This documentation is automatically generated by online-judge-tools/verification-helper
#include <bits/stdc++.h>
#include "ugilib/base/constants.hpp"
#include "ugilib/base/definitions.hpp"
#include "ugilib/graph/tsp.hpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_2_A"
using namespace std;
// debug settings
// #define DEBUG
#ifdef DEBUG
// debug input
string _INPUT = R"(
5
1 2 3 4 5
)";
auto _cin = stringstream(_INPUT.substr(1)); // remove '\n' at _INPUT[0]
#else
// standard input
auto& _cin = cin;
#endif
// speed up
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
// reader
struct rd {
// T
template<typename T> static T i() { T x; _cin >> x; return x; } // T item
// vector<T>
template<typename T> static vector<T> v(int n) {vector<T> v(n); rep(i, n) _cin >> v[i]; return v;} // vector<T>
// vector<pair<T, T>>
template<typename T> static vector<pair<T, T>> vp(int n) {vector<pair<T, T>> v(n); rep(i, n) _cin >> v[i].first >> v[i].second; return v;} // vector<pair<T, T>>
// tuple
template<typename... Args> static tuple<Args...> t() {
tuple<Args...> values;
apply([](auto&... args) { ((_cin >> args), ...); }, values);
return values;
}
};
// debug print utility
namespace deb {
#include <cxxabi.h>
// demangle type name
string demangle(const char* name) {
int status = -4;
unique_ptr<char, void(*)(void*)> res{
abi::__cxa_demangle(name, NULL, NULL, &status),
free
};
return (status == 0) ? string(res.get()) : name ;
}
// meta functions for type traits
template<typename T>
constexpr bool isArithmeticContainer() { return is_arithmetic<typename T::value_type>::value; }
// for SFINAE
template<typename T, typename = void> struct has_key_and_mapped_type : false_type {};
template<typename T> struct has_key_and_mapped_type<T, void_t<typename T::key_type, typename T::mapped_type>> : true_type {};
// for map or unordered_map
template<typename T>
constexpr bool isMapLike() { return has_key_and_mapped_type<T>::value; }
// for values
template<typename T, typename enable_if<is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& x) { cout << x << " "; }
// for pairs
template <typename T, typename S>
void p(const pair<T, S>& _p){ p(_p.first); p(_p.second); cout << endl; }
// for containers
template<typename T, typename enable_if<!is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& container) {
// map and unordered_map
if constexpr (isMapLike<T>()) {
cout << demangle(typeid(T).name()) << ":" << endl;
for (const auto& kv : container) {
cout << "[" << kv.first << "] => ";
p(kv.second);
if constexpr (is_arithmetic_v<typename T::mapped_type>) cout << endl;
}
// vector or set or others
} else {
if constexpr (!isArithmeticContainer<T>()) cout << demangle(typeid(T).name()) << ":" << endl;
for (auto it = begin(container); it != end(container); ++it) {
p(*it);
}
if constexpr (isArithmeticContainer<T>()) cout << endl;
}
}
}; // namespace deb
int main() {
auto& cin = _cin;
// speed up io
cin.tie(nullptr);
ios::sync_with_stdio(false);
// code
auto [V, E] = rd::t<int, int>();
vector<vector<pair<int, int>>> graph(V);
rep(i, E) {
auto [s, t, d] = rd::t<int, int, int>();
graph[s].emplace_back(t, d);
}
int ans = ugilib::tsp_bitDP(V, 0, graph, ugilib::constants::INF<int>);
// どこを始点にしても結果は同じ
for (int i = 1; i < V; i++) {
int another_ans = ugilib::tsp_bitDP(V, i, graph);
assert(ans == another_ans);
}
if (ans == ugilib::constants::INF<int>) cout << -1 << endl;
else cout << ans << endl;
return 0;
}
#line 1 "tests/graph/tsp.test.cpp"
#include <bits/stdc++.h>
#line 2 "ugilib/base/definitions.hpp"
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#define rep(i, n) for(size_t i = 0; i < n; i++) // rep macro
#define all(v) begin(v), end(v) // all iterator
#line 3 "ugilib/base/constants.hpp"
namespace ugilib::constants {
template<typename T>
inline constexpr T INF = std::numeric_limits<T>::max() / 2;
} // namespace ugilib::constants
const ll INF = ugilib::constants::INF<ll>;
#line 4 "ugilib/bit/bit_util.hpp"
using namespace std;
namespace ugilib {
/**
* @brief 数値 -> ビット配列
* @param num ビット配列にするための数値
* @param digit ビット数
* @return vector<bool> 変換されたビット配列. 0番目が一番下の桁
* @details 数値を指定桁のビット配列に変換する
*/
vector<bool> num_to_bits(const ll num, const size_t &digit) {
vector<bool> bits(digit);
for (int i = 0; i < digit; i++) {
bits[i] = (num >> i) & 1U;
}
return bits;
}
/**
* @brief ビット配列 -> 数値
* @param bits 数値にするためのビット配列. 0番目が一番下の桁
* @return ll 変換された数値
* @details ビット配列を数値に戻す. num_to_bitsの逆変換
*/
ll bits_to_num(const vector<bool> &bits) {
ll num = 0;
