Phoenix Holmes - 1 year ago 81
C++ Question

Shortest route modification

Is there a way to modify this to show the route of the shortest path? For example, if i had a list of numbers like (3,1),(3,0),(4,3),(2,1) the output for getting from 4 to 1 would be 4->3,3->1

``````// Prints shortest paths from src to all other vertices
void Graph::shortestPath(int src)
{
// Create a priority queue to store vertices that
// are being preprocessed. This is weird syntax in C++.
// Refer below link for details of this syntax
// http://geeksquiz.com/implement-min-heap-using-stl/
priority_queue< iPair, vector <iPair> , greater<iPair> > pq;

// Create a vector for distances and initialize all
// distances as infinite (INF)
vector<int> dist(V, INF);

// Insert source itself in priority queue and initialize
// its distance as 0.
pq.push(make_pair(0, src));
dist[src] = 0;

/* Looping till priority queue becomes empty (or all
distances are not finalized) */
while (!pq.empty())
{
// The first vertex in pair is the minimum distance
// vertex, extract it from priority queue.
// vertex label is stored in second of pair (it
// has to be done this way to keep the vertices
// sorted distance (distance must be first item
// in pair)
int u = pq.top().second;
pq.pop();

// 'i' is used to get all adjacent vertices of a vertex
list< pair<int, int> >::iterator i;
{
// Get vertex label and weight of current adjacent
// of u.
int v = (*i).first;
int weight = (*i).second;

//  If there is shorted path to v through u.
if (dist[v] > dist[u] + weight)
{
// Updating distance of v
dist[v] = dist[u] + weight;
pq.push(make_pair(dist[v], v));
}
}
}

// Print shortest distances stored in dist[]
printf("Vertex   Distance from Source\n");
for (int i = 0; i < V; ++i)
printf("%d \t\t %d\n", i, dist[i]);
}
``````

Putting in an array that stores the numbers of the path like 4,3,3,1 (using above example) seems like the best idea but i don't know where to insert the array in this code to do that.

Just as you save the distances for each vertex in the `dist` vector, save the predecessor vertex that last updated it in a vector called `predecessor`.

``````vector<int> dist(V, INF);
vector<int> predecessor(V, 0);
``````

Then whenever you update the distance, update the predecessor:

``````dist[v] = dist[u] + weight;
predecessor[v] = u;
``````

Finally, you can trace for any vertex the shortest path (Backward) to the source:

``````printf("Vertex   Distance from Source      shortest path from source\n");
for (int i = 0; i < V; ++i)
{
printf("%d \t\t %d\t\t", i, dist[i]);
int j = i;
do
{
printf("%d,", j);
j = predecessor[j];
} while(j != src);
printf("\n");
}
``````
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