#include<iostream>
#define INFINITY 999
using namespace std;
class Dijkstra{
private:
int adjMatrix[15][15];
int predecessor[15],distance[15];
bool mark[15]; //keep track of visited node
int source;
int numOfVertices;
public:
/*
* Function read() reads No of vertices, Adjacency Matrix and source
* Matrix from the user. The number of vertices must be greather than
* zero, all members of Adjacency Matrix must be postive as distances
* are always positive. The source vertex must also be positive from 0
* to noOfVertices - 1
*/
void read();
/*
* Function initialize initializes all the data members at the begining of
* the execution. The distance between source to source is zero and all other
* distances between source and vertices are infinity. The mark is initialized
* to false and predecessor is initialized to -1
*/
void initialize();
/*
* Function getClosestUnmarkedNode returns the node which is nearest from the
* Predecessor marked node. If the node is already marked as visited, then it search
* for another node.
*/
int getClosestUnmarkedNode();
/*
* Function calculateDistance calculates the minimum distances from the source node to
* Other node.
*/
void calculateDistance();
/*
* Function output prints the results
*/
void output();
void printPath(int);
};
void Dijkstra::read(){
cout<<"Enter the number of vertices of the graph(should be > 0)\n";
cin>>numOfVertices;
while(numOfVertices <= 0) {
cout<<"Enter the number of vertices of the graph(should be > 0)\n";
cin>>numOfVertices;
}
cout<<"Enter the adjacency matrix for the graph\n";
cout<<"To enter infinity enter "<<INFINITY<<endl;
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for(int i=0;i<numOfVertices;i++) {
cout<<"Enter the (+ve)weights for the row "<<i<<endl;
for(int j=0;j<numOfVertices;j++) {
cin>>adjMatrix[i][j];
while(adjMatrix[i][j]<0) {
cout<<"Weights should be +ve. Enter the weight again\n";
cin>>adjMatrix[i][j];
}
}
}
cout<<"Enter the source vertex\n";
cin>>source;
while((source<0) && (source>numOfVertices-1)) {
cout<<"Source vertex should be between 0 and"<<numOfVertices-1<<endl;
cout<<"Enter the source vertex again\n";
cin>>source;
}
}
void Dijkstra::initialize(){
for(int i=0;i<numOfVertices;i++) {
mark[i] = false;
predecessor[i] = -1;
distance[i] = INFINITY;
}
distance[source]= 0;
}
int Dijkstra::getClosestUnmarkedNode(){
int minDistance = INFINITY;
int closestUnmarkedNode;
for(int i=0;i<numOfVertices;i++) {
if((!mark[i]) && (minDistance >= distance[i])) {
minDistance = distance[i];
closestUnmarkedNode = i;
}
}
return closestUnmarkedNode;
}
void Dijkstra::calculateDistance(){
initialize();
int minDistance = INFINITY;
int closestUnmarkedNode;
int count = 0;
while(count < numOfVertices) {
closestUnmarkedNode = getClosestUnmarkedNode();
mark[closestUnmarkedNode] = true;
for(int i=0;i<numOfVertices;i++) {
if((!mark[i]) && (adjMatrix[closestUnmarkedNode][i]>0)) {
if(distance[i] > distance[closestUnmarkedNode]+adjMatrix[closestUnmarkedNode][i]) {
distance[i] = distance[closestUnmarkedNode]+adjMatrix[closestUnmarkedNode][i];
predecessor[i] = closestUnmarkedNode;
}
}
}
count++;
}
}
void Dijkstra::printPath(int node){
if(node == source)
cout<<(char)(node + 97)<<"..";
else if(predecessor[node] == -1)
cout<<"No path from “<<source<<”to "<<(char)(node + 97)<<endl;
else {
printPath(predecessor[node]);
cout<<(char) (node + 97)<<"..";
}
}
void Dijkstra::output(){
for(int i=0;i<numOfVertices;i++) {
if(i == source)
cout<<(char)(source + 97)<<".."<<source;
else
printPath(i);
cout<<"->"<<distance[i]<<endl;
}
}
int main(){
Dijkstra G;
G.read();
G.calculateDistance();
G.output();
return 0;
}
BFS
#include <iostream>
#include <ctime>
using namespace std;
/****************************************************************
Performs the Breadth-First Graph search for both directed and
undirected graphs. This algorithm explores all the findable nodes
in "layers".
@author Bibek Subedi
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*****************************************************************/
/****************************************************************
Class Queue represent a Queue data structure which is First In
First Out [FIFO] structured. It has operations like Enqueue which
adds an element at the rear side and Dequeue which removes the
element from front.
*****************************************************************/
struct node {
int info;
node *next;
};
class Queue {
private:
node *front;
node *rear;
public:
Queue();
~Queue();
bool isEmpty();
void enqueue(int);
int dequeue();
void display();
};
void Queue::display(){
node *p = new node;
p = front;
if(front == NULL){
cout<<"\nNothing to Display\n";
}else{
while(p!=NULL){
cout<<endl<<p->info;
p = p->next;
}
}
}
Queue::Queue() {
front = NULL;
rear = NULL;
}
Queue::~Queue() {
delete front;
}
void Queue::enqueue(int data) {
node *temp = new node();
temp->info = data;
temp->next = NULL;
if(front == NULL){
front = temp;
}else{
rear->next = temp;
}
rear = temp;
}
int Queue::dequeue() {
node *temp = new node();
int value;
if(front == NULL){
cout<<"\nQueue is Emtpty\n";
}else{
temp = front;
value = temp->info;
front = front->next;
delete temp;
}
return value;
}
bool Queue::isEmpty() {
return (front == NULL);
}
/************************************************************
Class Graph represents a Graph [V,E] having vertices V and
edges E.
