#655232 (C++17) No.1502 Many Simple Additions

• 問題: No.1502 Many Simple Additions
• ユーザー: emthrm
• 提出日時: 2021-05-07 22:30:11
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 62 ms / 2,000 ms
• コード長: 9,023 bytes
• コンパイル時間: 2,294 ms
• コンパイル使用メモリ: 207,320 KB
• 最終ジャッジ日時: 2025-01-21 08:26:01
• ジャッジサーバーID （参考情報）: judge5 / judge4

ファイルパターン	結果
sample	AC * 5
other	AC * 39

ソースコード

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <int M>
struct MInt {
  unsigned int val;
  MInt(): val(0) {}
  MInt(long long x) : val(x >= 0 ? x % M : x % M + M) {}
  static constexpr int get_mod() { return M; }
  static void set_mod(int divisor) { assert(divisor == M); }
  static void init(int x = 10000000) { inv(x, true); fact(x); fact_inv(x); }
  static MInt inv(int x, bool init = false) {
    // assert(0 <= x && x < M && std::__gcd(x, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    int prev = inverse.size();
    if (init && x >= prev) {
      // "x!" and "M" must be disjoint.
      inverse.resize(x + 1);
      for (int i = prev; i <= x; ++i) inverse[i] = -inverse[M % i] * (M / i);
    }
    if (x < inverse.size()) return inverse[x];
    unsigned int a = x, b = M; int u = 1, v = 0;
    while (b) {
      unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }
  static MInt fact(int x) {
    static std::vector<MInt> f{1};
    int prev = f.size();
    if (x >= prev) {
      f.resize(x + 1);
      for (int i = prev; i <= x; ++i) f[i] = f[i - 1] * i;
    }
    return f[x];
  }
  static MInt fact_inv(int x) {
    static std::vector<MInt> finv{1};
    int prev = finv.size();
    if (x >= prev) {
      finv.resize(x + 1);
      finv[x] = inv(fact(x).val);
      for (int i = x; i > prev; --i) finv[i - 1] = finv[i] * i;
    }
    return finv[x];
  }
  static MInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    if (n - k > k) k = n - k;
    return fact(n) * fact_inv(k) * fact_inv(n - k);
  }
  static MInt nPk(int n, int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); }
  static MInt nHk(int n, int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); }
  static MInt large_nCk(long long n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    inv(k, true);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) res *= inv(i) * n--;
    return res;
  }
  MInt pow(long long exponent) const {
    MInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  MInt &operator+=(const MInt &x) { if((val += x.val) >= M) val -= M; return *this; }
  MInt &operator-=(const MInt &x) { if((val += M - x.val) >= M) val -= M; return *this; }
  MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % M; return *this; }
  MInt &operator/=(const MInt &x) { return *this *= inv(x.val); }
  bool operator==(const MInt &x) const { return val == x.val; }
  bool operator!=(const MInt &x) const { return val != x.val; }
  bool operator<(const MInt &x) const { return val < x.val; }
  bool operator<=(const MInt &x) const { return val <= x.val; }
  bool operator>(const MInt &x) const { return val > x.val; }
  bool operator>=(const MInt &x) const { return val >= x.val; }
  MInt &operator++() { if (++val == M) val = 0; return *this; }
  MInt operator++(int) { MInt res = *this; ++*this; return res; }
  MInt &operator--() { val = (val == 0 ? M : val) - 1; return *this; }
  MInt operator--(int) { MInt res = *this; --*this; return res; }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(val ? M - val : 0); }
  MInt operator+(const MInt &x) const { return MInt(*this) += x; }
  MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt &x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt &x) const { return MInt(*this) /= x; }
  friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; }
  friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
};
namespace std { template <int M> MInt<M> abs(const MInt<M> &x) { return x; } }
using ModInt = MInt<MOD>;

template <typename CostType>
struct Edge {
  int src, dst; CostType cost;
  Edge(int src, int dst, CostType cost = 0) : src(src), dst(dst), cost(cost) {}
  inline bool operator<(const Edge &x) const {
    return cost != x.cost ? cost < x.cost : dst != x.dst ? dst < x.dst : src < x.src;
  }
  inline bool operator<=(const Edge &x) const { return !(x < *this); }
  inline bool operator>(const Edge &x) const { return x < *this; }
  inline bool operator>=(const Edge &x) const { return !(*this < x); }
};

