comments have been used to explain working of the code.
#include <bits/stdc++.h>
#define V 5 // update NO of vertices according to question.
using namespace std;
// 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;
}
// A utility function to print the constructed distance array
int printSolution(int dist[] , int n)
{
cout<<"Vertex Distance from Source"<<endl;
for (int i = 0; i < V; i++)
cout<<i<<" "<<dist[i]<<endl;
}
// Function 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)
{
int dist[V]; // The output array. dist[i] will hold the
shortest
// distance from src to i
bool sptSet[V]; // sptSet[i] will true if vertex i is included in
shortest
// path tree or shortest distance from src to i is finalized
// Initialize all distances as INFINITE and stpSet[] as false
for (int i = 0; i < V; i++)
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 the 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] !=
INT_MAX
&& dist[u]+graph[u][v] < dist[v])
dist[v] = dist[u] + graph[u][v];
}
// print the constructed distance array
printSolution(dist, V);
}
// driver program to test above function
int main()
{
int src, des,weight;
int graph[V][V];
memset(graph,0,sizeof(graph));
char ch;
cout<<"Enter the edges and weigths"<<endl;
while(1){
cin>>src>>des>>weight; // adding edges in a egde
table
graph[src][des]=weight;
graph[des][src]=weight;
cout<<"More edges(Y for yes and N for no)
:"<<endl;
cin>>ch;
if(ch!='Y'){
break;
}
}
dijkstra(graph, 0);
return 0;
}
output
Dijstra Shortest path 3. Implement Dijkstra Shortest Path algorithm for any input graph. Implementation will be...
PYTHON ONLY Implement the Dijkstra’s Shortest path algorithm in Python. A graph with 10 nodes (Node 0 to node 9) must be implemented. You are supposed to denote the distance of the edges via an adjacency matrix (You can assume the edge weights are either 0 or a positive value). The adjacency matrix is supposed to be a 2-D array and it is to be inputted to the graph. Remember that the adjacency list denotes the edge values for the...
Please help me with this answer. Performance Comparison for Dijkstra Algorithm and Bellman-Ford Algorithm Problem Description The shortest path problem is one of most important problems in graph theory and computer science in general. Shortest path problem is one of typical optimization problems. Given a graph G = (V,E), the goal is to nd a minimum cost path from s → t, s,t ∈ V . This variant is called one-to-one shortest path problem. Other variants are one-to-all (compute shortest...
Consider the graph below. Use Dijkstra's algorithm to find the shortest path from vertex A to vertex F. Write your answer as a sequence of nodes separated by commas (no blank spaces) starting with the source node: _______ What's the weight of the shortest path? _______
Consider the graph below. Use Dijkstra's algorithm to find the shortest path from vertex A to vertex C. Write your answer as a sequence of nodes with no blank spaces or any separators in between, starting with the source node: What's the weight of the shortest path?
Wouldn't the Dijkstra algorithm visit the negative edge if the weights were changed as follows; A > B = 1, B > C = 2, A > D = 4? I assume that the algorithm goes as follows, Node A is known, shortest path is to Node B at weight 1, and then it goes to Node C because of the smallest weight being 3, and then it would visit Node D via the negative weighted edge. Dijkstra's Algorithm Shortest...
code Dijkstra's Algorithm for a directed graph example graph.txt: 0 (1,3) (3,5) 1 (2,6) 2 (4,2) 3 (1,1) (2,4) (4,6) 4 (0,3) (2,7) example dist.txt: 0 1 2 3 4 0 8 9 5 7 using a priority queue implemented as a heap. Input is from a file "graph.txt" which contains adjacency lists. Format of the file will be discussed in class. Source vertex is the first vertex in the list. Output is to the file "dist.txt" which contains the...
Implement Dijkstra's algorithm to find the shortest path from vertex O to all other vertices in the graph below. Use the adjacency list representation to store and use the graph in memory. Do not use any other representation Use vertex 'A' as your source vertex (begin the algorithm from A). Your output should be of the following format with the second column filled out. The distance from the source vertex (second column) is the sum of weights on the shortest...
Dijkstra’s Algorithm: You have to implement the Dijkstra’s algorithm and apply it on the graph provided below. You have to take the input from the user as an adjacency matrix representing the graph, the source, the destination. Then you have to apply the Dijkstra’s algorithm to find the shortest path from the source and the destination, and find the shortest route between the source and the destination. For the input you have to read it from a file. It will...
Dijkstra's single source shortest path algorithm when run from vertex a in the below graph, in what order do the nodes get included into the set of vertices for which the shortest path distances are finalized?
Find the shortest path algorithm tables (for the graph on the homework sheet) using the (a) Dijkstra algorithm (b) Ford-Fulkerson algorithm Label the columns B,C,D from left to right. Node A is the root node. Use pointers for only the Ford Fulkerson algorithm as in the Networks and Grids book. (c) Let the link number be bandwidth (data rate). Create the routing table that allows you find paths to the root node that maximize the bottleneck bandwidth Uhe