UVa 10986 : Sending Email

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Symbols : 524 字

Servers 互相用雙向電纜連接，求從指定開始 Server 到指定結束 Server 的最短路徑長

測資
Input :

3
2 1 0 1
0 1 100
3 3 2 0
0 1 100
0 2 200
1 2 50
2 0 0 1

Output :

Case #1: 100
Case #2: 150
Case #3: unreachable


解法

因為沒有負權重的邊，因此使用 Dijkstra Algorithm
並用 Adjacent List 和 Priority Queue 來實作


完整程式碼

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#include <iostream>
#include <vector>
#include <list>
#include <queue>

using namespace std;

template<typename T>
using Matrix = vector<list<T>>;

constexpr int INF = 100000;


struct Edge
{
	int idx;
	int weight;

	Edge(int i = -1, int w = INF) : idx{ i }, weight{ w } {}
};

// 由於 c++ 的 priority queue 是 max priority queue，所以要相反比較
inline bool operator<(const Edge &lhs, const Edge &rhs)
{
	return lhs.weight > rhs.weight;
}


class Solution
{
public:
	Solution()
	{
		ios::sync_with_stdio(false);
		cin.tie(nullptr);
		cout.tie(nullptr);
	}

	int calculate(const Matrix<Edge> &w, const int Vertices, const int start, const int end)
	{
		initialize(Vertices);

		priority_queue<Edge> que;

		int min_idx = start;

		dist[min_idx] = 0;

		que.push({ min_idx,0 });

		while (true)
		{
			min_idx = get_min_edge(que);

			if (min_idx == end || min_idx == -1)
				break;

			checked[min_idx] = true;

			relax(w, min_idx, que);
		}

		return dist[end];
	}

private:
	vector<int> dist;
	vector<bool> checked;

	void initialize(const int Vertices)
	{
		dist.clear();
		checked.clear();

		dist.resize(Vertices, INF);
		checked.resize(Vertices, false);
	}

	int get_min_edge(priority_queue<Edge> &que) const
	{
		int min_idx = -1;

		// get the min distance
		while (!que.empty() && checked[min_idx = que.top().idx])
			que.pop();

		return min_idx;
	}
	
	void relax(const Matrix<Edge> &w, const int pivot, priority_queue<Edge> &que)
	{
		int d;

		//            out.weight
		//  pivot ------------------>  out.idx

		for (auto &out : w[pivot])
		{
			if (!checked[out.idx] && (d = dist[pivot] + out.weight) < dist[out.idx])
			{
				dist[out.idx] = d;
				que.push({ out.idx,d });
			}
		}
	}
};

int main(void)
{
	int total_cases;
	int vertices, edges;
	int start, end;
	int ans;
	
	Solution s;
	Matrix<Edge> w(20000);

	int t = 0;
	int a, b, v;

	cin >> total_cases;


	while (t++ < total_cases)
	{
		cin >> vertices >> edges >> start >> end;

		w.clear();
		w.resize(vertices);

		while (edges--)
		{
			cin >> a >> b >> v;

			// 雙向
			w[a].push_back({ b,v });
			w[b].push_back({ a,v });
		}

		ans = s.calculate(w, vertices, start, end);

		cout << "Case #" << t << ": ";
		if (ans >= INF)
			cout << "unreachable" << endl;
		else
			cout << ans << endl;
	}

	return 0;
}
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