結果
| 問題 |
No.1812 Uribo Road
|
| コンテスト | |
| ユーザー |
 iiljj
|
| 提出日時 | 2022-01-14 23:08:57 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 149 ms / 5,000 ms |
| コード長 | 18,156 bytes |
| コンパイル時間 | 6,060 ms |
| コンパイル使用メモリ | 154,828 KB |
| 最終ジャッジ日時 | 2025-01-27 12:13:54 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 30 |
ソースコード
/* #region Head */
// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath> // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;
#define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))
#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))
#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))
#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))
#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))
#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define ISIZE(x) ((int)(x).size())
#define PERM(c) \
sort(ALL(c)); \
for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b)-1) / (b))
#define endl '\n'
constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;
template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
for (T &x : vec) is >> x;
return is;
}
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)
os << "{";
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
return os;
}
template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
REP(i, 0, SIZE(arr)) is >> arr[i];
return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
os << "{";
REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
is >> pair_var.first >> pair_var.second;
return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力
os << "(" << pair_var.first << ", " << pair_var.second << ")";
return os;
}
// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, const T &map_var) {
os << "{";
REPI(itr, map_var) {
os << *itr;
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {
return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {
os << "{";
REPI(itr, map_var) {
auto [key, value] = *itr;
os << "(" << key << ", " << value << ")";
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {
pq<T> pq_cp(pq_var);
os << "{";
if (!pq_cp.empty()) {
os << pq_cp.top(), pq_cp.pop();
while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
}
return os << "}";
}
// tuple 出力
template <size_t N = 0, bool end_line = false, typename... Args> ostream &operator<<(ostream &os, tuple<Args...> &a) {
if constexpr (N < std::tuple_size_v<tuple<Args...>>) {
os << get<N>(a);
if constexpr (N + 1 < std::tuple_size_v<tuple<Args...>>) {
os << ' ';
} else if constexpr (end_line) {
os << '\n';
}
return operator<<<N + 1, end_line>(os, a);
}
return os;
}
template <typename... Args> void print_tuple(tuple<Args...> &a) { operator<<<0, true>(cout, a); }
void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
cout << head;
if (sizeof...(Tail) > 0) cout << ' ';
pprint(move(tail)...);
}
// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {
DUMPOUT << head;
if (sizeof...(Tail) > 0) DUMPOUT << ", ";
dump_func(move(tail)...);
}
// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
if (comp(xmax, x)) {
xmax = x;
return true;
}
return false;
}
// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
if (comp(x, xmin)) {
xmin = x;
return true;
}
return false;
}
// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif
#ifndef MYLOCAL
#undef DEBUG_
#endif
#ifdef DEBUG_
#define DEB
#define dump(...) \
DUMPOUT << " " << string(#__VA_ARGS__) << ": " \
<< "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \
<< " ", \
dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif
#define VAR(type, ...) \
type __VA_ARGS__; \
cin >> __VA_ARGS__;
template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }
