結果

問題 No.931 Multiplicative Convolution
ユーザー hitonanodehitonanode
提出日時 2019-11-23 00:06:50
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 278 ms / 2,000 ms
コード長 6,419 bytes
コンパイル時間 1,882 ms
コンパイル使用メモリ 175,472 KB
実行使用メモリ 12,748 KB
最終ジャッジ日時 2024-10-11 06:34:42
合計ジャッジ時間 5,874 ms
ジャッジサーバーID
（参考情報） 		judge2 / 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 2 ms
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 2 ms
5,248 KB
testcase_05 AC 2 ms
5,248 KB
testcase_06 AC 3 ms
5,248 KB
testcase_07 AC 28 ms
5,248 KB
testcase_08 AC 278 ms
12,704 KB
testcase_09 AC 265 ms
12,628 KB
testcase_10 AC 274 ms
12,420 KB
testcase_11 AC 269 ms
12,380 KB
testcase_12 AC 263 ms
10,880 KB
testcase_13 AC 276 ms
12,504 KB
testcase_14 AC 278 ms
12,748 KB
testcase_15 AC 277 ms
12,728 KB
testcase_16 AC 276 ms
12,532 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
///// This part below is only for debug, not used /////
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
///// END /////

lint power(lint x, lint n, lint MOD)
{
    lint ans = 1;
    while (n>0)
    {
        if (n & 1) (ans *= x) %= MOD;
        (x *= x) %= MOD;
       n >>= 1;
    }
   return ans %= MOD;
}
// Solve ax+by=gcd(a, b)
lint extgcd(lint a, lint b, lint &x, lint &y)
{
    lint d = a;
    if (b != 0) d = extgcd(b, a % b, y, x), y -= (a / b) * x;
    else x = 1, y = 0;
    return d;
}
// Calc a^(-1) (MOD m)
lint mod_inverse(lint a, lint m)
{
    lint x, y;
    extgcd(a, m, x, y);
    return (m + x % m) % m;
}

// mod: 素数, primitive_root: modの原始根 is_inverse: trueならば逆変換
void fft_mod(vector<lint> &a, lint mod, lint primitive_root, bool is_inverse=false)
{
    int n = a.size();
    lint h = power(primitive_root, (mod - 1) / n, mod);
    if (is_inverse) h = mod_inverse(h, mod);

    int i = 0;
    FOR(j, 1, n - 1) {
        for (int k = n >> 1; k > (i ^= k); k >>= 1);
        if (j < i) swap(a[i], a[j]);
    }
    for (int m = 1; m < n; m *= 2) {
        int m2 = 2 * m;
        lint base = power(h, n / m2, mod);
        lint w = 1;
        REP(x, m) {
            for (int s = x; s < n; s += m2) {
                lint u = a[s], d = a[s + m] * w % mod;
                a[s] = u + d - (u + d >= mod ? mod : 0), a[s + m] = u - d + (u - d < 0 ? mod : 0);
            }
            w = w * base % mod;
        }
    }
    for (auto &v : a) v = (v < 0 ? v + mod : v);
    if (is_inverse)
    {
        lint n_inv = mod_inverse(n, mod);
        for (auto &v : a) v = v * n_inv % mod;
    }
}
// MOD modにおける畳み込み演算 retval[i] = \sum_j a[j] b[i - j]
vector<lint> convolution_mod(vector<lint> a, vector<lint> b, lint mod, lint primitive_root)
{
    int sz = 1;
    while (sz < a.size() + b.size()) sz <<= 1;
    a.resize(sz), b.resize(sz);
    fft_mod(a, mod, primitive_root, false), fft_mod(b, mod, primitive_root, false);
    REP(i, sz) a[i] = a[i] * b[i] % mod;
    fft_mod(a, mod, primitive_root, true);
    return a;
}

constexpr lint MOD = 998244353;

int find_primitive_root(lint p)
{
    vector<lint> fac;
    lint pp = 2;
    lint v = p - 1;
    while (v >= pp * pp) // prime factorization of p - 1
    {
        int e = 0;
        while (v % pp == 0)
        {
            e++;
            v /= pp;
        }
        if (e) fac.push_back(pp);
        pp++;
    }
    if (v > 1) fac.push_back(v);

    int g = 2;
    while (g < p)
    {
        if (power(g, p - 1, p) != 1) return -1;
        bool ok = true;
        for (auto pp : fac)
        {
            if (power(g, (p - 1) / pp, p) == 1)
            {
                ok = false;
                break;
            }
        }
        if (ok) return g;
        g++;
    }
    return -1;
}

int main()
{
    int P;
    cin >> P;
    vector<lint> A(P - 1), B(P - 1);
    cin >> A >> B;
    if (P == 2)
    {
        cout << A[0] * B[0] % MOD << endl;
        return 0;
    }
    lint b = find_primitive_root(P);
    vector<lint> pp(P, 1), ppinv(P);
    FOR(i, 1, P) pp[i] = pp[i - 1] * b % P;
    REP(i, P) ppinv[pp[i]] = i;
    vector<lint> AS(P), BS(P);
    REP(i, P - 1) AS[ppinv[i + 1]] = A[i];
    REP(i, P - 1) BS[ppinv[i + 1]] = B[i];
    vector<lint> v = convolution_mod(AS, BS, MOD, 3);
    vector<lint> ret(P + 1);
    FOR(i, 1, v.size())
    {
        (ret[power(b, i, P)] += v[i]) %= MOD;
    }
    FOR(i, 1, P) printf("%lld ", ret[i]);
}
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