結果

問題 No.1502 Many Simple Additions
ユーザー KoDKoD
提出日時 2021-05-07 21:41:35
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 107 ms / 2,000 ms
コード長 7,956 bytes
コンパイル時間 2,484 ms
コンパイル使用メモリ 214,888 KB
実行使用メモリ 21,380 KB
最終ジャッジ日時 2023-10-13 22:26:25
合計ジャッジ時間 5,371 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge13
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 ms
4,348 KB
testcase_01 AC 2 ms
4,352 KB
testcase_02 AC 2 ms
4,352 KB
testcase_03 AC 2 ms
4,352 KB
testcase_04 AC 1 ms
4,348 KB
testcase_05 AC 2 ms
4,348 KB
testcase_06 AC 2 ms
4,348 KB
testcase_07 AC 1 ms
4,348 KB
testcase_08 AC 1 ms
4,348 KB
testcase_09 AC 2 ms
4,352 KB
testcase_10 AC 2 ms
4,348 KB
testcase_11 AC 2 ms
4,348 KB
testcase_12 AC 2 ms
4,348 KB
testcase_13 AC 2 ms
4,352 KB
testcase_14 AC 1 ms
4,348 KB
testcase_15 AC 1 ms
4,352 KB
testcase_16 AC 1 ms
4,352 KB
testcase_17 AC 1 ms
4,348 KB
testcase_18 AC 1 ms
4,348 KB
testcase_19 AC 2 ms
4,348 KB
testcase_20 AC 1 ms
4,352 KB
testcase_21 AC 2 ms
4,352 KB
testcase_22 AC 2 ms
4,352 KB
testcase_23 AC 2 ms
4,352 KB
testcase_24 AC 1 ms
4,352 KB
testcase_25 AC 1 ms
4,348 KB
testcase_26 AC 1 ms
4,348 KB
testcase_27 AC 49 ms
12,120 KB
testcase_28 AC 49 ms
12,596 KB
testcase_29 AC 8 ms
7,192 KB
testcase_30 AC 107 ms
21,380 KB
testcase_31 AC 105 ms
21,288 KB
testcase_32 AC 106 ms
21,116 KB
testcase_33 AC 70 ms
17,508 KB
testcase_34 AC 74 ms
18,080 KB
testcase_35 AC 74 ms
17,740 KB
testcase_36 AC 40 ms
13,748 KB
testcase_37 AC 42 ms
13,616 KB
testcase_38 AC 52 ms
15,956 KB
testcase_39 AC 28 ms
10,704 KB
testcase_40 AC 17 ms
6,088 KB
testcase_41 AC 4 ms
4,536 KB
testcase_42 AC 80 ms
17,856 KB
testcase_43 AC 2 ms
4,348 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 i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

class rep {
    struct Iter {
        usize itr;
        constexpr Iter(const usize pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { ++itr; }
        constexpr bool operator!=(const Iter& other) const noexcept {
            return itr != other.itr;
        }
        constexpr usize operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr rep(const usize first, const usize last) noexcept
        : first(first), last(std::max(first, last)) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

template <class F> struct RecLambda : private F {
    template <class G>
    explicit constexpr RecLambda(G&& g) : F(std::forward<G>(g)) {}
    template <class... Args>
    constexpr decltype(auto) operator()(Args&&... args) const {
        return F::operator()(*this, std::forward<Args>(args)...);
    }
};

template <class G> explicit RecLambda(G&&) -> RecLambda<std::decay_t<G>>;

template <class T> bool setmin(T& lhs, const T& rhs) {
    if (lhs > rhs) {
        lhs = rhs;
        return true;
    }
    return false;
}

template <class T> bool setmax(T& lhs, const T& rhs) {
    if (lhs < rhs) {
        lhs = rhs;
        return true;
    }
    return false;
}

template <class T> constexpr T totient(T x) {
    T ret = x;
    for (T i = 2; i * i <= x; ++i) {
        if (x % i == 0) {
            ret /= i;
            ret *= i - 1;
            while (x % i == 0) x /= i;
        }
    }
    if (x > 1) {
        ret /= x;
        ret *= x - 1;
    }
    return ret;
}

template <class T> constexpr T rem_euclid(T value, const T& mod) {
    return (value %= mod) >= 0 ? value : value + mod;
}

template <u32 MOD,
          std::enable_if_t<((u32)1 <= MOD and MOD <= ((u32)1 << 31))>* =
              nullptr>
class StaticModint {
    using Mint = StaticModint;

    static inline constexpr u32 PHI = totient(MOD);
    u32 v;

  public:
    static constexpr u32 mod() noexcept { return MOD; }

    template <class T,
              std::enable_if_t<std::is_signed_v<T> and std::is_integral_v<T>>* =
                  nullptr>
    static constexpr T normalize(const T x) noexcept {
        return rem_euclid<std::common_type_t<T, i64>>(x, MOD);
    }
    template <class T,
              std::enable_if_t<std::is_unsigned_v<T> and
                               std::is_integral_v<T>>* = nullptr>
    static constexpr T normalize(const T x) noexcept {
        return x % MOD;
    }