struct AtCoderInitialize {
static constexpr int IOS_PREC = 15;
static constexpr bool AUTOFLUSH = false;
AtCoderInitialize() {
ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) cout << unitbuf;
}
} ATCODER_INITIALIZE;
void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }
/* #endregion */
// #include <atcoder/all>
// using namespace atcoder;
/* #region Graph */
// エッジ（本来エッジは双方向だが，ここでは単方向で管理）
template <class weight_t = int, class flow_t = int> struct Edge {
int src; // エッジ始点となる頂点
int dst; // エッジ終点となる頂点
weight_t weight; // 重み
flow_t cap;
Edge() : src(0), dst(0), weight(0) {}
Edge(int src, int dst, weight_t weight) : src(src), dst(dst), weight(weight) {}
Edge(int src, int dst, weight_t weight, flow_t cap) : src(src), dst(dst), weight(weight), cap(cap) {}
// Edge 標準出力
friend ostream &operator<<(ostream &os, Edge &edge) {
os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";
return os;
}
};
// 同じ頂点を始点とするエッジ集合
template <class weight_t = int, class flow_t = int> class Node : public vc<Edge<weight_t, flow_t>> {
public:
int idx;
Node() : vc<Edge<weight_t, flow_t>>() {}
// void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b, w, cap); };
};
// graph[i] := 頂点 i を始点とするエッジ集合
template <class weight_t = int, class flow_t = int> class Graph : public vc<Node<weight_t, flow_t>> {
public:
Graph() : vc<Node<weight_t, flow_t>>() {}
Graph(int n) : vc<Node<weight_t, flow_t>>(n) { REP(i, 0, n)(*this)[i].idx = i; }
/** 単方向 */
void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) { (*this)[a].emplace_back(a, b, w, cap); }
/** 双方向 */
void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) { add_arc(a, b, w, cap), add_arc(b, a, w, cap); }
/** ノード追加 */
int add_node() {
int idx = (int)this->size();
this->emplace_back();
Node<weight_t, flow_t> &node = this->back();
node.idx = idx;
return idx;
}
};
// using Array = vc<Weight>;
// using Matrix = vc<Array>;
/* #endregion */
/* #region Dijkstra */
// ダイクストラ法
// グラフを陽に持つ
template <class Weight = ll> struct Dijkstra {
// pair 比較よりも struct 比較のほうが速い
struct state {
Weight cost;
int dst;
state(Weight cost, int dst) : cost(cost), dst(dst) {}
bool operator<(const state &o) const { return cost > o.cost; }
// bool operator>(const state &o) const { return cost > o.cost; }
};
Graph<Weight> graph;
vc<Weight> dist;
vc<int> bs; // 経路復元用情報
Weight inf;
/** コンストラクタ */
Dijkstra(const int n, const Weight inf = INF) : graph(n), dist(n, inf), bs(n, -1), inf(inf) {}
/** コンストラクタ，グラフを使って初期化するバージョン */
Dijkstra(const Graph<Weight> &graph, const Weight inf = INF)
: graph(graph), dist(graph.size(), inf), bs(graph.size(), -1), inf(inf) {}
// 有向辺の追加
void add_edge(const int src, const int dst, const Weight cost) { graph.add_arc(src, dst, cost); }
void build(const int start, const Weight init = 0) {
priority_queue<state> que; // 昇順に並べ替え，小さい順に取り出す
fill(ALL(dist), inf);
fill(ALL(bs), -1);
dist[start] = init;
que.emplace(init, start);
while (que.size()) {
const state cur = que.top(); // tie(d, v) = que.top();
que.pop();
const int cur_node = cur.dst;
const Weight cur_cost = cur.cost;
if (dist[cur_node] < cur_cost) continue;
for (const Edge<Weight> &edge : graph[cur_node])
if (chmin(dist[edge.dst], dist[cur_node] + edge.weight)) {
que.emplace(dist[edge.dst], edge.dst);
bs[edge.dst] = cur_node;
}
}
}
// あるノードまでの距離を返す
Weight operator[](const int dst) const { return dist[dst]; }
// 経路復元
// dst がスタート地点の場合は空ベクトルが返るため注意
vc<int> restore(int dst) const {
vc<int> res;
if (bs[dst] < 0) return res;
while (~dst) res.emplace_back(dst), dst = bs[dst];
reverse(ALL(res));
return res;
}
};
/* #endregion */
// Problem
void solve() {
VAR(ll, n, m, k);
vll r(k);
cin >> r;
REP(i, 0, k) r[i]--;
vll a(m), b(m), c(m);
REP(i, 0, m) {
