Write a program to perform the following in C++: 1)Implement Dijkstra’s Algorith

Question

Write a program to perform the following in C++:

1)Implement Dijkstra’s Algorithm .

2)Read a graph data file. Each line contains weighted edge: “vertex, vertex, weight”

3)Using the implemented algorithm, find the shortest-paths tree from vertex M.

4)Report the shortest-paths tree from vertex M and distance to each other vertex.

graph.txt:

A,J,91
A,H,86
A,B,38
A,N,37
A,L,100
A,V,64
A,S,84
A,M,9
A,W,54
A,K,46
B,J,27
B,V,93
B,H,40
B,G,49
B,F,94
B,N,95
B,C,45
B,Z,42
B,L,15
C,Q,14
C,W,10
C,L,87
C,R,77
C,N,92
C,S,79
C,T,3
C,D,60
C,J,43
D,P,26
D,W,12
D,K,21
D,Q,5
D,V,75
D,T,59
D,J,2
D,R,11
F,J,63
F,X,72
F,L,88
F,G,51
F,V,61
F,P,39
F,M,69
F,W,65
G,N,76
G,X,13
G,Z,56
G,H,82
G,Q,32
G,W,20
G,V,18
H,Z,74
H,P,85
H,L,62
H,M,44
H,K,25
H,J,98
H,R,19
J,V,31
J,M,50
J,S,57
J,Q,17
J,T,22
J,P,68
K,T,67
K,L,81
K,M,55
K,P,52
K,S,83
K,X,41
L,R,36
L,N,30
L,T,53
L,S,23
L,Q,66
M,S,6
M,Q,29
M,N,71
M,R,8
M,T,96
N,T,16
N,R,78
N,Q,73
N,V,24
P,Z,28
P,W,48
P,Q,7
P,T,47
Q,W,99
Q,S,1
Q,Z,89
R,V,70
R,X,35
R,S,33
S,T,34
S,X,90
T,X,4
T,W,58
V,X,80
W,Z,97

Explanation / Answer

// C++ program for Dijkstra's single

// source shortest path algorithm.

// The program is for adjacency matrix

// representation of the graph.

#include <iostream>

#include <climits>

#include <fstream>

using namespace std;

// Number of vertices

// in the graph

#define V 26

// A utility function to find the

// vertex with minimum distance

// value, from the set of vertices

// not yet included in shortest

// path tree

int minDistance(int dist[],

bool sptSet[])

{

// Initialize min value

int min = INT_MAX, min_index;

for (int v = 0; v < V; v++)

if (sptSet[v] == false &&

dist[v] <= min)

min = dist[v], min_index = v;

return min_index;

}

// Function to print shortest

// path from source to j

// using parent array

void printPath(int parent[], int j)

{

// Base Case : If j is source

if (parent[j] == - 1)

return;

printPath(parent, parent[j]);

printf("%d ", j);

}

// A utility function to print

// the constructed distance

// array

void printSolution(int dist[], int n,

int parent[])

{

int src = 0;

printf("Vertex Distance Path");

for (int i = 1; i < V; i++)

{

printf(" %d -> %d %d %d ",

src, i, dist[i], src);

printPath(parent, i);

}

}

// Funtion that implements Dijkstra's

// single source shortest path

// algorithm for a graph represented

// using adjacency matrix representation

void dijkstra(int graph[V][V], int src)

{

// The output array. dist[i]

// will hold the shortest

// distance from src to i

int dist[V];

// sptSet[i] will true if vertex

// i is included / in shortest

// path tree or shortest distance

// from src to i is finalized

bool sptSet[V];

// Parent array to store

// shortest path tree

int parent[V];

// Initialize all distances as

// INFINITE and stpSet[] as false

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

{

parent[0] = -1;

dist[i] = INT_MAX;

sptSet[i] = false;

}

// Distance of source vertex

// from itself is always 0

dist[src] = 0;

// Find shortest path

// for all vertices

for (int count = 0; count < V - 1; count++)

{

// Pick the minimum distance

// vertex from the set of

// vertices not yet processed.

// u is always equal to src

// in first iteration.

int u = minDistance(dist, sptSet);

// Mark the picked vertex

// as processed

sptSet[u] = true;

// Update dist value of the

// adjacent vertices of the

// picked vertex.

for (int v = 0; v < V; v++)

// Update dist[v] only if is

// not in sptSet, there is

// an edge from u to v, and

// total weight of path from

// src to v through u is smaller

// than current value of

// dist[v]

if (!sptSet[v] && graph[u][v] &&

dist[u] + graph[u][v] < dist[v])

{

parent[v] = u;

dist[v] = dist[u] + graph[u][v];

}

}

// print the constructed

// distance array

printSolution(dist, V, parent);

}

void readFromFile(int graph[26][26]) {

char start, end;

int weight;

ifstream inFile;

inFile.open("graph.txt");

if (!inFile) {

printf("Unable to open file");

return;

}

while (inFile >> start >> end >> weight) {

graph[start-65][end-65] = weight;

}

inFile.close();

}

// Driver Code

int main()

{

// Let us create the example

// graph discussed above

int graph[V][V];

for(int i=0; i<V; i++) {

for(int j=0; j<V; j++) {

graph[i][j] = 0;

}

}

readFromFile(graph);

dijkstra(graph, 12); // 12 represents 'M'

return 0;

}

NOTE: Please note that due to lack of time, my reading from file logic reads only space separated lines (not comma separated). Hence, you might need to change the graph.txt to something like this:

graph.txt:

A J 91
A H 86
A B 38

............

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