Question

1. Implement the public function BFTraversal ), which outputs a breadth-first traversal of the graph. To do so, you need to implement a private function BFS (), which performs breadth-first search from a given vertex. In BFTraversal (), you may need to call BFS () multiple times (in loops) in order to perform breadth-first search in sub-graphs that are not connected NOTE: in both BFTraversal) and BFS (), whenever you can choose from multiple un visited vertices to proceed, please choose the one with the lowest index for better grading consistence. For example, you always start BFTraversal by performing BFS () or vertex 0, and then other vertices if necessary. Hint: You will need to use a queue to implement the function BFS(). You may use an int queue to store the indices to represent vertices in queue. The C++ Standard Template Library (STL) provides the template class queue for you to use by # include<queue>. See plusplus.com/reference/queue/queue/ to learn the syntax of the declaration of an int queue and its member functions Implement the public function DFTraversal (), which outputs a depth-first traversal of the graph. To do so, you need to implement a private function DFS (), which performs depth-first search from a given vertex. In DFTraversal (), you may need to call DFS () multiple times (in loops) in order to perform depth-first search in sub-graphs that are not connected. Furthermore, you are asked to implement DFS () using recursion NOTE: in both DFTraversal) and DFS (, whenever you can choose from multiple un visited vertices to proceed, please choose the one with the lowest index for better grading consistence. For example, you always start DFTraversal ) by performing DFS () on vertex 0, and then other vertices if necessary. Hint: You are expected to implement DFS () using recursion. Nonetheless, a for loop is also expected within DFS (), i.e., the recursive calls are within the loop. (This is a counterexample to disprove "a recursive function must have absolutely no loop inside".) 2.

#include <iostream>

#include <queue>

using namespace std;

class Graph {

public:

Graph(int n);

~Graph();

void addEdge(int src, int tar);

void BFTraversal();

void DFTraversal();

void printVertices();

void printEdges();

private:

int vertexCount;

int edgeCount;

bool** adjMat;

void BFS(int n, bool marked[]);

void DFS(int n, bool marked[]);

};

Graph::Graph(int n=0) {

vertexCount = n;

edgeCount = 0;

if(n == 0)

adjMat = 0;

else {

adjMat = new bool* [n];

for(int i=0; i < n; i++)

adjMat[i] = new bool [n];

for(int i=0; i < n; i++)

for(int j=0; j < n; j++)

adjMat[i][j] = 0;

}

}

Graph::~Graph() {

for(int i=0; i < vertexCount; i++)

delete [] adjMat[i];

delete [] adjMat;

}

void Graph::addEdge(int src, int tar) {

if(src < 0 || tar < 0 || src > vertexCount-1 || tar > vertexCount-1)

cout << "Invalid vertex index! No edge has been added." << endl;

else if(src == tar)

cout << "No self loop! No edge has been added." << endl;

else if (adjMat[src][tar] == 1)

cout << "This edge already exists. No edge has been added." << endl;

else {

adjMat[src][tar] = 1;

edgeCount++;

}

}

void Graph::BFTraversal() {

// TO DO

// You are expected to call BFS() in this function,

// potentially multiple times in loops.

}

void Graph::BFS(int n, bool marked[]) {

// TO DO

// You are expected to use a queue<int> from C++ STL.

// This function is not recursive, and you are expected to use a while loop.

}

void Graph::DFTraversal() {

// TO DO

// You are expected to call DFS() in this function,

// potentially multiple times in loops.

}

void Graph::DFS(int n, bool marked[]) {

// TO DO

// You are asked to implement this function using recursion.

// However, a for loop is expected --- the recursive calls are within the loop.

