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Implement the BFS and DFS traversal methods for directed graphs in Java.

For BFS$,$ implement it to find the distance $($shortest path length$)$ from

a source vertex s to every vertex in the graph.

You will need to complete the method bodies of:

void bfs$($Vertex s$)$

void dfs$($Vertex s$)$

void dfsVisit$($Vertex current$)$

The BFS class is coded as a subclass of the MyGraph class and is also

using the MyLinkedQueue class, which is a modified version of the

LinkedQueue class from Module $3.$ These two classes are provided in the

"MyGraph.java" and "MyLinkedQueue.java" files. Please place them under

the same package$/$folder$.$

Your output may look as follows:

$--------------------------------$

DFS traversal starting from vertex $3$: $3406578912$

BFS traversal starting from vertex $3$: $3460597812$

Shortest path lengths from $3$ to every vertex:

Vertices: $0123456789$

Distances: $2340121332$

$==========$ Note $============$

$1.$ DO NOT MODIFY OR DELETE ANY GIVEN CODE OR COMMENTS!!!

$2.$ You ONLY need to write code under each comment "YOUR CODE GOES HERE".

$3.$ Modify the file name to "GraphSearch.java" to compile and run.

$4.$ Make sure that you place the "MyGraph.java" and "MyLinkedQueue.java"

files under the same package$/$folder as your current file to compile

and run the code.

$============================$

import java.util.ArrayList;

import java.util.LinkedList;

$//-----$ Vertex class $-------$

class Vertex $\{$

L label;

int color; $//0=$ GRAY, $1=$ RED, $2=$ BLACK

int distance;

public Vertex$($L label$)\{$

this.label $=$ label;

this.color $=0$; $//$ GRAY

this.distance $=$ Integer.MAX$\_$VALUE;

$\}$

$\}//----$ End of Vertex class $-----$

public class GraphSearch extends MyGraph$>\{$

$//$ Breadth$-$First Search to find shortest path lengths from source vertex s to every vertex

public void bfs$($Vertex s$)\{$

if $(!$vertices.contains$($s$))$

throw new IllegalArgumentException$("$Source vertex $"+$ s$.$label $+"$ not found!"$)$;

MyLinkedQueue$>$ queue $=$ new MyLinkedQueue;

$//$ YOUR CODE GOES HERE $--$Part $1/3--$

$\}$

$//$ Depth$-$First Search starting from vertex s

public void dfs$($Vertex s$)\{$

if $(!$vertices.contains$($s$))$

throw new IllegalArgumentException$("$Source vertex $"+$ s$.$label $+"$ not found!"$)$;

$//$ YOUR CODE GOES HERE $--$Part $2/3--$

$\}$

private void dfsVisit$($Vertex current$)\{$

$//$ YOUR CODE GOES HERE $--$Part $3/3--$

$\}$

public ArrayList$>$ getVertices$()\{$

return vertices;

$\}$

$//------$ Driver $-------$

public static void main$($String$[]$ args$)\{$

$//$ Create a graph

GraphSearch graph $=$ new GraphSearch;

$//$ Add ten vertices with integer labels

Vertex$[]$ vertices $=$ new Vertex$[10]$;

for $($int i $=0$; i $<mtext></mtext><mn>1</mn><mn>0</mn>$; i$++)\{$

vertices$[$i$]=$ new Vertexi$)$;

graph.addVertex$($vertices$[$i$])$;

$\}$

$//$ Define $18$ edges

int$[][]$ edges $=\{$

$\{1,2\},\{1,3\},\{1,5\},\{2,4\},\{2,5\},\{2,7\},$

$\{3,4\},\{3,6\},\{4,0\},\{5,7\},\{5,8\},\{6,5\},$

$\{6,9\},\{7,0\},\{8,9\},\{8,0\},\{9,0\},\{9,1\}$

$\}$;

$//$ Add the edges

for $($int$[]$ edge : edges$)\{$

int u $=$ edge$[0]$;

int v $=$ edge$[1]$;

graph.addEdge$($vertices$[$u$],$ vertices$[$v$])$;

$\}$

int s $=3$;

$//$ Perform DFS from vertex $3$

$//$ Print out the order of vertices being first visited by DFS

System.out.print$("$DFS traversal starting from vertex $"+$ vertices$[$s$].$label $+"$: $")$;

graph.dfs$($vertices$[$s$])$;

System.out.println$()$;

$//$ Perform BFS from vertex $3$

$//$ Print out the order of vertices being first visited by BFS

System.out.print$("$BFS traversal starting from vertex $"+$ vertices$[$s$].$label $+"$: $")$;

graph.bfs$($vertices$[$s$])$;

System.out.println$()$;

$//$ Print the distance$/$shortest path lengths from vertex $3$ to other vertices

System.out.println$("$Shortest path lengths from $"+$ s $+"$ to every vertex:"$)$;

System.out.print$("$Vertices: $")$;

for $($Vertex vertex : graph.getVertices$())$

System.out.print$($vertex$.$label $+"")$;

System.out.println$()$;

System.out.print$("$Distances: $")$;

for $($Vertex vertex : graph.getVertices$())$

System.out.print$($vertex$.$distance $+"")$;

$\}$

$\}$