結果

問題 No.1222 -101
ユーザー kimiyukikimiyuki
提出日時 2020-09-06 17:50:27
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 156 ms / 2,000 ms
コード長 6,972 bytes
コンパイル時間 3,362 ms
コンパイル使用メモリ 203,532 KB
最終ジャッジ日時 2025-01-14 07:57:03
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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ファイルパターン 結果
sample AC * 4
other AC * 35
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 # 

#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 2 "/home/user/Library/utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 4 "/home/user/Library/modulus/modpow.hpp"

inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
    assert (/* 0 <= x and */ x < (uint_fast64_t)MOD);
    uint_fast64_t y = 1;
    for (; k; k >>= 1) {
        if (k & 1) (y *= x) %= MOD;
        (x *= x) %= MOD;
    }
    assert (/* 0 <= y and */ y < (uint_fast64_t)MOD);
    return y;
}
#line 5 "/home/user/Library/modulus/modinv.hpp"

inline int32_t modinv_nocheck(int32_t value, int32_t MOD) {
    assert (0 <= value and value < MOD);
    if (value == 0) return -1;
    int64_t a = value, b = MOD;
    int64_t x = 0, y = 1;
    for (int64_t u = 1, v = 0; a; ) {
        int64_t q = b / a;
        x -= q * u; std::swap(x, u);
        y -= q * v; std::swap(y, v);
        b -= q * a; std::swap(b, a);
    }
    if (not (value * x + MOD * y == b and b == 1)) return -1;
    if (x < 0) x += MOD;
    assert (0 <= x and x < MOD);
    return x;
}

inline int32_t modinv(int32_t x, int32_t MOD) {
    int32_t y = modinv_nocheck(x, MOD);
    assert (y != -1);
    return y;
}
#line 6 "/home/user/Library/modulus/mint.hpp"

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
#line 4 "main.cpp"
using namespace std;

constexpr int64_t MOD = 1000000007;
mint<MOD> solve_zero(int n, int m, const vector<int>& l, const vector<int>& r) {
    if (m < 10) {
        cerr << "zero" << endl;
        cerr << "n = " << n << endl;
        cerr << "m = " << m << endl;
        REP (i, m) {
            cerr << "[" << l[i] << ", " << r[i] << ")" << endl;
        }
    }

    vector<int> event(n + 1, -1);
    REP (j, m) {
        event[r[j]] = l[j];
    }

    vector<mint<MOD> > dp(n + 2);
    dp[0] = 1;
    int j = 0;
    mint<MOD> cur = dp[0];
    REP (i, n + 1) {
        for (; j < event[i] + 1; ++ j) {
            cur -= mint<MOD>(2).pow(i - j) * dp[j];
        }
        dp[i + 1] = cur;
        cur = 2 * cur + dp[i + 1];
    }

    if (m < 10) {
        cerr << "ans = " << dp[n + 1] << endl;
    }
    return dp[n + 1];
}

mint<MOD> solve_nonzero(int n, int m, const vector<int>& l, const vector<int>& r, const vector<int>& p) {
    if (m < 10) {
        cerr << "nonzero" << endl;
        cerr << "n = " << n << endl;
        cerr << "m = " << m << endl;
        REP (i, m) {
            cerr << "[" << l[i] << ", " << r[i] << ") " << p[i] << endl;
        }
    }
    return mint<MOD>(2).pow(n - m);
}

mint<MOD> solve(int n, int m, const vector<int>& l, const vector<int>& r, const vector<int>& p) {  // [l, r)
    // list events
    vector<vector<int> > event_l(n + 1);
    vector<int> event_r(n + 1, -1);
    REP (j, m) {
        event_l[l[j]].push_back(j);
        event_r[r[j]] = j;
    }

    // split queries
    int n0 = 0;
    int m0 = 0;
    vector<int> l0, r0;
    int n1 = 0;
    int m1 = 0;
    vector<int> l1, r1, p1;
    vector<int> table(m, -1);
    int cnt = 0;
    REP (i, n + 1) {
        for (int j : event_l[i]) {
            if (p[j] == 0) {
                int k = m0;
                table[j] = k;
                ++ m0;
                l0.push_back(n0);
                r0.push_back(-1);
            } else {
                int k = m1;
                table[j] = k;
                ++ m1;
                l1.push_back(n1);
                r1.push_back(-1);
                p1.push_back(p[j]);
                ++ cnt;
            }
        }
        if (event_r[i] != -1) {
            int j = event_r[i];
            int k = table[j];
            if (p[j] == 0) {
                r0[k] = n0;
            } else {
                r1[k] = n1;
                -- cnt;
            }
        }
        if (i < n) {
            if (cnt) {
                ++ n1;
            } else {
                ++ n0;
            }
        }
    }

    return solve_zero(n0, m0, l0, r0) * solve_nonzero(n1, m1, l1, r1, p1);
}

// generated by online-judge-template-generator v4.6.0 (https://github.com/online-judge-tools/template-generator)
int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    constexpr char endl = '\n';
    int N, M;
    cin >> N >> M;
    vector<int> L(M), R(M), P(M);
    REP (i, M) {
        cin >> L[i] >> R[i] >> P[i];
        -- L[i];
    }
    auto ans = solve(N, M, L, R, P);
    cout << ans << endl;
    return 0;
}
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