/**
	Алгоритъм на Прим за минимално покриващо дърво с корен s (с priority_queue)
*/

#include <iostream>
#include <vector>
#include <queue>
#include <functional>
#define Inf 2000000000
using namespace std;

typedef pair <int, int> pr;

const int n = 8;

vector <pr> graph[n] = {
	{ pr(1, 1), pr(3, 3), pr(4, 5) },
	{ pr(0, 1), pr(2, 2), pr(5, 2) },
	{ pr(1, 2), pr(4, 6) },
	{ pr(0, 3), pr(6, 10) },
	{ pr(0, 5), pr(2, 6), pr(6, 7), pr(7, 2) },
	{ pr(1, 2), pr(7, 5) },
	{ pr(3, 10), pr(4, 7), pr(7, 20) },
	{ pr(4, 2), pr(5, 5), pr(6, 20) } };

bool finalized[n];
int key[n];
int parent[n];

int MST_Prim(int s)
{
	for (int i = 0; i < n; i++){ key[i] = Inf; finalized[i] = false; parent[i] = -1; }

	priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > q; // minHeap

	q.push(pair<int, int>(0, s));
	key[s] = 0;

	int sum = 0;

	while (!q.empty())
	{
		int u = q.top().second;
		q.pop();

		if (!finalized[u])
		{
			finalized[u] = true;
			sum += key[u];
			for (pr e : graph[u])
			{
				int v = e.first, w = e.second;
				if (!finalized[v] && w < key[v])
				{
					parent[v] = u;
					key[v] = w;
					q.push(pair<int, int>(key[v], v));
				}
			}
		}
	}

	return sum;
}

int main()
{
	cout << "MPD_Sum = " << MST_Prim(0) << endl;

	return 0;
}