// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/minimum_steiner_tree
#include "../../../graph/graph-template.hpp"
#include "../../../graph/minimum-steiner-tree.hpp"
#include "../../../template.hpp"
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
INT(n, m);
Graph<ll> graph(n);
graph.read(m, 0, 1, 0);
INT(k);
vector<int> terminal(k);
input(terminal);
MinimumSteinerTree mst(graph, terminal);
auto edges = mst.restore();
print(mst.cost, edges.size());
for(auto &e : edges) {
write(e.idx);
write(" ");
}
print();
}
#line 1 "test/library_checker/graph/minimum_steiner_tree.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/minimum_steiner_tree
#line 2 "other/fastio.hpp"
// ref: https://maspypy.com/library-checker-many-a-b , Nyaanさん
#line 2 "other/type-utils.hpp"
#include <bits/stdc++.h>
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using vi = std::vector<int>;
using vii = std::vector<std::vector<int>>;
using pii = std::pair<int, int>;
using vl = std::vector<ll>;
using vll = std::vector<vl>;
using pll = std::pair<ll, ll>;
template <class T>
concept extended_integral =
std::integral<T> || std::same_as<std::remove_cv_t<T>, i128> ||
std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept extended_signed_integral =
std::signed_integral<T> || std::same_as<std::remove_cv_t<T>, i128>;
template <class T>
concept extended_unsigned_integral =
std::unsigned_integral<T> || std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept Streamable =
requires(std::ostream &os, T &x) { os << x; } || extended_integral<T>;
template <class mint>
concept is_modint = requires(mint &x) {
{ x.val() } -> std::convertible_to<int>;
};
#line 4 "other/fastio.hpp"
namespace fastio {
constexpr int SZ = 1 << 17;
constexpr int offset = 64;
constexpr int mod = 10000;
char in_buf[SZ];
int in_left{}, in_right{};
char out_buf[SZ];
char out_tmp[offset];
int out_right{};
struct Pre {
char num[4 * mod]{};
constexpr Pre() {
for(int i = 0; i < mod; ++i) {
for(int n = i, j = 3; j >= 0; --j, n /= 10)
num[4 * i + j] = '0' + n % 10;
}
}
constexpr const char *operator[](int i) const { return &num[4 * i]; }
} constexpr pre;
void load() {
memmove(in_buf, in_buf + in_left, in_right - in_left);
in_right += -in_left + std::fread(in_buf + in_right - in_left, 1,
SZ - (in_right - in_left), stdin);
in_left = 0;
if(in_right < SZ)
in_buf[in_right++] = '\n';
}
void read(char &c) {
do {
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(isspace(c));
}
void read(std::string &s) {
s.clear();
char c;
do {
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(isspace(c));
do {
s += c;
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(!isspace(c));
}
template <extended_integral T> void read(T &x) {
if(in_right - in_left < offset)
load();
char c;
do
c = in_buf[in_left++];
while(c < '-'); // \n:10 space:32 -:45 '0':48
bool minus{};
if constexpr(extended_signed_integral<T>) {
if(c == '-') {
c = in_buf[in_left++];
minus = true;
}
}
x = 0;
while(c >= '0') {
x = 10 * x + (c & 15);
c = in_buf[in_left++];
}
if constexpr(extended_signed_integral<T>) {
if(minus)
x = -x;
}
}
void flush() { fwrite(out_buf, 1, std::exchange(out_right, 0), stdout); }
void write_range(const char *c, int n) {
int pos{};
while(pos < n) {
if(out_right == SZ)
flush();
int len = std::min(n - pos, SZ - out_right);
memcpy(out_buf + out_right, c + pos, len);
out_right += len;
pos += len;
}
}
void write(char c) {
if(SZ == out_right)
flush();
out_buf[out_right++] = c;
}
void write(const char *c) { write_range(c, strlen(c)); }
void write(const std::string &s) { write_range(s.data(), s.size()); }
template <std::floating_point T> void write(T x) {
int n = std::snprintf(out_tmp, sizeof(out_tmp), "%.16g", x);
write_range(out_tmp, n);
}
void write(bool x) { write(x ? '1' : '0'); }
template <extended_integral T> void write(T x) {
if(x == 0) {
write('0');
}
if constexpr(extended_signed_integral<T>) {
if(x < 0) {
write('-');
x = -x;
}
}
if(SZ - out_right < offset)
flush();
int cur = offset;
for(; x >= 1000; x /= mod) {
cur -= 4;
memcpy(out_tmp + cur, pre[x % mod], 4);
}
if(x >= 100) {
cur -= 3;
memcpy(out_tmp + cur, pre[x % mod] + 1, 3);
} else if(x >= 10) {
cur -= 2;
memcpy(out_tmp + cur, pre[x % mod] + 2, 2);
} else if(x >= 1) {
cur -= 1;
memcpy(out_tmp + cur, pre[x % mod] + 3, 1);
}
write_range(out_tmp + cur, offset - cur);
}
struct Dummy {
// プログラム終了時に出力
~Dummy() { flush(); }
} dummy;
} // namespace fastio
using fastio::write;
#line 4 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#line 8 "template.hpp"
using namespace std;
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...)
