Phoenix Holmes - 1 month ago 24

C++ Question

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;

for (i = adj[u].begin(); i != adj[u].end(); ++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.

Answer

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");
}
```