Added Prim's algorithm
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4 changed files with 225 additions and 0 deletions
6
min_spanning_tree/prim/CMakeLists.txt
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6
min_spanning_tree/prim/CMakeLists.txt
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cmake_minimum_required(VERSION 3.10)
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project(prim)
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add_executable(prim
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../../weighted_graph.cpp
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../../weighted_graph.h
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prim.cpp)
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97
min_spanning_tree/prim/prim.cpp
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min_spanning_tree/prim/prim.cpp
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// 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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}
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weighted_graph.cpp
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weighted_graph.cpp
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#include "weighted_graph.h"
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#include <unordered_map>
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#include <iostream>
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Node::Node(std::list<std::pair<int, double>> neighbours_) : neighbours(std::move(neighbours_))
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{
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}
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void Node::add_edge(int node_id, double weight)
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{
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neighbours.push_back(std::make_pair(node_id,weight));
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}
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int Node::deg() const
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{
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return neighbours.size();
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}
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WeightedGraph::WeightedGraph(size_t num_nodes) : nodes(num_nodes)
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{
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}
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void WeightedGraph::add_edge(int from, int to, double weight)
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{
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nodes[from].add_edge(to, weight);
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nodes[to].add_edge(from, weight);
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}
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std::list<std::pair<int, double>> WeightedGraph::adjList(int node_id) const
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{
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return (nodes[node_id]).neighbours;
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}
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int WeightedGraph::deg(int node_id) const
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{
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return nodes[node_id].deg();
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}
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size_t WeightedGraph::num_nodes() const
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{
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return nodes.size();
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}
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std::pair<int,double> WeightedGraph::min_neighbour(int node_id) const
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{
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if (adjList(node_id).empty())
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{
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return std::make_pair(0,0);
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}
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int result = (adjList(node_id).front()).first;
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int current_min = (adjList(node_id).front()).second;
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for (const auto& i : adjList(node_id))
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{
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if (current_min > i.second)
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{
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current_min = i.second;
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result = i.first;
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}
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}
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return std::make_pair(result,current_min);
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}
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// removes duplicate edges, leaving only the lightest edge (guarantees m = O(n^2))
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WeightedGraph WeightedGraph::remove_parallel() const
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{
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WeightedGraph G(num_nodes());
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for (int i = 0; i < num_nodes(); i++)
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{
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std::unordered_map<int, double> lightestEdges;
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for (const auto& j: adjList(i))
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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 (lightestEdges.find(to) == lightestEdges.end() || weight < lightestEdges[to])
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{
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lightestEdges[to] = weight;
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}
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}
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for (const auto& [to, weight] : lightestEdges)
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{
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G.nodes[i].add_edge(to, weight);
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}
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}
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return G;
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}
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33
weighted_graph.h
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33
weighted_graph.h
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#ifndef C___WEIGHTEDGRAPH_H
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#define C___WEIGHTEDGRAPH_H
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#include <list>
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#include <vector>
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#include <algorithm>
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struct Node {
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std::list<std::pair<int, double>> neighbours;
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Node() = default;
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Node(std::list<std::pair<int, double>> neighbours);
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void add_edge(int node_id, double weight);
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int deg() const;
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};
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class WeightedGraph {
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public:
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WeightedGraph(size_t num_nodes);
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void add_edge(int from, int to, double weight);
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std::list<std::pair<int, double>> adjList(int node_id) const;
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size_t num_nodes() const;
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int deg(int v) const;
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std::pair<int,double> min_neighbour(int node_id) const;
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WeightedGraph remove_parallel() const;
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private:
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std::vector<Node> nodes;
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};
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#endif //C___WEIGHTEDGRAPH_H
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