#655434 (C++17) No.1502 Many Simple Additions

• 問題: No.1502 Many Simple Additions
• ユーザー: NyaanNyaan
• 提出日時: 2021-05-08 00:18:37
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 105 ms / 2,000 ms
• コード長: 13,633 bytes
• コンパイル時間: 3,231 ms
• コンパイル使用メモリ: 275,348 KB
• 実行使用メモリ: 32,896 KB
• 最終ジャッジ日時: 2024-09-15 18:23:53
• 合計ジャッジ時間: 5,512 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

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; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	2 ms; 5,376 KB
testcase_22	AC	2 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB
testcase_25	AC	2 ms; 5,376 KB
testcase_26	AC	2 ms; 5,376 KB
testcase_27	AC	66 ms; 27,136 KB
testcase_28	AC	67 ms; 27,264 KB
testcase_29	AC	55 ms; 32,896 KB
testcase_30	AC	105 ms; 30,748 KB
testcase_31	AC	101 ms; 30,632 KB
testcase_32	AC	100 ms; 30,500 KB
testcase_33	AC	47 ms; 11,420 KB
testcase_34	AC	50 ms; 12,528 KB
testcase_35	AC	48 ms; 11,708 KB
testcase_36	AC	29 ms; 5,632 KB
testcase_37	AC	30 ms; 5,632 KB
testcase_38	AC	27 ms; 5,760 KB
testcase_39	AC	20 ms; 5,376 KB
testcase_40	AC	9 ms; 5,376 KB
testcase_41	AC	20 ms; 11,648 KB
testcase_42	AC	30 ms; 7,296 KB
testcase_43	AC	2 ms; 5,376 KB

ソースコード

/**
 *  date : 2021-05-08 00:18:30
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  T &x() { return first; }
  const T &x() const { return first; }
  U &y() { return second; }
  const U &y() const { return second; }

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

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

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//
using namespace Nyaan;


template <class T>
struct UnionFindWithPotential {
  vector<int> dat;
  vector<T> pot;

  UnionFindWithPotential(int N) : dat(N, -1), pot(N, T()) {}

  int root(int x) {
    if (dat[x] < 0) return x;
    int r = root(dat[x]);
    pot[x] += pot[dat[x]];
    return dat[x] = r;
  }

  // return P(x) - P(root(x))
  T potential(int x) {
    root(x);
    return pot[x];
  }

  bool same(int x, int y) { return root(x) == root(y); }

  // return P(x) - P(y)
  T diff(int x, int y) {
    return potential(x) - potential(y);
  }

  // s.t. P(x) = P(y) + p
  // return Satisfiablility
  bool merge(int x, int y, T p) {
    p += potential(y) - potential(x);
    x = root(x), y = root(y);
    if (x == y) return p == T();
    if (dat[x] < dat[y]) swap(x, y), p = -p;
    dat[y] += dat[x];
    dat[x] = y;
    pot[x] = p;
    return true;
  }

  // return size of CC including x
  int size(int x) { return -dat[root(x)]; }
};

void Nyaan::solve() {
  inl(N, M, K);

  vl X(M), Y(M), Z(M);
  in3(X, Y, Z);
  each(x, X)-- x;
  each(x, Y)-- x;

  // A_x - (-A_y) = z
  // max(A) = K

  UnionFindWithPotential<ll> uf(2 * N);

  rep(i, M) {
    ll x = X[i], y = Y[i], z = Z[i];
    if (uf.same(x, y + N)) {
      if (uf.diff(x, y + N) != z) die(0);
    } else {
      uf.merge(x, y + N, z);
    }
    if (uf.same(y, x + N)) {
      if (uf.diff(y, x + N) != z) die(0);
    } else {
      uf.merge(y, x + N, z);
    }
  }

  // p(x)-p(root(x))の最大,最小を求める
  vvl diff1(2 * N);
  vvl diff2(2 * N);
  vvl group(2 * N);
  rep(i, 2 * N) {
    group[uf.root(i)].push_back(i);
    if (i < N) {
      diff1[uf.root(i)].push_back(uf.potential(i));
    } else {
      diff2[uf.root(i)].push_back(uf.potential(i));
    }
  }

  ll ans1 = 1, ans2 = 1;
  vi vis(2 * N);

  rep(i, 2 * N) trc(i, uf.potential(i));

  rep(i, 2 * N) {
    if (vis[i % N]) continue;
    if (group[i].empty()) continue;
    unordered_set<int> st;
    each(x, group[i]) vis[x % N] = 1, st.insert(x % N);
    auto& d1 = diff1[i];
    auto& d2 = diff2[i];
    sort(all(d1));
    sort(all(d2));

    trc(d1);
    trc(d2);

    ll L1 = -infLL, R1 = infLL;
    ll L2 = -infLL, R2 = infLL;
    ll al = 0;

    // 片方
    if (!d1.empty()) {
      // 1 <= x + d1[0] <= x + d1.back() <= K
      // 1 - d1[0] <= x <= K - d1.back()
      L1 = 1 - d1[0];
      R1 = K - d1.back();
      if (L1 > R1) die(0);
    }
    if (!d2.empty()) {
      // 1 <= -(x + d2.back()) <= -(x + d2[0]) <= K
      // -K <= x + d2[0] <= x + d2.back() <= -1
      L2 = -K - d2[0];
      R2 = -1 - d2.back();
      if (L2 > R2) die(0);
    }
    trc(L1, R1);
    trc(L2, R2);
    {
      //
      L1 = max(L1, L2);
      R1 = min(R1, R2);
      if (L1 > R1) die(0);
      al = R1 + 1 - L1;
    }

    if (sz(st) == sz(d1) and sz(d1) == sz(d2)) {
      unordered_set<ll> st2;
      each(x, st) { st2.insert(uf.potential(x) + uf.potential(x + N)); }
      if (st2.size() != 1u) die(0);
      ll x = *st2.begin();
      if (x % 2 != 0) die(0);
      x /= 2;
      x = -x;
      trc("st", x);
      if (!(L1 <= x and x <= R1)) die(0);
      L1 = R1 = x;
      al = 1;
    }

    ll cur = 0;
    ll x1 = infLL, x2 = infLL;
    if (!d1.empty()) {
      x1 = K - d1.back();
      if (L1 <= x1 and x1 <= R1) cur++;
    }
    if (!d2.empty()) {
      x2 = -K - d2[0];
      if (x2 != x1 and L1 <= x2 and x2 <= R1) cur++;
    }

    ans1 = ans1 * al % (TEN(9) + 7);
    ans2 = ans2 * (al - cur) % (TEN(9) + 7);
  }
  ans1 -= ans2;
  ans1 %= TEN(9) + 7;
  ans1 += TEN(9) + 7;
  ans1 %= TEN(9) + 7;
  out(ans1);
}