#endif
template <Streamable T> void print_one(const T &value) { fastio::write(value); }
template <is_modint T> void print_one(const T &value) {
print_one(value.val());
}
void print() { print_one('\n'); }
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
print_one(a);
((print_one(' '), print_one(b)), ...);
print();
}
template <ranges::range Iterable>
requires(!Streamable<Iterable>)
void print(const Iterable &v) {
for(auto it = v.begin(); it != v.end(); ++it) {
if(it != v.begin())
print_one(' ');
print_one(*it);
}
print();
}
#define all(v) begin(v), end(v)
template <class T> void UNIQUE(T &v) {
ranges::sort(v);
v.erase(unique(all(v)), end(v));
}
template <typename T> inline bool chmax(T &a, T b) {
return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
return ((a > b) ? (a = b, true) : (false));
}
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
return max(initializer_list<common_type_t<T...>>{a...});
}
void input() {}
template <class Head, class... Tail> void input(Head &head, Tail &...tail) {
#ifdef LOCAL
cin >> head;
#else
fastio::read(head);
#endif
input(tail...);
}
template <class T> void input(vector<T> &a) {
for(T &x : a)
input(x);
}
#define INT(...) \
int __VA_ARGS__; \
input(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
input(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
input(__VA_ARGS__)
#define REP1_0(n, c) REP1_1(n, c)
#define REP1_1(n, c) \
for(ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(n); REP_COUNTER_##c++)
#define REP1(n) REP1_0(n, __COUNTER__)
#define REP2(i, a) for(ll i = 0; i < (ll)(a); i++)
#define REP3(i, a, b) for(ll i = (ll)(a); i < (ll)(b); i++)
#define REP4(i, a, b, c) for(ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
template <class T> constexpr T floor(T x, T y) noexcept {
return x / y - ((x ^ y) < 0 and x % y);
}
template <class T> constexpr T ceil(T x, T y) noexcept {
return x / y + ((x ^ y) >= 0 and x % y);
}
// yの符号に関わらず非負で定義 \bmod:texコマンド
template <class T> constexpr T bmod(T x, T y) noexcept {
T m = x % y;
return (m < 0) ? m + (y > 0 ? y : -y) : m;
}
template <std::signed_integral T> constexpr int bit_width(T x) noexcept {
return std::bit_width((uint64_t)x);
}
template <std::signed_integral T> constexpr int popcount(T x) noexcept {
return std::popcount((uint64_t)x);
}
constexpr bool kth_bit(auto n, auto k) { return (n >> k) & 1; }
#line 3 "graph/graph-template.hpp"
/**
* @brief Graph Template(グラフテンプレート)
* @see https://ei1333.github.io/library/graph/graph-template.hpp
*/
template <class T = ll> struct Edge {
int from, to;
T cost;
int idx;
Edge() = default;
Edge(int from, int to, T cost = 1, int idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
Edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
};
template <class T = ll> struct Graph {
using cost_type = T;
vector<vector<Edge<T>>> g;
int es; // edge_size
Graph() = default;
