
testcase_09 AC 1,491 ms
6,940 KB
testcase_10 AC 1,492 ms
6,940 KB
testcase_11 AC 1,510 ms
6,940 KB
testcase_12 AC 1,482 ms
6,944 KB
testcase_13 AC 1,521 ms
6,944 KB
testcase_14 AC 1,543 ms
6,940 KB
testcase_15 AC 1,555 ms
6,944 KB
testcase_16 AC 1,367 ms
6,944 KB
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:31:36: warning: 'ld' may be used uninitialized [-Wmaybe-uninitialized]
   31 |         lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod;
      |                                ~~~~^~~~~~~~~~~~~
main.cpp:18:13: note: 'ld' was declared here
   18 |     int lf, ld;
      |             ^~
main.cpp:32:24: warning: 'lf' may be used uninitialized [-Wmaybe-uninitialized]
   32 |         vector<int> c(i-lf-1);
      |                       ~^~~
main.cpp:18:9: note: 'lf' was declared here
   18 |     int lf, ld;
      |         ^~

ソースコード

diff # 

#include <bits/stdc++.h>

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;
}


int main(void)
{
	cin.tie(0);
	ios::sync_with_stdio(false);

	long long int p;

	cin >> p;

	vector <long long int> a(301);

	a[0] = 0;
	a[1] = 0;
	a[2] = 1;

	for(int i=3;i<=300;i++)
	{
		long long int val = a[i-2];
		val += ((p*a[i-1])%mod);
		val%=mod;
		a[i] = val;
	}

	vector <int> b;
	b.push_back(0);
	b.push_back(0);
	for(int i=2;i<=30;i++)
	{
		long long int temp = 0;
		for(int j=1;j<i;j++)
		{
			temp += ((a[j]*a[i-j])%mod);
			temp%=mod;
		}
		b.push_back(temp);
	}

	int Q,q;

	cin >> Q;

	for(int i=0;i<Q;i++)
	{
		cin >> q;
		cout << guess_nth_term(b,q) << '\n';
	}
	return 0;
}
0