    constexpr StaticModint() noexcept : v(0) {}
    template <class T>
    constexpr StaticModint(const T x) noexcept : v(normalize(x)) {}
    template <class T> static constexpr Mint raw(const T x) noexcept {
        Mint ret;
        ret.v = x;
        return ret;
    }

    constexpr u32 get() const noexcept { return v; }
    constexpr Mint neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
    constexpr Mint inv() const noexcept { return pow(PHI - 1); }
    constexpr Mint pow(u64 exp) const noexcept {
        Mint ret(1), mult(*this);
        for (; exp > 0; exp >>= 1) {
            if (exp & 1) ret *= mult;
            mult *= mult;
        }
        return ret;
    }

    constexpr Mint operator-() const noexcept { return neg(); }
    constexpr Mint operator~() const noexcept { return inv(); }

    constexpr Mint operator+(const Mint& rhs) const noexcept {
        return Mint(*this) += rhs;
    }
    constexpr Mint& operator+=(const Mint& rhs) noexcept {
        if ((v += rhs.v) >= MOD) v -= MOD;
        return *this;
    }

    constexpr Mint operator-(const Mint& rhs) const noexcept {
        return Mint(*this) -= rhs;
    }
    constexpr Mint& operator-=(const Mint& rhs) noexcept {
        if (v < rhs.v) v += MOD;
        v -= rhs.v;
        return *this;
    }

    constexpr Mint operator*(const Mint& rhs) const noexcept {
        return Mint(*this) *= rhs;
    }
    constexpr Mint& operator*=(const Mint& rhs) noexcept {
        v = (u64)v * rhs.v % MOD;
        return *this;
    }

    constexpr Mint operator/(const Mint& rhs) const noexcept {
        return Mint(*this) /= rhs;
    }
    constexpr Mint& operator/=(const Mint& rhs) noexcept {
        return *this *= rhs.inv();
    }

    constexpr bool operator==(const Mint& rhs) const noexcept {
        return v == rhs.v;
    }
    constexpr bool operator!=(const Mint& rhs) const noexcept {
        return v != rhs.v;
    }
    friend std::ostream& operator<<(std::ostream& stream, const Mint& rhs) {
        return stream << rhs.v;
    }
};

using Modint1000000007 = StaticModint<1000000007>;
using Modint998244353 = StaticModint<998244353>;

template <class T> using Vec = std::vector<T>;

using Fp = Modint1000000007;

void D_main() {
    usize N, M;
    i64 K;
    std::cin >> N >> M >> K;
    Vec<Vec<std::pair<usize, i64>>> graph(N);
    for (const auto i : rep(0, M)) {
        usize x, y;
        i64 z;
        std::cin >> x >> y >> z;
        x -= 1;
        y -= 1;
        graph[x].emplace_back(y, z);
        graph[y].emplace_back(x, z);
    }
    const auto solve = [&](const i64 Max) {
        Vec<i64> A(N), B(N);  // A[i] * x + B[i]
        Vec<usize> seen;
        Vec<std::tuple<usize, usize, i64>> edge;
        seen.reserve(N);
        edge.reserve(M);
        const auto dfs = RecLambda([&](auto&& dfs, const usize u) -> void {
            seen.push_back(u);
            for (const auto [v, s] : graph[u]) {
                edge.emplace_back(u, v, s);
                if (A[v] == 0) {
                    A[v] = -A[u];
                    B[v] = s - B[u];
                    dfs(v);
                }
            }
        });
        Fp ret = 1;
        for (const auto src : rep(0, N)) {
            if (A[src] != 0) {
                continue;
            }
            A[src] = 1;
            dfs(src);
            ret *= [&] {
                std::optional<i64> val;
                for (const auto [u, v, s] : edge) {
                    if (A[u] == A[v]) {
                        if ((s - B[u] - B[v]) % 2 != 0) {
                            return Fp(0);
                        }
                        val = (s - B[u] - B[v]) / (A[u] + A[v]);
                    } else {
                        if (B[u] + B[v] != s) {
                            return Fp(0);
                        }
                    }
                }
                if (val) {
                    const auto x = val.value();
                    for (const auto u : seen) {
                        const auto y = A[u] * x + B[u];
                        if (!(1 <= y and y <= Max)) {
                            return Fp(0);
                        }
                    }
                    for (const auto [u, v, s] : edge) {
                        if (A[u] * x + B[u] + A[v] * x + B[v] != s) {
                            return Fp(0);
                        }
                    }
                    return Fp(1);
                }
                i64 low = 1, high = Max;
                for (const auto u : seen) {
                    if (A[u] == 1) {
                        setmin(high, Max - B[u]);
                        setmax(low, 1 - B[u]);
                    } else {
                        setmin(high, -(1 - B[u]));
                        setmax(low, -(Max - B[u]));
                    }
                }
                return Fp(std::max<i64>(high - low + 1, 0));
            }();
            seen.clear();
            edge.clear();
        }
        return ret;
    };
    std::cout << solve(K) - solve(K - 1) << '\n';
}

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    D_main();
    return 0;
}
0