Added Prim's algorithm

min_spanning_tree/prim/CMakeLists.txt

@@ -0,0 +1,6 @@
+cmake_minimum_required(VERSION 3.10)
+project(prim)
+add_executable(prim
+	../../weighted_graph.cpp
+	../../weighted_graph.h
+	prim.cpp)

min_spanning_tree/prim/prim.cpp

@@ -0,0 +1,97 @@
+//  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);
+
+    prim(G);
+    
+    return 0;
+
+}

weighted_graph.cpp

@@ -0,0 +1,89 @@
+#include "weighted_graph.h"
+#include <unordered_map>
+#include <iostream>
+
+Node::Node(std::list<std::pair<int, double>> neighbours_) : neighbours(std::move(neighbours_))
+{
+
+}
+
+void Node::add_edge(int node_id, double weight)
+{
+  neighbours.push_back(std::make_pair(node_id,weight));
+}
+
+int Node::deg() const
+{
+  return neighbours.size();
+}
+
+WeightedGraph::WeightedGraph(size_t num_nodes) : nodes(num_nodes)
+{
+
+}
+
+void WeightedGraph::add_edge(int from, int to, double weight)
+{
+  nodes[from].add_edge(to, weight);
+  nodes[to].add_edge(from, weight);
+}
+
+std::list<std::pair<int, double>> WeightedGraph::adjList(int node_id) const
+{
+  return (nodes[node_id]).neighbours;
+}
+
+int WeightedGraph::deg(int node_id) const
+{
+  return nodes[node_id].deg();
+}
+
+size_t WeightedGraph::num_nodes() const
+{
+  return nodes.size();
+}
+
+std::pair<int,double> WeightedGraph::min_neighbour(int node_id) const
+{
+  if (adjList(node_id).empty())
+  {
+    return std::make_pair(0,0);
+  }
+  int result = (adjList(node_id).front()).first;
+  int current_min = (adjList(node_id).front()).second;
+  for (const auto& i : adjList(node_id))
+  {
+    if (current_min > i.second)
+    {
+      current_min = i.second;
+      result = i.first;
+    }
+  }
+  return std::make_pair(result,current_min);
+}
+
+// removes duplicate edges, leaving only the lightest edge (guarantees m = O(n^2))
+
+WeightedGraph WeightedGraph::remove_parallel() const
+{
+  WeightedGraph G(num_nodes());
+  for (int i = 0; i < num_nodes(); i++)
+  {
+    std::unordered_map<int, double> lightestEdges;
+    for (const auto& j: adjList(i))
+    {
+      int to = j.first;
+      double weight = j.second;
+      if (lightestEdges.find(to) == lightestEdges.end() || weight < lightestEdges[to])
+      {
+         lightestEdges[to] = weight;
+      }
+    }
+    for (const auto& [to, weight] : lightestEdges)
+      {
+        G.nodes[i].add_edge(to, weight);
+      }
+  }
+  return G;
+}
+

weighted_graph.h

@@ -0,0 +1,33 @@
+#ifndef C___WEIGHTEDGRAPH_H
+#define C___WEIGHTEDGRAPH_H
+
+#include <list>
+#include <vector>
+#include <algorithm>
+
+
+struct Node {
+  std::list<std::pair<int, double>> neighbours;
+  Node() = default;
+  Node(std::list<std::pair<int, double>> neighbours);
+  void add_edge(int node_id, double weight);
+  int deg() const;
+};
+
+class WeightedGraph {
+public:
+  WeightedGraph(size_t num_nodes);
+  void add_edge(int from, int to, double weight);
+  std::list<std::pair<int, double>> adjList(int node_id) const;
+  size_t num_nodes() const;
+  int deg(int v) const;
+  std::pair<int,double> min_neighbour(int node_id) const;
+  WeightedGraph remove_parallel() const;
+
+private:
+  std::vector<Node> nodes;
+};
+
+#endif //C___WEIGHTEDGRAPH_H
+
+