cin >> a[i], b[i], c[i];
--a[i], --b[i];
}
Dijkstra<ll> dijkstra(n, INF);
REP(i, 0, m) {
dijkstra.add_edge(a[i], b[i], c[i]);
dijkstra.add_edge(b[i], a[i], c[i]);
}
// 辺 r[k] の両端点，始点，終点 の 2k+2 個を持つ
vvll dists(2 * k + 4, vll(2 * k + 4, INF));
ll S = 0, T = n - 1;
REP(i, 0, k) {
{
ll start = a[r[i]];
dijkstra.build(start, 0LL);
// dists[2 * i + 0] = dijkstra.dist;
REP(j, 0, k) {
dists[2 * i + 0][2 * j + 0] = dijkstra.dist[a[r[j]]];
dists[2 * i + 0][2 * j + 1] = dijkstra.dist[b[r[j]]];
}
dists[2 * i + 0][2 * k + 0] = dijkstra.dist[S];
dists[2 * i + 0][2 * k + 1] = dijkstra.dist[S];
dists[2 * i + 0][2 * k + 2] = dijkstra.dist[T];
dists[2 * i + 0][2 * k + 3] = dijkstra.dist[T];
}
{
ll start = b[r[i]];
dijkstra.build(start, 0LL);
// dists[2 * i + 1] = dijkstra.dist;
REP(j, 0, k) {
dists[2 * i + 1][2 * j + 0] = dijkstra.dist[a[r[j]]];
dists[2 * i + 1][2 * j + 1] = dijkstra.dist[b[r[j]]];
}
dists[2 * i + 1][2 * k + 0] = dijkstra.dist[S];
dists[2 * i + 1][2 * k + 1] = dijkstra.dist[S];
dists[2 * i + 1][2 * k + 2] = dijkstra.dist[T];
dists[2 * i + 1][2 * k + 3] = dijkstra.dist[T];
}
}
if (true) {
{
ll start = S;
dijkstra.build(start, 0LL);
// dists[2 * k] = dijkstra.dist;
REP(j, 0, k) {
dists[2 * k + 0][2 * j + 0] = dijkstra.dist[a[r[j]]];
dists[2 * k + 0][2 * j + 1] = dijkstra.dist[b[r[j]]];
dists[2 * k + 1][2 * j + 0] = dijkstra.dist[a[r[j]]];
dists[2 * k + 1][2 * j + 1] = dijkstra.dist[b[r[j]]];
}
dists[2 * k + 0][2 * k + 0] = dijkstra.dist[S];
dists[2 * k + 0][2 * k + 1] = dijkstra.dist[S];
dists[2 * k + 0][2 * k + 2] = dijkstra.dist[T];
dists[2 * k + 0][2 * k + 3] = dijkstra.dist[T];
dists[2 * k + 1][2 * k + 0] = dijkstra.dist[S];
dists[2 * k + 1][2 * k + 1] = dijkstra.dist[S];
dists[2 * k + 1][2 * k + 2] = dijkstra.dist[T];
dists[2 * k + 1][2 * k + 3] = dijkstra.dist[T];
}
{
ll start = T;
dijkstra.build(start, 0LL);
// dists[2 * k + 1] = dijkstra.dist;
REP(j, 0, k) {
dists[2 * k + 2][2 * j + 0] = dijkstra.dist[a[r[j]]];
dists[2 * k + 2][2 * j + 1] = dijkstra.dist[b[r[j]]];
dists[2 * k + 3][2 * j + 0] = dijkstra.dist[a[r[j]]];
dists[2 * k + 3][2 * j + 1] = dijkstra.dist[b[r[j]]];
}
dists[2 * k + 2][2 * k + 0] = dijkstra.dist[S];
dists[2 * k + 2][2 * k + 1] = dijkstra.dist[S];
dists[2 * k + 2][2 * k + 2] = dijkstra.dist[T];
dists[2 * k + 2][2 * k + 3] = dijkstra.dist[T];
dists[2 * k + 3][2 * k + 0] = dijkstra.dist[S];
dists[2 * k + 3][2 * k + 1] = dijkstra.dist[S];
dists[2 * k + 3][2 * k + 2] = dijkstra.dist[T];
dists[2 * k + 3][2 * k + 3] = dijkstra.dist[T];
}
}
// dump(dists);
// TSP
vc<vvll> dp(1 << (k + 2), vvll(k + 2, vll(2, INF))); // [state, last, flag] -> (min of max, min of sum, ...)
dp[1 << k][k][0] = 0; // 出発地点が S 限定
// dp[1 << k][k][1] = 0; // 出発地点が S 限定
REP(state, 1, 1 << (k + 2)) REP(from, 0, k + 2) {
if (~state & (1 << from)) continue; // 未訪問
if (dp[state][from][0] != INF) {
// from が最後になるような巡回で state に至ることが可能
REP(to, 0, k + 2) {
if (state & (1 << to)) continue; // 訪問済み
{
// from の 0 まで到達している→1を経由するので1からの距離で
ll dist00 = dp[state][from][0] + dists[2 * from + 1][2 * to + 0];
ll dist01 = dp[state][from][0] + dists[2 * from + 1][2 * to + 1];
chmin(dp[state | (1 << to)][to][0], dist00);
chmin(dp[state | (1 << to)][to][1], dist01);
}
{
// from の 1 まで到達している→0を経由するので0からの距離で
ll dist10 = dp[state][from][1] + dists[2 * from + 0][2 * to + 0];
ll dist11 = dp[state][from][1] + dists[2 * from + 0][2 * to + 1];
chmin(dp[state | (1 << to)][to][0], dist10);
chmin(dp[state | (1 << to)][to][1], dist11);
}
}
}
}
// dump(dp[(1 << (k + 2)) - 1][k + 1]);
// dump(dp);
ll ans = 0;
REP(i, 0, k) ans += c[r[i]];
ans += *min_element(ALL(dp[(1 << (k + 2)) - 1][k + 1]));
pprint(ans);
}
// entry point
int main() {
solve();
return 0;
}