I want you to solve this in java code and the graph use $4$ example with $7$ nodes for each

And find complexity time for each run

Project $-$ Phase $2($Coding$)$

Total marks: $[4+2]$

There are many applications of Breadth First Search $($BFS$)$ and Depth First Search $($DFS$)$ algorithms, such as:

Shortest Path Finding: Finding the shortest path between two nodes in an unweighted graph. By keeping track of the parent of each node during the traversal, the shortest path can be reconstructed.

Cycle Detection: Detecting cycles in a graph. If a node is visited twice during the traversal, it indicates the presence of a cycle.

Choose one from the above problems, and solve it using BFS$/$DFS$,$ and then implement the selected problem using BFS or DFS$.$ And then:

Explain the selected problem briefly. $(1$ mark$)$

Implement the selected algorithm BFS$/$DFS for solving the selected problem. $(1$ mark$)$

Run the selected algorithm with two different examples. This is to show that your algorithms work well. $(1$ mark$)$

Find computational complexity of each algorithm $($analyzing line of codes$).(1$ mark$)$

What to submit for phase$2?$

A report of your whole project phase$2$ including problem description, implementation code and screenshots of two different examples, and analysis for the algorithm. $(2$ marks; $1$ for organization and one for grammar$)$