}

void Graph::printVertices() {

cout << "This directed graph has " << vertexCount << " vertex (vertices), ";

cout << "indexed from 0 to " << vertexCount-1 << endl;

}

void Graph::printEdges() {

cout << "This directed graph has " << edgeCount << " edge(s):" << endl;

for(int i=0; i < vertexCount; i++)

for(int j=0; j < vertexCount; j++)

if(adjMat[i][j])

cout << "(" << i << "," << j << ")" << endl;

}

int main() {

cout << "Constructing a directed graph..." << endl;

cout << "Please enter the number of vertices in this graph: ";

int n = 0;

cin >> n;

Graph G(n);

while(1) {

cout << "Adding an directed edge..." << endl;

cout << "Trying to add an edge (-1,-1) indicates the end of adding edges and prints outputs." << endl;

cout << "Please enter the vertex index of the source of the edge to be added: ";

int a;

cin >> a;

cout << "Please enter the vertex index of the target of the edge to be added: ";

int b;

cin >> b;

if( a == -1 && b == -1)

break;

else

G.addEdge(a,b);

}

cout << "A directed graph has been constructed:" << endl;

G.printVertices();

G.printEdges();

cout << "Breadth-First Traversal: ";

G.BFTraversal();

cout << "Depth-First Traversal: ";

G.DFTraversal();

return 0;

}

Answer 1

#include <iostream>

#include <list>

#include <queue>

using namespace std;

class Graph {

public:

Graph(int n);

~Graph();

void addEdge(int src, int tar);

void BFTraversal();

void DFTraversal();

void printVertices();

void printEdges();

private:

int vertexCount;

int edgeCount;

bool** adjMat;

void BFS(int n, bool marked[]);

void DFS(int n, bool marked[]);

};

Graph::Graph(int n=0) {

vertexCount = n;

edgeCount = 0;

if(n == 0)

adjMat = 0;

else {

adjMat = new bool* [n];

for(int i=0; i < n; i++)

adjMat[i] = new bool [n];

for(int i=0; i < n; i++)

for(int j=0; j < n; j++)

adjMat[i][j] = 0;

}

}

Graph::~Graph() {

for(int i=0; i < vertexCount; i++)

delete [] adjMat[i];

delete [] adjMat;

}

void Graph::addEdge(int src, int tar) {

if(src < 0 || tar < 0 || src > vertexCount-1 || tar > vertexCount-1)

cout << "Invalid vertex index! No edge has been added." << endl;

else if(src == tar)

cout << "No self loop! No edge has been added." << endl;

else if (adjMat[src][tar] == 1)

cout << "This edge already exists. No edge has been added." << endl;

else {

adjMat[src][tar] = 1;

edgeCount++;

}

}

void Graph::BFTraversal() {

// TO DO

// You are expected to call BFS() in this function,

// potentially multiple times in loops.

bool *marked = new bool[vertexCount]; // array that mark the visited status of node

for(int i = 0; i < vertexCount; i++)

marked[i] = false; // initialize all elements of maeked array to false initially

  

// calling BFS on each untraversed node, basically this is useful when we have several components in graph that are not connected with each other

for(int j=0;j<vertexCount;j++)

{

if (marked[j]== false)

{

cout<<" \nTraversing from source : " <<j<<endl; // printing the source node

BFS(j,marked); // calling DFS on untraversed node

}

}

  

  

}

void Graph::BFS(int n, bool marked[]) {

// TO DO

// You are expected to use a queue<int> from C++ STL.

// This function is not recursive, and you are expected to use a while loop.

queue<int> queue;

  

queue.push(n); // pushing the element in queue

marked[n] = true; // mark the visisted element

  

while (!queue.empty()) {

  

n = queue.front();

queue.pop();

  

cout << n << " ";

  

// Enqueue all adjacent of n and mark them visited  

for (int i=n; i<vertexCount ;i++)

{

if (!marked[i] && adjMat[n][i]==1)

{

queue.push(i);

marked[i] = true;

}

}

}

}

void Graph::DFTraversal() {

// TO DO

// You are expected to call DFS() in this function,

// potentially multiple times in loops.

bool *marked = new bool[vertexCount]; // array that mark the visited status of node

for(int i = 0; i < vertexCount; i++)

marked[i] = false; // initialize all elements of maeked array to false initially

// calling DFS on each untraversed node, basically this is useful when we have several components in graph that are not connected with each other  

for(int j=0;j<vertexCount;j++)

{

if (marked[j]== false)

{

cout<<" \nTraversing from source : " <<j<<endl; // printing the source node

DFS(j,marked); // calling DFS on untraversed node

}

}

}

void Graph::DFS(int n, bool marked[]) {

// TO DO

// You are asked to implement this function using recursion.

