Test/yukicoder/yuki0114.test.cpp

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Last update: 2024-08-03 19:24:30+09:00
Problem: https://yukicoder.me/problems/no/114

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Code

#define PROBLEM "https://yukicoder.me/problems/no/114"

#include <bits/stdc++.h>
#include "Graph/dsu.hpp"
#include "Graph/steiner_tree.hpp"
using ll = long long;

using namespace std;

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int N, M, T;
	cin >> N >> M >> T;
	vector<int> ter(T);
	if(T <= 16){
		vector<vector<pair<int,int>>> G(N);
		for(int i = 0; i < M; i++){
			int u, v, w;
			cin >> u >> v >> w;
			u--, v--;
			G[u].emplace_back(v, w);
			G[v].emplace_back(u, w);
		}
		for(auto &&v : ter) cin >> v, v--;
		int tmp = ter.back();
		ter.pop_back();
		cout << steiner_tree(G, ter)[tmp] << '\n';
	}else{
		vector<tuple<int,int,int>> edge(M);
		for(auto &&[u, v, w] : edge){
			cin >> u >> v >> w;
			u--, v--;
			swap(u, w);
		}
		long long S = (1ll << N) - 1;
		int ans = 1 << 30;
		for(auto &&v : ter) {
			cin >> v;
			v--;
			S ^= 1ll << v;
		}
		sort(edge.begin(), edge.end());
		for(long long U = S; U >= 0; U = (U - 1) & S){
			int sv = 0;
			dsu uf(N);
			for(auto &&[w, u, v] : edge){
				if((U >> u & 1) || (U >> v & 1) || uf.same(u, v)) continue;
				uf.merge(u, v);
				sv += w;
			}
			if(uf.size(ter[0]) + __builtin_popcountll(U) == N){
				ans = min(ans, sv);
			}
			if(U == 0) break;
		}
		cout << ans << '\n';
	}
}

#line 1 "Test/yukicoder/yuki0114.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/114"

#include <bits/stdc++.h>
#line 1 "Graph/dsu.hpp"
struct dsu {
    public:
    dsu() : _n(0) {}
    dsu(int n) : _n(n), num_component(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        num_component--;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size() { 
        return num_component;
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

    private:
    int _n, num_component;
    // root node: -1 * component size
    // otherwise: parent
    std::vector<int> parent_or_size;
};
#line 1 "Graph/steiner_tree.hpp"
template <class T> std::vector<T> steiner_tree(std::vector<std::vector<std::pair<int, T>>> &G, 
								std::vector<int> &terminal){
    const int N = G.size(), t = terminal.size();
	if(t == 0) {
		std::vector<T> ans(N);
		return ans;
	}
	std::vector<std::vector<T>> dp(1 << t, std::vector<T>(N, std::numeric_limits<T>::max() / 2));
	for(int i = 0; i < t; i++){
		assert(0 <= terminal[i] && terminal[i] < N);
		dp[1 << i][terminal[i]] = 0;
	}
	std::priority_queue<std::pair<T, int>, 
		std::vector<std::pair<T, int>>, std::greater<std::pair<T, int>>> pq;
	for(int S = 1; S < (1 << t); S++){
		for(int v = 0; v < N; v++){
			for(int U = S & (S - 1); U > 0; U = (U - 1) & S){
				dp[S][v] = std::min(dp[S][v], dp[U][v] + dp[U ^ S][v]);
			}
		}
		for(int v = 0; v < N; v++) pq.emplace(dp[S][v], v);
		while(!pq.empty()){
			auto [d, v] = pq.top();
			pq.pop();
			if(d > dp[S][v])continue;
			for(auto &&[u, w] : G[v]){
				if(d + w >= dp[S][u]) continue;
				dp[S][u] = d + w;
				pq.emplace(dp[S][u], u);
			}
		}
	}
	return dp.back();
}
#line 6 "Test/yukicoder/yuki0114.test.cpp"
using ll = long long;

using namespace std;

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int N, M, T;
	cin >> N >> M >> T;
	vector<int> ter(T);
	if(T <= 16){
		vector<vector<pair<int,int>>> G(N);
		for(int i = 0; i < M; i++){
			int u, v, w;
			cin >> u >> v >> w;
			u--, v--;
			G[u].emplace_back(v, w);
			G[v].emplace_back(u, w);
		}
		for(auto &&v : ter) cin >> v, v--;
		int tmp = ter.back();
		ter.pop_back();
		cout << steiner_tree(G, ter)[tmp] << '\n';
	}else{
		vector<tuple<int,int,int>> edge(M);
		for(auto &&[u, v, w] : edge){
			cin >> u >> v >> w;
			u--, v--;
			swap(u, w);
		}
		long long S = (1ll << N) - 1;
		int ans = 1 << 30;
		for(auto &&v : ter) {
			cin >> v;
			v--;
			S ^= 1ll << v;
		}
		sort(edge.begin(), edge.end());
		for(long long U = S; U >= 0; U = (U - 1) & S){
			int sv = 0;
			dsu uf(N);
			for(auto &&[w, u, v] : edge){
				if((U >> u & 1) || (U >> v & 1) || uf.same(u, v)) continue;
				uf.merge(u, v);
				sv += w;
			}
			if(uf.size(ter[0]) + __builtin_popcountll(U) == N){
				ans = min(ans, sv);
			}
			if(U == 0) break;
		}
		cout << ans << '\n';
	}
}