// do a DFS traversal from all nodes
//
// nodes     = list of all nodes from G
// adj[node] = the adjacency list of node
//              example: adj[node] = {..., neigh, ...} => edge (node, neigh)
//
DFS(G=(nodes, adj)) {
    // STEP 0: initialize results
    // p[node]     = parent of node in the BFS traversal started from source
    // start[node] = the timestamp (the order) when we started visiting the node subtree
    // finish[node] = the timestamp (the order) when we finished visiting the node subtree
    // [optional] color[node] = white/gray/black
    //                              * white = not yet visited
    //                              * gray  = visit in progress
    //                              * black = visited
    foreach (node in nodes) {
        p[node] = null;                             // parent not yet found
        // [optional] color[node] = white;
    }

    timestamp = 0;                                  // the first timestamp before the DFS traversal

    foreach (node in nodes) {
        if (p[node] == null) {                      // or [optional] color[node] == white
            DFS_RECURSIVE(node, G, p, timestamp)
        }
    }
}

DFS_RECURSIVE(node, G=(node, adj), p, ref timestamp) {
    start[node] = ++timestamp;                      // start visiting its subtree
    // [optional] color[node] = gray;

    for (neigh in adj[node]) {                      // for each neighbour
        if (p[neigh] == null) {                     // or [optional] color[neigh] = white;
            p[neigh] = node;                        // save parent
            DFS_RECURSIVE(neigh, G, p, timestamp);  // continue traversal
        }
    }

    finish[node] = ++timestamp;                     // finish visiting its subtree
    // [optional] color[node] = black;
}