// However, a for loop is expected --- the recursive calls are within the loop.

cout << n << " "; // printing the node

marked[n] = true; // making visited node true

for (int i=n; i<vertexCount ;i++)

{

if (!marked[i] && adjMat[n][i]==1)

{

DFS(i,marked); // calling DFS again for unvisited node

  

}

}

}

void Graph::printVertices() {

cout << "This directed graph has " << vertexCount << " vertex (vertices), ";

cout << "indexed from 0 to " << vertexCount-1 << endl;

}

void Graph::printEdges() {

cout << "This directed graph has " << edgeCount << " edge(s):" << endl;

for(int i=0; i < vertexCount; i++)

for(int j=0; j < vertexCount; j++)

if(adjMat[i][j])

cout << "(" << i << "," << j << ")" << endl;

}

int main() {

cout << "Constructing a directed graph..." << endl;

cout << "Please enter the number of vertices in this graph: ";

int n = 0;

cin >> n;

Graph G(n);

while(1) {

cout << "Adding an directed edge..." << endl;

cout << "Trying to add an edge (-1,-1) indicates the end of adding edges and prints outputs." << endl;

cout << "Please enter the vertex index of the source of the edge to be added: ";

int a;

cin >> a;

cout << "Please enter the vertex index of the target of the edge to be added: ";

int b;

cin >> b;

if( a == -1 && b == -1)

break;

else

G.addEdge(a,b);

}

cout << "A directed graph has been constructed:" << endl;

G.printVertices();

G.printEdges();

cout << "Breadth-First Traversal: ";

G.BFTraversal();

cout << "\nDepth-First Traversal: ";

G.DFTraversal();

return 0;

}

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screenshot of output (examp​le containing a single connected components) $CANew folder\HomeworkLib queue.exe Please enter the vertex index of the source of the edge to be added: 0 Please enter the vertex index of the target of the edge to be added: 1 Adding an directed edge... Trying to add an edge (-1,-1) indicates the end of adding edges and prints outputs. Please enter the vertex index of the source of the edge to be added: 0 Please enter the vertex index of the target of the edge to be added: 2 Adding an directed edge... Trying to add an edge (-1,-1) indicates the end of adding edges and prints outputs. Please enter the vertex index of the source of the edge to be added: 1 Please enter the vertex index of the target of the edge to be added: 3 Adding an directed edge... Trying to add an edge (-1,-1) indicates the end of adding edges and prints outputs. Please enter the vertex index of the source of the edge to be added: 2 Please enter the vertex index of the target of the edge to be added: 4 Adding an directed edge... Trying to add an edge (-1,-1) indicates the end of adding edges and prints outputs. Please enter the vertex index of the source of the edge to be added: 2 Please enter the vertex index of the target of the edge to be added: 5 Adding an directed edge... Trying to add an edge (-1,-1) indicates the end of adding edges and prints outputs. Please enter the vertex index of the source of the edge to be added: -1 Please enter the vertex index of the target of the edge to be added: -1 A directed graph has been constructed: This directed graph has 6 vertex (vertices), indexed from 0 to 5 This directed graph has 5 edge(s) (0,2) (2,4) (2,5) Breadth-First Traversal: Traversing from source0 01 2 3 45 Depth-First Traversal: Traversing from source0 0 1 3 2 45 Process exited after 23.89 seconds with return value 0 Press any key to continue . . .$

screenshot of output (examp​le containing a two connected components)

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