結果

問題 No.160 最短経路のうち辞書順最小
コンテスト
ユーザー keijak
提出日時 2021-09-06 20:38:25
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 7 ms / 5,000 ms
コード長 4,748 bytes
コンパイル時間 2,287 ms
コンパイル使用メモリ 205,952 KB
最終ジャッジ日時 2025-01-24 08:30:08
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 26
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>
#define REP_(i, a_, b_, a, b, ...) \
  for (int i = (a), END_##i = (b); i < END_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using i64 = long long;

template<typename T, typename U>
inline bool chmax(T &a, U b) {
  return a < b and ((a = std::move(b)), true);
}
template<typename T, typename U>
inline bool chmin(T &a, U b) {
  return a > b and ((a = std::move(b)), true);
}
template<typename T>
inline int ssize(const T &a) {
  return (int) std::size(a);
}

template<typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &a) {
  for (auto &x: a) is >> x;
  return is;
}
template<typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &a) {
  return os << "(" << a.first << ", " << a.second << ")";
}
template<typename Container>
std::ostream &print_seq(const Container &a, std::string_view sep = " ",
                        std::string_view ends = "\n",
                        std::ostream &os = std::cout) {
  auto b = std::begin(a), e = std::end(a);
  for (auto it = std::begin(a); it != e; ++it) {
    if (it != b) os << sep;
    os << *it;
  }
  return os << ends;
}
template<typename T, typename = void>
struct is_iterable : std::false_type {};
template<typename T>
struct is_iterable<T, std::void_t<decltype(std::begin(std::declval<T>())),
                                  decltype(std::end(std::declval<T>()))>>
    : std::true_type {
};

template<typename T, typename = std::enable_if_t<
    is_iterable<T>::value &&
        !std::is_same<T, std::string_view>::value &&
        !std::is_same<T, std::string>::value>>
std::ostream &operator<<(std::ostream &os, const T &a) {
  return print_seq(a, ", ", "", (os << "{")) << "}";
}

void print() { std::cout << "\n"; }
template<class T>
void print(const T &x) {
  std::cout << x << "\n";
}
template<typename Head, typename... Tail>
void print(const Head &head, Tail... tail) {
  std::cout << head << " ";
  print(tail...);
}

struct Input {
  template<typename T>
  operator T() const {
    T x;
    std::cin >> x;
    return x;
  }
} in;

#ifdef MY_DEBUG
#include "debug_dump.hpp"
#else
#define DUMP(...)
#endif

using namespace std;

template<int sign = 1>
struct Infinity {
  template<typename T>
  constexpr operator T() const {
    static_assert(sign == 1 or not std::is_unsigned_v<T>,
                  "must be positive in an unsigned type");
    if constexpr (std::numeric_limits<T>::has_infinity) {
      return T(sign) * std::numeric_limits<T>::infinity();
    } else {
      return T(sign) * (std::numeric_limits<T>::max() / T(2));
    }
  }
  constexpr Infinity<sign * -1> operator-() const { return {}; }
  template<typename T>
  friend constexpr bool operator==(const T &x, const Infinity &y) {
    return x == T(y);
  }
  template<typename T>
  friend constexpr bool operator!=(const T &x, const Infinity &y) {
    return x != T(y);
  }
};
constexpr Infinity<> kBig;

template<class T>
using MinHeap = priority_queue<T, vector<T>, greater<T>>;

struct Edge {
  i64 cost;
  int to;
};

struct State {
  i64 cost;
  int node;
};
bool operator>(const State &x, const State &y) { return x.cost > y.cost; }

// Returns min distance from the start node to each node (if exists).
auto search_shortest_path(const vector<vector<Edge>> &g, int start) {
  const int n = g.size();
  auto mincost = vector(n, (i64) kBig);
  MinHeap<State> que;
  auto push = [&](i64 cost, int node) -> bool {
    if (chmin(mincost[node], cost)) {
      que.push(State{cost, node});
      return true;
    }
    return false;
  };
  assert(push(0LL, start));

  while (not que.empty()) {
    State cur = que.top();
    que.pop();
    if (cur.cost != mincost[cur.node]) continue;
    for (const auto &e: g[cur.node]) {
      auto new_cost = cur.cost + e.cost;
      push(new_cost, e.to);
    }
  }
  return mincost;
}

auto solve() {
  int n = in, m = in, S = in, G = in;
  vector<vector<Edge>> g(n);
  REP(i, m) {
    int a = in, b = in, c = in;
    g[a].push_back({c, b});
    g[b].push_back({c, a});
  }
  auto dist = search_shortest_path(g, G);
  int mind = dist[S];
  DUMP(dist, mind);
  vector<int> path;
  int cur = S;
  path.push_back(cur);
  while (cur != G) {
    int nex = kBig;
    for (const auto &e: g[cur]) {
      if (e.to >= nex) continue;
      if (mind - e.cost == dist[e.to]) {
        nex = e.to;
      }
    }
    assert(nex != kBig);
    path.push_back(nex);
    cur = nex;
    mind = dist[cur];
  }
  return path;
}

auto main() -> int {
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  cout << std::fixed << std::setprecision(18);
  const int t = 1;
  REP(test_case, t) {
    auto ans = solve();
    print_seq(ans);
  }
}
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