// do a BFS traversal from source
//
// source    = the source for the BFS traversal
// nodes     = list of all nodes from G
// adj[node] = the adjacency list of node
//             example: adj[node] = {..., neigh, ...} => edge (node, neigh)
BFS(source, G=(nodes, adj)) {
    // STEP 0: initialize results
    // d[node] = distance from source to node
    // p[node] = parent of node in the BFS traversal started from source
    // [optional] color[node] = white/gray/black
    //                              * white = not yet visited
    //                              * gray  = visit in progress
    //                              * black = visited
    foreach (node in nodes) {
        d[node] = +oo;                          // distance not yet computed
        p(node) = null;                         // parent not yet found
        // [optional] color[node] = white;
    }

    // STEP 1: initialize a queue
    q = {}

    // STEP 2: add the source(s) into q
    d[source] = 0;                              // distance from source to source
    p[source] = null;                           // the source never has a parent (because it's the root of the traversal)
    q.push(source);
    // [optional] color[source] = gray;

    // STEP 3: start traversal using the node(s) from q
    while (!q.empty()) {                        // while still have nodes to explore
        // STEP 3.1: extract the next node from queue
        node = q.pop();

        // [optional] STEP 3.2: print/use the node

        // STEP 3.3: expand/visit the node
        foreach (neigh in adj[node]) {          // for each neighbour
            if (d[node] + 1 < d[neigh]) {       // a smaller distance <=> color[neigh] == white
                d[neigh] = d[node] + 1;         // update distance
                p[neigh] = node;                // save parent
                q.push(neigh);                  // add neigh to the queue of nodes to be visited
                // [optional] color[neigh] = gray;
            }
        }
        
       // [optional] color[node] = black;
    }
}