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