breadth_first_search.cpp File Reference

Breadth First Search Algorithm (Breadth First Search) More...

#include <algorithm>
#include <cassert>
#include <iostream>
#include <queue>
#include <vector>

Include dependency graph for breadth_first_search.cpp:

Namespaces
	graph
	Graph algorithms.

Typedefs
using	graph::adjacency_list = std::vector< std::vector< int > >
	Representation of the graph as an adjacency list. More...

Functions
void	graph::add_directed_edge (adjacency_list *graph, int u, int v)
	Adds a directed edge from vertex u to vertex v. More...
void	graph::add_undirected_edge (adjacency_list *graph, int u, int v)
	Adds an undirected edge from vertex u to vertex v. Essentially adds too directed edges to the adjacency list reprsentation of the graph. More...
std::vector< bool >	graph::breadth_first_search (const adjacency_list &graph, int start)
	Function performs the breadth first search algorithm over the graph. More...
static void	tests ()
int	main ()

Detailed Description

Breadth First Search Algorithm (Breadth First Search)

Author

Ayaan Khan

Breadth First Search also quoted as BFS is a Graph Traversal Algorithm. Time Complexity O(|V| + |E|) where V are the number of vertices and E are the number of edges in the graph.

Applications of Breadth First Search are

1. Finding shortest path between two vertices say u and v, with path length measured by number of edges (an advantage over depth first search algorithm)
2. Ford-Fulkerson Method for computing the maximum flow in a flow network.
3. Testing bipartiteness of a graph.
4. Cheney's Algorithm, Copying garbage collection.

And there are many more...

working

In the implementation below we first created a graph using the adjacency list representation of graph. Breadth First Search Works as follows it requires a vertex as a start vertex, Start vertex is that vertex from where you want to start traversing the graph. We maintain a bool array or a vector to keep track of the vertices which we have visited so that we do not traverse the visited vertices again and again and eventually fall into an infinite loop. Along with this boolen array we use a Queue.

1. First we mark the start vertex as visited.
2. Push this visited vertex in the Queue.
3. while the queue is not empty we repeat the following steps
   1. Take out an element from the front of queue
   2. Explore the adjacency list of this vertex if element in the adjacency list is not visited then we push that element into the queue and mark this as visited

Function Documentation

main()

int main

(

void

)

Main function

           {
    tests();
 
    size_t vertices = 0, edges = 0;
    std::cout << "Enter the number of vertices: ";
    std::cin >> vertices;
    std::cout << "Enter the number of edges: ";
    std::cin >> edges;
 
    graph::adjacency_list graph(vertices);
 
    std::cout << "Enter space-separated pairs of vertices that form edges: "
              << std::endl;
    while (edges--) {
        int u = 0, v = 0;
        std::cin >> u >> v;
        // Decrement the vertex index so that we can read more convenint
        // 1-based indexing from the user input.
        graph::add_directed_edge(&graph, u - 1, v - 1);
    }
 
    graph::breadth_first_search(graph, 0);
    return 0;
}

Here is the call graph for this function:

tests()

static void tests ( )

static

Test function

Test 1 Begin

Test 2 Begin

Test 3 Begins

                    {
    /// Test 1 Begin
    graph::adjacency_list graph(4, std::vector<int>());
    graph::add_undirected_edge(&graph, 0, 1);
    graph::add_undirected_edge(&graph, 1, 2);
    graph::add_undirected_edge(&graph, 2, 3);
 
    std::vector<bool> returned_result = graph::breadth_first_search(graph, 2);
    std::vector<bool> correct_result = {true, true, true, true};
 
    assert(std::equal(correct_result.begin(), correct_result.end(),
                      returned_result.begin()));
    std::cout << "Test 1 Passed..." << std::endl;
 
    /// Test 2 Begin
    returned_result = graph::breadth_first_search(graph, 0);
 
    assert(std::equal(correct_result.begin(), correct_result.end(),
                      returned_result.begin()));
    std::cout << "Test 2 Passed..." << std::endl;
 
    /// Test 3 Begins
    graph.clear();
    graph.resize(6);
    graph::add_directed_edge(&graph, 0, 1);
    graph::add_directed_edge(&graph, 0, 2);
    graph::add_directed_edge(&graph, 1, 3);
    graph::add_directed_edge(&graph, 2, 3);
    graph::add_directed_edge(&graph, 1, 4);
    graph::add_directed_edge(&graph, 3, 5);
 
    returned_result = graph::breadth_first_search(graph, 2);
    correct_result = {false, false, true, true, false, true};
 
    assert(std::equal(correct_result.begin(), correct_result.end(),
                      returned_result.begin()));
    std::cout << "Test 3 Passed..." << std::endl;
}

Here is the call graph for this function: