Problem p01919 (C++) — buggy submission, verdict: Time Limit Exceeded

// need
#include <algorithm>
#include <iostream>

// data structure
#include <bitset>
// #include <list>
#include <array>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <tuple>
// #include <unordered_map>
#include <complex>
#include <unordered_set>
// #include <deque>
#include <valarray>

// stream
// #include <istream>
// #include <sstream>
// #include <ostream>
// #include <fstream>

// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
// #include <typeinfo>
#include <chrono>
#include <numeric>
#include <random>

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int i = 0; i < n; ++i) {                                                \\
    MACRO_VEC_ROW_Scan(i, __VA_ARGS__);                                        \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &r : c)                                                            \\
    for (auto &i : r)                                                          \\
      std::cin >> i;

// output
#define OUT(d) std::cout << d;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << d;
#define SOUT(n, c, d) std::cout << std::setw(n) << std::setfill(c) << d;
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(i, n) std::cout << (i + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(d)                                                                \\
  { std::cerr << #d << "\\t:" << d << "\\n"; }
#define SHOWVECTOR(v)                                                          \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWVECTOR2(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << yyy << " ";                                               \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWQUEUE(a)                                                           \\
  {                                                                            \\
    auto tmp(a);                                                               \\
    std::cerr << #a << "\\t:";                                                  \\
    while (!tmp.empty()) {                                                     \\
      std::cerr << tmp.front() << " ";                                         \\
      tmp.pop();                                                               \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }

// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define RREP(i, n) for (int i = int(n) - 1; i >= 0; --i)
#define FORLL(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define RFORLL(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define REPLL(i, n) for (ll i = 0; i < ll(n); ++i)
#define RREPLL(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define IN(a, x, b) (a <= x && x < b)
template <typename T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
#define EXCEPTION(msg)                                                         \\
  throw std::string("Exception : " msg " [ in ") + __func__ + " : " +          \\
      std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg)                                                         \\
  try {                                                                        \\
    if (cond)                                                                  \\
      EXCEPTION(msg);                                                          \\
  } catch (std::string s) {                                                    \\
    std::cerr << s << std::endl;                                               \\
  }
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\\n";
}

// test
template <class T> std::vector<std::vector<T>> VV(int n) {
  return std::vector<std::vector<T>>(n);
}
template <class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

// type/const

#define int ll
using ll = long long;
using ull = unsigned long long;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                         // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

signed main() {
  INIT;
  VAR(int, n, m);
  VEC_ROW(int, m, x, y, t);
  VAR(int, v0, a, b, c);

  struct Edge {
    int to, cost;
    Edge() {}
    Edge(int to, int cost) : to(to), cost(cost) {}
    bool operator<(const Edge &r) const { return cost < r.cost; }
  };
  std::vector<std::vector<Edge>> g(n + n);
  // ????????????
  REP(i, m) {
    --x[i];
    --y[i];
    g[x[i]].emplace_back(y[i], t[i]);
    g[y[i]].emplace_back(x[i], t[i]);
    int xx = x[i] + n;
    int yy = y[i] + n;
    if (xx == n - 1 + n)
      xx = n - 1;
    if (yy == n - 1 + n)
      yy = n - 1;
    g[xx].emplace_back(yy, t[i]);
    g[yy].emplace_back(xx, t[i]);
  }
  //
  std::map<PAIR, int> dist;
  std::function<void(PAIR)> Dijkstra = [&](PAIR s) {
    using P = std::pair<int, PAIR>;
    std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
    dist.clear();
    dist[s] = 0;
    pq.push(P(0, s));
    while (!pq.empty()) {
      P p = pq.top();
      pq.pop();
      PAIR v = p.second;
      if (dist[v] < p.first)
        continue;
      for (int i = 0; i < g[v.first].size(); ++i) {
        Edge e = g[v.first][i];
        int vne = (a * v.second + b) % c;
        PAIR to = PAIR(e.to, vne);
        if (dist.find(to) == dist.end())
          dist[to] = INFLL;
        int cost = v.second * e.cost;
        if (dist[to] > dist[v] + cost) {
          dist[to] = dist[v] + cost;
          pq.push(P(dist[to], to));
        }
      }
    }
  };
  Dijkstra(PAIR(0, v0));
  int ans = INFLL;
  REP(i, c) {
    if (dist.find(PAIR(n, i)) == dist.end())
      continue;
    CHMIN(ans, dist[PAIR(n, i)]);
  }
  OUT(ans) BR;
  return 0;
}

