#634779 (C++17) No.1442 I-wate Shortest Path Problem

• 問題: No.1442 I-wate Shortest Path Problem
• ユーザー: NyaanNyaan
• 提出日時: 2021-03-26 22:50:41
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 398 ms / 3,000 ms
• コード長: 18,876 bytes
• コンパイル時間: 3,271 ms
• コンパイル使用メモリ: 298,096 KB
• 実行使用メモリ: 125,440 KB
• 最終ジャッジ日時: 2024-05-06 16:43:58
• 合計ジャッジ時間: 9,911 ms
• ジャッジサーバーID （参考情報）: judge5 / judge4

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	8 ms; 5,376 KB
testcase_03	AC	44 ms; 5,376 KB
testcase_04	AC	6 ms; 5,376 KB
testcase_05	AC	4 ms; 5,376 KB
testcase_06	AC	42 ms; 5,376 KB
testcase_07	AC	5 ms; 5,376 KB
testcase_08	AC	33 ms; 5,376 KB
testcase_09	AC	12 ms; 5,376 KB
testcase_10	AC	51 ms; 5,376 KB
testcase_11	AC	39 ms; 5,376 KB
testcase_12	AC	274 ms; 31,616 KB
testcase_13	AC	109 ms; 13,568 KB
testcase_14	AC	248 ms; 27,868 KB
testcase_15	AC	238 ms; 27,240 KB
testcase_16	AC	250 ms; 30,312 KB
testcase_17	AC	376 ms; 40,064 KB
testcase_18	AC	360 ms; 40,192 KB
testcase_19	AC	286 ms; 31,872 KB
testcase_20	AC	343 ms; 40,064 KB
testcase_21	AC	364 ms; 40,192 KB
testcase_22	AC	106 ms; 24,832 KB
testcase_23	AC	398 ms; 125,440 KB
testcase_24	AC	78 ms; 13,324 KB
testcase_25	AC	260 ms; 48,768 KB
testcase_26	AC	161 ms; 33,196 KB

ソースコード

/**
 *  date : 2021-03-26 22:50:33
 */

#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 <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <exception>
#include <forward_list>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ratio>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <system_error>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <valarray>
#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, size_t N>
void mem(T (&a)[N], int c) {
  memset(a, c, sizeof(T) * N);
}

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>
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<T> reord(const vector<T> &v, const vector<T> &ord) {
  int N = v.size();
  vector<T> ret(N);
  for (int i = 0; i < N; i++) ret[i] = v[ord[i]];
  return ret;
};

template <typename T = int>
vector<T> mkiota(int N) {
  vector<T> ret(N);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
vector<int> mkinv(vector<T> &v, int max_val = -1) {
  if (max_val < (int)v.size()) max_val = v.size() - 1;
  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);
}

__attribute__((target("bmi"))) inline int lsb(const u64 &a) {
  return _tzcnt_u64(a);
}
__attribute__((target("bmi"))) inline int ctz(const u64 &a) {
  return _tzcnt_u64(a);
}

__attribute__((target("lzcnt"))) inline int msb(const u64 &a) {
  return 63 - _lzcnt_u64(a);
}
__attribute__((target("lzcnt"))) inline int clz64(const u64 &a) {
  return _lzcnt_u64(a);
}

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) {
  a ^= (gbit(a, i) == b ? 0 : (T(b) << 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; }

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 (is_signed<T>::value)
    if (t == -Nyaan::inf) res = "-inf";
  if (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if (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(...)
#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 repc(i, a, cond) for (long long i = (a); (cond); i++)
#define enm(i, val, vec)                                  \
  for (long long i = 0; i < (long long)(vec).size(); i++) \
    if (auto& val = vec[i]; false)                        \
      ;                                                   \
    else

#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 inc(...)    \
  char __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(); }

//

template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}




// i : d[i][i] < 0 exists -> negative cycle
template <typename T>
void warshall_floyd(T& d) {
  int N = d[0].size();
  for (int i = 0; i < N; i++) d[i][i] = 0;
  for (int k = 0; k < N; k++)
    for (int i = 0; i < N; i++)
      for (int j = 0; j < N; j++) d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
}




template <typename G>
struct HeavyLightDecomposition {
 private:
  void dfs_sz(int cur) {
    size[cur] = 1;
    for (auto& dst : g[cur]) {
      if (dst == par[cur]) {
        if (g[cur].size() >= 2 && int(dst) == int(g[cur][0]))
          swap(g[cur][0], g[cur][1]);
        else
          continue;
      }
      depth[dst] = depth[cur] + 1;
      par[dst] = cur;
      dfs_sz(dst);
      size[cur] += size[dst];
      if (size[dst] > size[g[cur][0]]) {
        swap(dst, g[cur][0]);
      }
    }
  }

  void dfs_hld(int cur) {
    down[cur] = id++;
    for (auto dst : g[cur]) {
      if (dst == par[cur]) continue;
      nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst));
      dfs_hld(dst);
    }
    up[cur] = id;
  }

  // [u, v)
  vector<pair<int, int>> ascend(int u, int v) const {
    vector<pair<int, int>> res;
    while (nxt[u] != nxt[v]) {
      res.emplace_back(down[u], down[nxt[u]]);
      u = par[nxt[u]];
    }
    if (u != v) res.emplace_back(down[u], down[v] + 1);
    return res;
  }