for (int i = 0; i < bits.size(); i++) {
num += bits[i] << i;
}
return num;
}
} // namespace ugilib
#line 5 "ugilib/graph/tsp.hpp"
using namespace std;
namespace ugilib {
/**
* @brief 巡回セールスマン問題を解くDP
* @param n 都市数
* @param start 始点
* @param graph グラフ. vector<pair<int, weight_t>> で隣接頂点とコストを表す
* @param weight_inf 無限大の値. パスが存在しない場合のコスト
* @return 始点から各頂点を一度だけ通って戻ってくる最小コスト
* @note O(2^n * n^2)
*/
template <typename weight_t>
weight_t tsp_bitDP(int n, int start, const vector<vector<pair<int, weight_t>>> &graph, const weight_t weight_inf = ugilib::constants::INF<weight_t>) {
const int num_states = (1 << n);
// dp[これまでに取った都市集合. [0, 2^n-1]][現在地. [0, n-1]]
vector<vector<weight_t>> dp(num_states, vector<weight_t>(n, weight_inf));
dp[0][start] = 0;
// 全状態についてDPする
for (int i = 0; i < num_states; i++) {
// 状態をビット表現する
auto bits = ugilib::num_to_bits(i, n);
// 今どの都市にいるか
for (int j = 0; j < n; j++) {
if (dp[i][j] == weight_inf) continue; // この状態に辿り着かない場合
// 次どの都市に行くか
for (const auto [node, cost] : graph[j]) {
if (bits[node]) continue; // 訪問済み
// 訪問する
bits[node] = true;
auto &dest = dp[ugilib::bits_to_num(bits)][node];
dest = min(dest, dp[i][j] + cost);
bits[node] = false;
}
}
}
return dp[num_states-1][start]; // 全状態訪問後にstartに戻って来る最小コスト
}
} // namespace ugilib
#line 5 "tests/graph/tsp.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_2_A"
using namespace std;
// debug settings
// #define DEBUG
#ifdef DEBUG
// debug input
string _INPUT = R"(
5
1 2 3 4 5
)";
auto _cin = stringstream(_INPUT.substr(1)); // remove '\n' at _INPUT[0]
#else
// standard input
auto& _cin = cin;
#endif
// speed up
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
// reader
struct rd {
// T
template<typename T> static T i() { T x; _cin >> x; return x; } // T item
// vector<T>
template<typename T> static vector<T> v(int n) {vector<T> v(n); rep(i, n) _cin >> v[i]; return v;} // vector<T>
// vector<pair<T, T>>
template<typename T> static vector<pair<T, T>> vp(int n) {vector<pair<T, T>> v(n); rep(i, n) _cin >> v[i].first >> v[i].second; return v;} // vector<pair<T, T>>
// tuple
template<typename... Args> static tuple<Args...> t() {
tuple<Args...> values;
apply([](auto&... args) { ((_cin >> args), ...); }, values);
return values;
}
};
// debug print utility
namespace deb {
#include <cxxabi.h>
// demangle type name
string demangle(const char* name) {
int status = -4;
unique_ptr<char, void(*)(void*)> res{
abi::__cxa_demangle(name, NULL, NULL, &status),
free
};
return (status == 0) ? string(res.get()) : name ;
}
// meta functions for type traits
template<typename T>
constexpr bool isArithmeticContainer() { return is_arithmetic<typename T::value_type>::value; }
// for SFINAE
template<typename T, typename = void> struct has_key_and_mapped_type : false_type {};
template<typename T> struct has_key_and_mapped_type<T, void_t<typename T::key_type, typename T::mapped_type>> : true_type {};
// for map or unordered_map
template<typename T>
constexpr bool isMapLike() { return has_key_and_mapped_type<T>::value; }
// for values
template<typename T, typename enable_if<is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& x) { cout << x << " "; }
// for pairs
template <typename T, typename S>
void p(const pair<T, S>& _p){ p(_p.first); p(_p.second); cout << endl; }
// for containers
template<typename T, typename enable_if<!is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& container) {
// map and unordered_map
if constexpr (isMapLike<T>()) {
cout << demangle(typeid(T).name()) << ":" << endl;
for (const auto& kv : container) {
cout << "[" << kv.first << "] => ";
p(kv.second);
if constexpr (is_arithmetic_v<typename T::mapped_type>) cout << endl;
}
// vector or set or others
} else {
if constexpr (!isArithmeticContainer<T>()) cout << demangle(typeid(T).name()) << ":" << endl;
for (auto it = begin(container); it != end(container); ++it) {
p(*it);
}
if constexpr (isArithmeticContainer<T>()) cout << endl;
}
}
}; // namespace deb
int main() {
auto& cin = _cin;
// speed up io
cin.tie(nullptr);
ios::sync_with_stdio(false);
// code
auto [V, E] = rd::t<int, int>();
vector<vector<pair<int, int>>> graph(V);
rep(i, E) {
auto [s, t, d] = rd::t<int, int, int>();
graph[s].emplace_back(t, d);
}
int ans = ugilib::tsp_bitDP(V, 0, graph, ugilib::constants::INF<int>);
// どこを始点にしても結果は同じ
for (int i = 1; i < V; i++) {
int another_ans = ugilib::tsp_bitDP(V, i, graph);
assert(ans == another_ans);
}
if (ans == ugilib::constants::INF<int>) cout << -1 << endl;
else cout << ans << endl;
return 0;
}