Error: TLE

Fixed submission:

// need
#include <algorithm>
#include <iostream>

// data structure
#include <bitset>
// #include <list>
#include <array>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <tuple>
// #include <unordered_map>
#include <complex>
#include <unordered_set>
// #include <deque>
#include <valarray>

// stream
// #include <istream>
// #include <sstream>
// #include <ostream>
// #include <fstream>

// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
// #include <typeinfo>
#include <chrono>
#include <numeric>
#include <random>

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int i = 0; i < n; ++i) {                                                \\
    MACRO_VEC_ROW_Scan(i, __VA_ARGS__);                                        \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &r : c)                                                            \\
    for (auto &i : r)                                                          \\
      std::cin >> i;

// output
#define OUT(d) std::cout << d;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << d;
#define SOUT(n, c, d) std::cout << std::setw(n) << std::setfill(c) << d;
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(i, n) std::cout << (i + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(d)                                                                \\
  { std::cerr << #d << "\\t:" << d << "\\n"; }
#define SHOWVECTOR(v)                                                          \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWVECTOR2(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << yyy << " ";                                               \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWQUEUE(a)                                                           \\
  {                                                                            \\
    auto tmp(a);                                                               \\
    std::cerr << #a << "\\t:";                                                  \\
    while (!tmp.empty()) {                                                     \\
      std::cerr << tmp.front() << " ";                                         \\
      tmp.pop();                                                               \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }

// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define RREP(i, n) for (int i = int(n) - 1; i >= 0; --i)
#define FORLL(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define RFORLL(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define REPLL(i, n) for (ll i = 0; i < ll(n); ++i)
#define RREPLL(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define IN(a, x, b) (a <= x && x < b)
template <typename T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
#define EXCEPTION(msg)                                                         \\
  throw std::string("Exception : " msg " [ in ") + __func__ + " : " +          \\
      std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg)                                                         \\
  try {                                                                        \\
    if (cond)                                                                  \\
      EXCEPTION(msg);                                                          \\
  } catch (std::string s) {                                                    \\
    std::cerr << s << std::endl;                                               \\
  }
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\\n";
}

// test
template <class T> std::vector<std::vector<T>> VV(int n) {
  return std::vector<std::vector<T>>(n);
}
template <class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

// type/const

#define int ll
using ll = long long;
using ull = unsigned long long;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                         // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

signed main() {
  INIT;
  VAR(int, n, m);
  VEC_ROW(int, m, x, y, t);
  VAR(int, v0, a, b, c);

  struct Edge {
    int to, cost;
    Edge() {}
    Edge(int to, int cost) : to(to), cost(cost) {}
    bool operator<(const Edge &r) const { return cost < r.cost; }
  };
  std::vector<std::vector<Edge>> g(n);
  // ????????????
  REP(i, m) {
    --x[i];
    --y[i];
    g[x[i]].emplace_back(y[i], t[i]);
    g[y[i]].emplace_back(x[i], t[i]);
  }
  //
  std::map<PAIR, int> dist;
  std::function<void(PAIR)> Dijkstra = [&](PAIR s) {
    using P = std::pair<int, PAIR>;
    std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
    dist.clear();
    dist[s] = 0;
    pq.push(P(0, s));
    while (!pq.empty()) {
      P p = pq.top();
      pq.pop();
      PAIR v = p.second;
      if (dist[v] < p.first)
        continue;
      for (int i = 0; i < g[v.first].size(); ++i) {
        Edge e = g[v.first][i];
        int vne = (a * v.second + b) % c;
        PAIR to = PAIR(e.to, vne);
        if (dist.find(to) == dist.end())
          dist[to] = INFLL;
        int cost = v.second * e.cost;
        if (dist[to] > dist[v] + cost) {
          dist[to] = dist[v] + cost;
          pq.push(P(dist[to], to));
        }
      }
    }
  };
  Dijkstra(PAIR(0, v0));
  std::vector<int> diN(c, INFLL);
  REP(i, c) {
    if (dist.find(PAIR(n - 1, i)) == dist.end())
      continue;
    diN[i] = dist[PAIR(n - 1, i)];
  }
  int ans = INFLL;
  REP(i, c) {
    if (diN[i] == INFLL)
      continue;
    Dijkstra(PAIR(n - 1, i));
    REP(j, c) {
      if (dist.find(PAIR(0, j)) == dist.end())
        continue;
      CHMIN(ans, diN[i] + dist[PAIR(0, j)]);
    }
  }
  OUT(ans) BR;
  return 0;
}