shyamtayal / daa_assign_6

Assignment - 3

Team Members

Enrollment No.	Name	GithubId
IIB2019007	Aditya Raj	Adityahulk
IIB2019008	Shyam Tayal	shyamTayal
IIB2019009	Abhijeet Sonkar	Abhijeet-sonkar

Group No-"22"

Faculty Name-"Dr. Rahul Kala"

Mentor Name- "Md. Meraz"

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Problem Statement

Given a directed graph, find out if a vertex v is reachable from another vertex u for all vertex pairs (u, v) in the given graph. Here reachable mean that there is a path from vertex u to v. The reach-ability matrix is called transitive closure of a graph.

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How to use code

First Step is to Download/clone the repository

git clone https://github.com/shyamTayal/daa_assign_6

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Run the Code

Change directory to the solution folder

cd daa_assign_6/Solution/
g++ closure_dfs.cpp -o dfs
./dfs

Output (by Solution files)

Testcase - 1

Enter the number of node : 4
Enter the number of edges : 5
0 1
0 2
1 2
2 0
2 3

****************** Reachability matrix ********************
1 1 1 1
1 1 1 1
1 1 1 1
0 0 0 1

***********************************************************

Enter the number of queries to check if v can reach u : 3
Enter the pair (v,u) to check if node v can reach node u : 2 1
Yes, 2 can reach 1
Enter the pair (v,u) to check if node v can reach node u : 3 0
No, 3 cannot reach 0
Enter the pair (v,u) to check if node v can reach node u : 1 3
Yes, 1 can reach 3

Personalised Initialization Method (optional)

Change Directory to Testing Directory

cd daa_assign_6/testing/
g++ testcase_gen.cpp -o inp
./inp

Above commands will create 1 testing file :

• input_testcase.txt

Above testing file contains graph input for 100 testcases with with value of No. of nodes ranging from 20 to 220 and No. of edges ranging from 10 to 2010

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Testing

Testing files have already been added so above step can be skipped. To be run in Testing Directory

Test Flloyd Warshal Algorithm

g++ test_flloyd -o flloyd
./floyyd

Test DFS Algorithm

g++ test_dfs -o dfs
./floyyd

• Both Above commands create two files one containing the reachability matrix generated by the input graph and other containing the Time complexity calculation data.

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Theory

• Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.

• The Floyd Warshall Algorithm is for solving the All Pairs Shortest Path problem. The problem is to find shortest distances between every pair of vertices in a given edge weighted directed Graph.

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Analysis-

Time Complexity

Space Complexity

Both algorithms have space complexity O(N²)
Since for the purpose of storing the graph elements (nodes and edges) and reachability matrix in form of a 2D - array

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References

https://en.wikipedia.org/wiki/Floyd\%E2\%80\%93Warshall\_algorithm

https://www.geeksforgeeks.org/depth-first-search-or-dfs-for-a-graph/