結果

問題 No.1025 Modular Equation
コンテスト
ユーザー satashun
提出日時 2020-12-15 19:23:22
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 4,879 bytes
コンパイル時間 2,360 ms
コンパイル使用メモリ 204,500 KB
最終ジャッジ日時 2025-01-17 01:10:24
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 24 WA * 8
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 ‘int pr_root(int)’:
main.cpp:140:1: warning: control reaches end of non-void function [-Wreturn-type]
  140 | }
      | ^

ソースコード

diff # 

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

template <unsigned int MOD>
struct ModInt {
    using uint = unsigned int;
    using ull = unsigned long long;
    using M = ModInt;

    uint v;

    ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
    M& set_norm(uint _v) {  //[0, MOD * 2)->[0, MOD)
        v = (_v < MOD) ? _v : _v - MOD;
        return *this;
    }

    explicit operator bool() const { return v != 0; }
    M operator+(const M& a) const { return M().set_norm(v + a.v); }
    M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
    M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
    M operator/(const M& a) const { return *this * a.inv(); }
    M& operator+=(const M& a) { return *this = *this + a; }
    M& operator-=(const M& a) { return *this = *this - a; }
    M& operator*=(const M& a) { return *this = *this * a; }
    M& operator/=(const M& a) { return *this = *this / a; }
    M operator-() const { return M() - *this; }
    M& operator++(int) { return *this = *this + 1; }
    M& operator--(int) { return *this = *this - 1; }

    M pow(ll n) const {
        if (n < 0) return inv().pow(-n);
        M x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }

    M inv() const {
        ll a = v, b = MOD, p = 1, q = 0, t;
        while (b != 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(p -= t * q, q);
        }
        return M(p);
    }

    bool operator==(const M& a) const { return v == a.v; }
    bool operator!=(const M& a) const { return v != a.v; }
    friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
    static uint get_mod() { return MOD; }
};

using Mint = ModInt<1000000007>;

int pr_root(int p) {
    for (int i = 1; i < p; ++i) {
        set<int> st;
        int x = 1;
        bool ok = 1;
        rep(t, p - 1) {
            if (st.count(x)) {
                ok = 0;
                break;
            }
            st.insert(x);
            x = x * i % p;
        }
        if (ok) {
            return i;
        }
    }
}

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

    int p, n, k, b;
    cin >> p >> n >> k >> b;
    V<int> a(n);
    rep(i, n) cin >> a[i];

    k = __gcd(k, p - 1);
    int g = pr_root(p);

    // dp[i][j] : ..i, mod p = r^j, j = k : 0

    VV<Mint> dp(n + 1, V<Mint>(k + 1));
    dp[0][k] = 1;

    V<int> rk(p), pw(p);
    {
        int x = 1;
        rep(t, p - 1) {
            pw[t] = x;
            rk[x] = t;
            x = x * g % p;
        }
    }

    debug(k, rk);

    rep(i, n) {
        rep(j, k + 1) {
            // x=0
            dp[i + 1][j] += dp[i][j];
            int v = j == k ? 0 : pw[j];
            for (int x = 0; x < (p - 1) / k; ++x) {
                int nv = (v + ll(pw[x * k]) * a[i]) % p;
                if (nv == 0) {
                    dp[i + 1][k] += dp[i][j] * k;
                } else {
                    dp[i + 1][rk[nv] % k] += dp[i][j] * k;
                }
            }
        }
    }
    int c = b == 0 ? k : rk[b] % k;
    int cnt = 0;
    for (int i = 1; i < p; ++i) {
        if (rk[i] % k == c) cnt++;
    }
    debug(dp[n]);
    if (cnt > 0) {
        cout << dp[n][c] / cnt << endl;
    } else {
        cout << 0 << endl;
    }

    return 0;
}
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