  // (u, v]
  vector<pair<int, int>> descend(int u, int v) const {
    if (u == v) return {};
    if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}};
    auto res = descend(u, par[nxt[v]]);
    res.emplace_back(down[nxt[v]], down[v]);
    return res;
  }

 public:
  G& g;
  int id;
  vector<int> size, depth, down, up, nxt, par;
  HeavyLightDecomposition(G& _g, int root = 0)
      : g(_g),
        id(0),
        size(g.size(), 0),
        depth(g.size(), 0),
        down(g.size(), -1),
        up(g.size(), -1),
        nxt(g.size(), root),
        par(g.size(), root) {
    dfs_sz(root);
    dfs_hld(root);
  }

  void build(int root) {
    dfs_sz(root);
    dfs_hld(root);
  }

  pair<int, int> idx(int i) const { return make_pair(down[i], up[i]); }

  template <typename F>
  void path_query(int u, int v, bool vertex, const F& f) {
    int l = lca(u, v);
    for (auto&& [a, b] : ascend(u, l)) {
      int s = a + 1, t = b;
      s > t ? f(t, s) : f(s, t);
    }
    if (vertex) f(down[l], down[l] + 1);
    for (auto&& [a, b] : descend(l, v)) {
      int s = a, t = b + 1;
      s > t ? f(t, s) : f(s, t);
    }
  }

  template <typename F>
  void path_noncommutative_query(int u, int v, bool vertex, const F& f) {
    int l = lca(u, v);
    for (auto&& [a, b] : ascend(u, l)) f(a + 1, b);
    if (vertex) f(down[l], down[l] + 1);
    for (auto&& [a, b] : descend(l, v)) f(a, b + 1);
  }

  template <typename F>
  void subtree_query(int u, bool vertex, const F& f) {
    f(down[u] + int(!vertex), up[u]);
  }

  int lca(int a, int b) {
    while (nxt[a] != nxt[b]) {
      if (down[a] < down[b]) swap(a, b);
      a = par[nxt[a]];
    }
    return depth[a] < depth[b] ? a : b;
  }
};

/**
 * @brief Heavy Light Decomposition(重軽分解)
 * @docs docs/tree/heavy-light-decomposition.md
 */

using namespace Nyaan;

void Nyaan::solve() {
  ini(N, K);
  auto g = wgraph<ll>(N);
  if (K == 0) {
    vl d2(N);
    {
      auto dfs = [&](auto rec, int cur, int par = -1) -> void {
        each(dst, g[cur]) {
          if (dst == par) continue;
          d2[dst] = d2[cur] + dst.cost;
          rec(rec, dst, cur);
        }
      };
      dfs(dfs, 0);
    }
    HeavyLightDecomposition<decltype(g)> hld(g);

    ini(Q);
    while (Q--) {
      ini(u, v);
      --u, --v;
      ll ans = d2[u] + d2[v] - 2 * d2[hld.lca(u, v)];
      out(ans);
    }
    return;
  }

  vl M(K), p(K);
  vvi col(N);
  rep(i, K) {
    in(M[i], p[i]);
    vi X(M[i]);
    in(X);
    each(x, X) col[x - 1].push_back(i);
  }

  vvl pre(N);
  {
    auto dfs = [&](auto rec, int cur, int par = -1) -> void {
      vl dp(K, infLL);
      each(dst, g[cur]) {
        if (dst == par) continue;
        rec(rec, dst, cur);
        rep(i, K) amin(dp[i], pre[dst][i] + dst.cost);
      }
      each(c, col[cur]) dp[c] = 0;
      pre[cur] = dp;
      return;
    };
    dfs(dfs, 0);
  }

  vvl dp(N);
  {
    auto dfs = [&](auto rec, int cur, int par, vl ps) -> void {
      {
        vl ans(K);
        rep(i, K) ans[i] = min(ps[i], pre[cur][i]);
        dp[cur] = ans;
      }
      each(c, col[cur]) ps[c] = 0;

      vvl chd;
      each(dst, g[cur]) {
        if (dst == par) continue;
        chd.push_back(pre[dst]);
        each(x, chd.back()) x += dst.cost;
      }

      vvl left{ps};
      rep(i, sz(chd)) {
        vl v(K);
        rep(j, K) v[j] = min(left.back()[j], chd[i][j]);
        left.push_back(v);
      }
      vvl right{ps};
      repr(i, sz(chd)) {
        vl v(K);
        rep(j, K) v[j] = min(right.back()[j], chd[i][j]);
        right.push_back(v);
      }
      reverse(all(right));

      int id = 0;
      each(dst, g[cur]) {
        if (dst == par) continue;
        vl L = left[id];
        vl R = right[id];
        rep(i, K) amin(L[i], R[i]);
        rep(i, K) L[i] += dst.cost;
        rec(rec, dst, cur, L);
        id++;
      }
    };

    dfs(dfs, 0, -1, pre[0]);
  }
  trc(dp);

  vvl ds(K, vl(K, infLL));
  rep(i, N) each(u, col[i]) rep(v, K) {
    amin(ds[u][v], dp[i][v] + p[v]);
    amin(ds[v][u], dp[i][v] + p[u]);
  }
  warshall_floyd(ds);
  trc(ds);

  vl d2(N);
  {
    auto dfs = [&](auto rec, int cur, int par = -1) -> void {
      each(dst, g[cur]) {
        if (dst == par) continue;
        d2[dst] = d2[cur] + dst.cost;
        rec(rec, dst, cur);
      }
    };
    dfs(dfs, 0);
  }
  HeavyLightDecomposition<decltype(g)> hld(g);

  ini(Q);
  while (Q--) {
    ini(u, v);
    --u, --v;
    ll ans = d2[u] + d2[v] - 2 * d2[hld.lca(u, v)];
    rep(i, K) rep(j, K) {
      if (ds[i][j] < TEN(18)) {
        amin(ans, ds[i][j] + dp[u][i] + dp[v][j] + p[i]);
      }
    }
    out(ans);
  }
}