100 lines
No EOL
2.9 KiB
C++
100 lines
No EOL
2.9 KiB
C++
// Algorithm generating a minimum spanning tree using Prim's algorithm
|
|
// Authors: Georǵi Kocharyan
|
|
|
|
#include <iostream>
|
|
#include <cstdio>
|
|
#include <vector>
|
|
#include <list>
|
|
#include <queue>
|
|
#include <algorithm>
|
|
#include <string>
|
|
#include <functional>
|
|
#include "../../weighted_graph.h"
|
|
|
|
|
|
struct key_compare
|
|
{
|
|
bool operator()(const std::pair<int, double>& l, const std::pair<int, double>& r)
|
|
{
|
|
return l.second > r.second;
|
|
}
|
|
};
|
|
|
|
void next_edge(WeightedGraph const & G, std::vector<std::pair<int, double>> & min_neighbours, std::priority_queue<std::pair<int, double>, std::vector<std::pair<int, double>>, key_compare> & notMST, std::vector<bool> & inMST, int & last_added, double & total_weight) {
|
|
// update the priority queue
|
|
for (const auto& j: G.adjList(last_added))
|
|
{
|
|
int to = j.first;
|
|
double weight = j.second;
|
|
if (weight < min_neighbours[to].second)
|
|
{
|
|
min_neighbours[to] = std::make_pair(last_added, weight);
|
|
notMST.push(std::make_pair(to, weight));
|
|
}
|
|
}
|
|
// add the next edge
|
|
std::pair<int, double> node = notMST.top();
|
|
notMST.pop();
|
|
if (!inMST[node.first])
|
|
{
|
|
std::cout << node.first << "-" << min_neighbours[node.first].first << "\t" << node.second << std::endl;
|
|
last_added = node.first;
|
|
inMST[node.first] = true;
|
|
total_weight = total_weight + node.second;
|
|
}
|
|
|
|
}
|
|
|
|
void prim(WeightedGraph const & G) {
|
|
// preprocessing: remove all double edges except the minimal ones
|
|
|
|
WeightedGraph H = G.remove_parallel();
|
|
|
|
// preprocessing: create a vector with the min MST neighbour of all vertices
|
|
|
|
std::vector<std::pair<int, double>> min_neighbours(H.num_nodes(), std::make_pair(0,std::numeric_limits<double>::infinity()));
|
|
|
|
// preprocessing: track with a vector which elements are in the MST
|
|
|
|
std::vector<bool> inMST(H.num_nodes(), false);
|
|
inMST[0] = true;
|
|
|
|
// preprocessing: create a priority queue of vertices not yet in the MST
|
|
|
|
std::priority_queue<std::pair<int, double>, std::vector<std::pair<int, double>>, key_compare> notMST;
|
|
for (int i = 1; i < H.num_nodes(); i++)
|
|
{
|
|
notMST.push(std::make_pair(i, std::numeric_limits<double>::infinity()));
|
|
}
|
|
int last_added = 0;
|
|
double total_weight = 0;
|
|
while (!notMST.empty())
|
|
{
|
|
next_edge(H, min_neighbours, notMST, inMST, last_added, total_weight);
|
|
}
|
|
std::cout << "The total weight of the MST is " << total_weight << std::endl;
|
|
}
|
|
|
|
int main() {
|
|
|
|
int size = 8;
|
|
WeightedGraph G(size);
|
|
G.add_edge(3,4,2);
|
|
G.add_edge(4,3,3);
|
|
G.add_edge(5,6,6);
|
|
G.add_edge(6,7,1);
|
|
G.add_edge(1,2,3);
|
|
G.add_edge(2,3,8);
|
|
G.add_edge(7,5,0.2);
|
|
G.add_edge(7,3,9);
|
|
G.add_edge(0,3,1);
|
|
G.add_edge(3,0,5);
|
|
G.add_edge(4,6,3);
|
|
G.add_edge(0,7,0.5);
|
|
G.add_edge(4,2,1);
|
|
|
|
prim(G);
|
|
|
|
return 0;
|
|
|
|
} |