int main() {
  int n, m, k; cin >> n >> m >> k;
  vector<vector<Edge<int>>> graph(n);
  while (m--) {
    int x, y, z; cin >> x >> y >> z; --x; --y;
    graph[x].emplace_back(x, y, z);
    graph[y].emplace_back(y, x, z);
  }
  ModInt ans1 = 1, ans2 = 0;
  vector<int> visited(n, 0);
  vector<bool> visited2(n, false);
  vector<ll> sum(n, 0);
  REP(i, n) {
    if (visited[i] != 0) continue;
    auto f = [&](auto &&f, int par, int ver) -> bool {
      for (const Edge<int> &e : graph[ver]) {
        if (e.dst == par) continue;
        if (visited[ver] * visited[e.dst] == 1) {
          ll r = e.cost - sum[ver] - sum[e.dst];
          if (visited[ver] == -1) r = -r;
          if (r % 2 == 1 || r / 2 <= 0 || r / 2 > k) {
            cout << 0 << '\n';
            exit(0);
          }
          sum[i] = r / 2;
          return true;
        } else if (visited[ver] * visited[e.dst] == -1) {
          if (sum[ver] + sum[e.dst] != e.cost) {
            cout << 0 << '\n';
            exit(0);
          }
        } else {
          visited[e.dst] = -visited[ver];
          sum[e.dst] = e.cost - sum[ver];
          if (f(f, ver, e.dst)) return true;
        }
      }
      return false;
    };
    visited[i] = 1;
    if (f(f, -1, i)) {
      auto g = [&](auto &&g, int par, int ver) -> bool {
        bool exist_k = false;
        for (const Edge<int> &e : graph[ver]) {
          if (e.dst == par) continue;
          if (visited2[e.dst]) {
            if (sum[ver] + sum[e.dst] != e.cost) {
              cout << 0 << '\n';
              exit(0);
            }
          } else {
            sum[e.dst] = e.cost - sum[ver];
            if (sum[e.dst] <= 0 || k < sum[e.dst]) {
              cout << 0 << '\n';
              exit(0);
            }
            visited[e.dst] = 1;
            visited2[e.dst] = true;
            exist_k |= sum[e.dst] == k || g(g, ver, e.dst);
          }
        }
        return exist_k;
      };
      visited2[i] = true;
      if (g(g, -1, i) || sum[i] == k) {
        ans2 += ans1;
        ans1 = 0;
      }
    } else {
      int lb = 1, ub = k;
      vector<int> check;
      auto g = [&](auto &&g, int par, int ver) -> void {
        for (const Edge<int> &e : graph[ver]) {
          if (e.dst != par && !visited2[e.dst]) {
            if (visited[e.dst] == 1) {
              chmax(lb, 1 - sum[e.dst]);
              chmin(ub, k - sum[e.dst]);
            } else {
              chmax(lb, sum[e.dst] - k);
              chmin(ub, sum[e.dst] - 1);
            }
            visited2[e.dst] = true;
            check.emplace_back(e.dst);
            g(g, ver, e.dst);
          }
        }
      };
      visited2[i] = true;
      g(g, -1, i);
      if (lb > ub) {
        cout << 0 << '\n';
        return 0;
      }
      bool lb_has_k = lb == k, ub_has_k = ub == k;
      for (int ver : check) {
        if (visited[ver] == 1) {
          assert(1 <= sum[ver] + lb && sum[ver] + lb <= k);
          lb_has_k |= sum[ver] + lb == k;
          assert(1 <= sum[ver] + ub && sum[ver] + ub <= k);
          ub_has_k |= sum[ver] + ub == k;
        } else {
          assert(1 <= sum[ver] - lb && sum[ver] - lb <= k);
          lb_has_k |= sum[ver] - lb == k;
          assert(1 <= sum[ver] - ub && sum[ver] - ub <= k);
          ub_has_k |= sum[ver] - ub == k;
        }
      }
      if (lb < ub) {
        ModInt nx_ans1 = 0, nx_ans2 = ans2 * (ub - lb + 1);
        (lb_has_k ? nx_ans2 : nx_ans1) += ans1;
        (ub_has_k ? nx_ans2 : nx_ans1) += ans1;
        nx_ans1 += ans1 * (ub - lb - 1);
        swap(ans1, nx_ans1);
        swap(ans2, nx_ans2);
      } else {
        assert(lb_has_k == ub_has_k);
        if (lb_has_k) {
          ans2 += ans1;
          ans1 = 0;
        }
      }
    }
  }
  cout << ans2 << '\n';
  return 0;
}