// c++ program to find uhortest weighted 
// cycle in undirected graph 

#include <iostream>
#include <list>
#include <utility>
#include <vector>
#include <algorithm>
#include <set>
#include <climits>
using namespace std;
# define INF 0x3f3f3f3f 
struct Edge
{
	int u;
	int v;
	int weight;
};

// weighted undirected Graph 
class Graph
{
	int V;
	list < pair <int, int > >* adj;

	// used to store all edge information 
	vector < Edge > edge;
	vector<int> pi;


public:
	Graph(int V)
	{
		this->V = V;
		adj = new list < pair <int, int > >[V];
		pi.assign(V, INF);
	}

	void addEdge(int u, int v, int w);
	void removeEdge(int u, int v, int w);
	int ShortestPath(int u, int v);
	void RemoveEdge(int u, int v);
	void FindMinimumCycle();

};

//function add edge to graph 
void Graph::addEdge(int u, int v, int w)
{
	adj[u].push_back(make_pair(v, w));
	adj[v].push_back(make_pair(u, w));

	// add Edge to edge list 
	Edge e{ u, v, w };
	edge.push_back(e);
}

// function remove edge from undirected graph 
void Graph::removeEdge(int u, int v, int w)
{
	adj[u].remove(make_pair(v, w));
	adj[v].remove(make_pair(u, w));
}

// find shortest path from source to sink using 
// Dijkstra’s shortest path algorithm [ Time complexity 
// O(E logV )] 
int Graph::ShortestPath(int u, int v) //uはソース、vはシンク
{
	pi.assign(V, INF);
	// Create a set to store vertices that are being 
	// prerocessed 
	set< pair<int, int> > setds;

	// Create a vector for distances and initialize all 
	// distances as infinite (INF) 
	vector<int> dist(V, INF); //値がINFであるV個の要素からなるベクター

	// Insert source itself in Set and initialize its 
	// distance as 0. 
	setds.insert(make_pair(0, u)); //ペアの最初の要素は距離、2番目の要素は点のラベル
	dist[u] = 0;

	/* Looping till all shortest distance are finalized
	then setds will become empty */
	while (!setds.empty())
	{
		// The first vertex in Set is the minimum distance 
		// vertex, extract it from set. 
		pair<int, int> tmp = *(setds.begin());
		setds.erase(setds.begin());

		// vertex label is stored in second of pair (it 
		// has to be done this way to keep the vertices 
		// sorted distance (distance must be first item 
		// in pair) 
		int u = tmp.second;

		// 'i' is used to get all adjacent vertices of 
		// a vertex 
		list< pair<int, int> >::iterator i;
		for (i = adj[u].begin(); i != adj[u].end(); ++i) //uに隣接するすべての点に対して
		{
			// Get vertex label and weight of current adjacent 
			// of u. 
			int v = (*i).first; //uに隣接する点のラベル
			int weight = (*i).second; //辺(u, v)の重み

			// If there is shorter path to v through u. 
			if (dist[v] > dist[u] + weight)
			{
				/* If distance of v is not INF then it must be in
					our set, so removing it and inserting again
					with updated less distance.
					Note : We extract only those vertices from Set
					for which distance is finalized. So for them,
					we would never reach here. */
				if (dist[v] != INF) //vの暫定的な距離が∞でないということは、既に、(dist[v], v)はsetdsに入っているので、消去する。（↓でdist[v]を更新して再度setdsに挿入している。）
					setds.erase(setds.find(make_pair(dist[v], v)));

				// Updating distance of v 
				dist[v] = dist[u] + weight;
				setds.insert(make_pair(dist[v], v));
				pi[v] = u;
			}
		}
	}

	// return shortest path from current source to sink 
	return dist[v];
}

// function return minimum weighted cycle 
//int Graph::FindMinimumCycle()
void Graph::FindMinimumCycle()
{
	int min_cycle = INT_MAX;
	int E = edge.size();
	vector<int> pi2;
	int u = 0, v = 0;
	for (int i = 0; i < E; i++)
	{
		// current Edge information 
		Edge e = edge[i];

		// get current edge vertices which we currently 
		// remove from graph and then find shortest path 
		// between these two vertices using Dijkstra’s 
		// shortest path algorithm . 
		removeEdge(e.u, e.v, e.weight);

		// minimum distance between these two vertices 
		int distance = ShortestPath(e.u, e.v);

		// to make a cycle we have to add weight of 
		// currently removed edge if this is the shortest 
		// cycle then update min_cycle 
		//min_cycle = min(min_cycle, distance + e.weight);
		if (distance + e.weight < min_cycle)
		{
			min_cycle = distance + e.weight;
			pi2 = pi;
			u = e.u;
			v = e.v;
		}

		// add current edge back to the graph 
		addEdge(e.u, e.v, e.weight);
	}


	// return shortest cycle 
	//return min_cycle;

	std::cout << "A minimum weight cycle is:" << endl;

	int v1;
	v1 = v;
	while (pi2[v1] != INF)
	{
		std::cout << v1 << " -> ";
		v1 = pi2[v1];
	}
	std::cout << u << " -> " << v << endl;

	std::cout << "The weight of the cycle is " << min_cycle << endl;
}

// vriver program to test above function 
int main()
{
	int V = 9;
	Graph g(V);

	// making above shown graph 
	g.addEdge(0, 1, 4);
	g.addEdge(0, 7, 8);
	g.addEdge(1, 2, 8);
	g.addEdge(1, 7, 11);
	g.addEdge(2, 3, 7);
	g.addEdge(2, 8, 2);
	g.addEdge(2, 5, 4);
	g.addEdge(3, 4, 9);
	g.addEdge(3, 5, 14);
	g.addEdge(4, 5, 10);
	g.addEdge(5, 6, 2);
	g.addEdge(6, 7, 1);
	g.addEdge(6, 8, 6);
	g.addEdge(7, 8, 7);

	g.FindMinimumCycle();
	return 0;
}