explicit Graph(int n) : g(n), es(0) {};
int size() const { return ssize(g); }
void add_directed_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es++);
}
void add_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
vector<Edge<T>> &operator[](const int &k) { return g[k]; }
const vector<Edge<T>> &operator[](const int &k) const { return g[k]; }
void read(int m, int padding = -1, bool weighted = false,
bool directed = false) {
for(int i = 0; i < m; ++i) {
int a, b;
T c(1);
input(a, b);
a += padding;
b += padding;
if(weighted)
input(c);
if(directed)
add_directed_edge(a, b, c);
else
add_edge(a, b, c);
}
}
};
#line 3 "graph/minimum-steiner-tree.hpp"
/**
* @brief 最小シュタイナー木
* @see https://www.slideshare.net/wata_orz/ss-12131479#50
* @see
* https://ei1333.github.io/library/graph/others/minimum-steiner-tree.hpp.html
*/
template <class T> struct MinimumSteinerTree {
int n, k;
// 必要に応じて&外す
const Graph<T> &g;
const vector<int> &terminal;
T cost;
const T infty = numeric_limits<T>::max();
vector<vector<T>> dp;
vector<vector<pair<int, int>>> prev;
MinimumSteinerTree(const Graph<T> &g, const vector<int> &terminal)
: n(g.size()), k(terminal.size()), g(g), terminal(terminal), cost(0),
dp(1 << k, vector<T>(n, infty)),
prev(1 << k, vector<pair<int, int>>(n)) {
assert(!terminal.empty());
rep(i, k) { dp[1 << i][terminal[i]] = 0; }
rep(bit, 1, 1 << k) {
rep(i, n) {
for(int sub = (bit - 1) & bit; sub > 0; sub = (sub - 1) & bit) {
if(dp[sub][i] != infty and dp[bit ^ sub][i] != infty)
if(chmin(dp[bit][i], dp[sub][i] + dp[bit ^ sub][i])) {
prev[bit][i] = {sub, -1};
}
}
}
using pti = pair<T, int>;
priority_queue<pti, vector<pti>, greater<pti>> pq;
rep(i, n) pq.push(pti(dp[bit][i], i));
while(pq.size()) {
auto [c, v] = pq.top();
pq.pop();
if(c != dp[bit][v] or c == infty)
continue;
for(int i = 0; i < ssize(g[v]); ++i) {
auto &e = g[v][i];
T nc = c + e.cost;
if(chmin(dp[bit][e.to], nc)) {
pq.push(pti(nc, e.to));
prev[bit][e.to] = {v, i};
}
}
}
}
cost = dp.back()[terminal.front()];
}
// 最小シュタイナー木に使われた辺たちを返す
// 順序・向きは未定義
vector<Edge<T>> restore() const {
vector<Edge<T>> res;
vector<pair<int, int>> que;
que.emplace_back((1 << k) - 1, terminal[0]);
while(!que.empty()) {
auto [bit, cur] = que.back();
que.pop_back();
if(dp[bit][cur] == T(0))
continue;
auto [x, y] = prev[bit][cur];
if(y == -1) {
que.emplace_back(x, cur);
que.emplace_back(bit ^ x, cur);
} else {
res.emplace_back(g[x][y]);
que.emplace_back(bit, x);
}
}
return res;
}
};
#line 5 "test/library_checker/graph/minimum_steiner_tree.test.cpp"
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
INT(n, m);
Graph<ll> graph(n);
graph.read(m, 0, 1, 0);
INT(k);
vector<int> terminal(k);
input(terminal);
MinimumSteinerTree mst(graph, terminal);
auto edges = mst.restore();
print(mst.cost, edges.size());
for(auto &e : edges) {
write(e.idx);
write(" ");
}
print();
}
test/library_checker/graph/minimum_steiner_tree.test.cpp