************************************************************/
class Graph {
private:
int n; /// n is the number of vertices in the graph
int **A; /// A stores the edges between two vertices
public:
Graph(int size = 2);
~Graph();
bool isConnected(int, int);
void addEdge(int u, int v);
void BFS(int);
};
Graph::Graph(int size) {
int i, j;
if (size < 2) n = 2;
else n = size;
A = new int*[n];
for (i = 0; i < n; ++i)
A[i] = new int[n];
for (i = 0; i < n; ++i)
for (j = 0; j < n; ++j)
A[i][j] = 0;
}
Graph::~Graph() {
for (int i = 0; i < n; ++i)
delete [] A[i];
delete [] A;
}
/******************************************************
Checks if two given vertices are connected by an edge
@param u vertex
@param v vertex
@return true if connected false if not connected
******************************************************/
bool Graph::isConnected(int u, int v) {
return (A[u-1][v-1] == 1);
}
/*****************************************************
adds an edge E to the graph G.
@param u vertex
@param v vertex
*****************************************************/
void Graph::addEdge(int u, int v) {
A[u-1][v-1] = A[v-1][u-1] = 1;
}
/*****************************************************
performs Breadth First Search
@param s initial vertex
*****************************************************/
void Graph::BFS(int s) {
Queue Q;
/** Keeps track of explored vertices */
bool *explored = new bool[n+1];
/** Initailized all vertices as unexplored */
for (int i = 1; i <= n; ++i)
explored[i] = false;
/** Push initial vertex to the queue */
Q.enqueue(s);
explored[s] = true; /** mark it as explored */
cout << "Breadth first Search starting from vertex ";
cout << s << ": " << endl;
/** Unless the queue is empty */
while (!Q.isEmpty()) {
/** Pop the vertex from the queue */
int v = Q.dequeue();
/** display the explored vertices */
cout << v << " ";
/** From the explored vertex v try to explore all the
connected vertices */
for (int w = 1; w <= n; ++w)
/** Explores the vertex w if it is connected to v
and and if it is unexplored */
if (isConnected(v, w) &&!explored[w]) {
/** adds the vertex w to the queue */
Q.enqueue(w);
/** marks the vertex w as visited */
explored[w] = true;
}
}
cout << endl;
delete [] explored;
}
int main() {
/** Creates a graph with 12 vertices */
Graph g(12);
/** Adds edges to the graph */
g.addEdge(1, 2); g.addEdge(1, 3);
g.addEdge(2, 4); g.addEdge(3, 4);
g.addEdge(3, 6); g.addEdge(4,7);
g.addEdge(5, 6); g.addEdge(5, 7);
clock_t t1;
t1 = clock();
/** Explores all vertices findable from vertex 1 */
g.BFS(1);
float diff = (double)(clock() - t1)/CLOCKS_PER_SEC;
cout <<endl<< "The time taken for Breadth first search: "<< diff << endl;
}
DFS
#include <iostream>
#include <ctime>
#include <malloc.h>
using namespace std;
struct node{
int info;
struct node *next;
};
class stack{
struct node *top;
public:
stack();
void push(int);
int pop();
bool isEmpty();
void display();
};
stack::stack(){
top = NULL;
}
void stack::push(int data){
node *p;
if((p=(node*)malloc(sizeof(node)))==NULL){
cout<<"Memory Exhausted";
exit(0);
}
p = new node;
p->info = data;
p->next = NULL;
if(top!=NULL){
p->next = top;
}
top = p;
}
int stack::pop(){
struct node *temp;
int value;
if(top==NULL){
cout<<"\nThe stack is Empty"<<endl;
}else{
temp = top;
top = top->next;
value = temp->info;
delete temp;
}
return value;
}
bool stack::isEmpty(){
return (top == NULL);
}
void stack::display(){
struct node *p = top;
if(top==NULL){
cout<<"\nNothing to Display\n";
}else{
cout<<"\nThe contents of Stack\n";
while(p!=NULL){
cout<<p->info<<endl;
p = p->next;
}
}
}
class Graph {
private:
int n;
int **A;
public:
Graph(int size = 2);
~Graph();
bool isConnected(int, int);
void addEdge(int x, int y);
void DFS(int, int);
};
Graph::Graph(int size) {
int i, j;
if (size < 2) n = 2;
else n = size;
A = new int*[n];
for (i = 0; i < n; ++i)
A[i] = new int[n];
for (i = 0; i < n; ++i)
for (j = 0; j < n; ++j)
A[i][j] = 0;
}
Graph::~Graph() {
for (int i = 0; i < n; ++i)
delete [] A[i];
delete [] A;
}
bool Graph::isConnected(int x, int y) {
return (A[x-1][y-1] == 1);
}
void Graph::addEdge(int x, int y) {
A[x-1][y-1] = A[y-1][x-1] = 1;
}
void Graph::DFS(int x, int required){
stack s;
bool *visited = new bool[n+1];
int i;
for(i = 0; i <= n; i++)
visited[i] = false;
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s.push(x);
visited[x] = true;
if(x == required) return;
cout << "Depth first Search starting from vertex ";
cout << x << ": " << endl;
while(!s.isEmpty()){
int k = s.pop();
if(k == required) break;
cout<<k<<" ";
for (i = n; i >= 0; --i)
if (isConnected(k, i) &&!visited[i]) {
s.push(i);
visited[i] = true;
}
}
cout<<endl;
delete [] visited;
}
int main(){
Graph g(8);
g.addEdge(1, 2); g.addEdge(1, 3); g.addEdge(1, 4);
g.addEdge(2, 5); g.addEdge(2, 6); g.addEdge(4, 7);
g.addEdge(4, 8);
g.DFS(1, 4);
return 0;
}
Trees