Daniel@0: function [d, pre, post, cycle, f, pred] = dfs(adj_mat, start, directed)
Daniel@0: % DFS Perform a depth-first search of the graph starting from 'start'.
Daniel@0: % [d, pre, post, cycle, f, pred] = dfs(adj_mat, start, directed)
Daniel@0: %
Daniel@0: % Input:
Daniel@0: % adj_mat(i,j)=1 iff i is connected to j.
Daniel@0: % start is the root vertex of the dfs tree; if [], all nodes are searched
Daniel@0: % directed = 1 if the graph is directed
Daniel@0: %
Daniel@0: % Output:
Daniel@0: % d(i) is the time at which node i is first discovered.
Daniel@0: % pre is a list of the nodes in the order in which they are first encountered (opened).
Daniel@0: % post is a list of the nodes in the order in which they are last encountered (closed).
Daniel@0: % 'cycle' is true iff a (directed) cycle is found.
Daniel@0: % f(i) is the time at which node i is finished.
Daniel@0: % pred(i) is the predecessor of i in the dfs tree.
Daniel@0: %
Daniel@0: % If the graph is a tree, preorder is parents before children,
Daniel@0: % and postorder is children before parents.
Daniel@0: % For a DAG, topological order = reverse(postorder).
Daniel@0: %
Daniel@0: % See Cormen, Leiserson and Rivest, "An intro. to algorithms" 1994, p478.
Daniel@0: 
Daniel@0: n = length(adj_mat);
Daniel@0: 
Daniel@0: global white gray black color
Daniel@0: white = 0; gray = 1; black = 2;
Daniel@0: color = white*ones(1,n);
Daniel@0: 
Daniel@0: global time_stamp
Daniel@0: time_stamp = 0;
Daniel@0: 
Daniel@0: global d f
Daniel@0: d = zeros(1,n);
Daniel@0: f = zeros(1,n);
Daniel@0: 
Daniel@0: global pred
Daniel@0: pred = zeros(1,n);
Daniel@0: 
Daniel@0: global cycle
Daniel@0: cycle = 0;
Daniel@0: 
Daniel@0: global pre post
Daniel@0: pre = [];
Daniel@0: post = [];
Daniel@0: 
Daniel@0: if ~isempty(start)
Daniel@0:   dfs_visit(start, adj_mat, directed);
Daniel@0: end
Daniel@0: for u=1:n
Daniel@0:   if color(u)==white
Daniel@0:     dfs_visit(u, adj_mat, directed);
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: 
Daniel@0: %%%%%%%%%%
Daniel@0: 
Daniel@0: function dfs_visit(u, adj_mat, directed)
Daniel@0: 
Daniel@0: global white gray black color time_stamp d f pred cycle  pre post
Daniel@0: 
Daniel@0: pre = [pre u];
Daniel@0: color(u) = gray;
Daniel@0: time_stamp = time_stamp + 1;
Daniel@0: d(u) = time_stamp;
Daniel@0: if directed
Daniel@0:   ns = children(adj_mat, u);
Daniel@0: else
Daniel@0:   ns = neighbors(adj_mat, u);
Daniel@0:   ns = setdiff(ns, pred(u)); % don't go back to visit the guy who called you!
Daniel@0: end
Daniel@0: for v=ns(:)'
Daniel@0:   %fprintf('u=%d, v=%d, color(v)=%d\n', u, v, color(v))
Daniel@0:   switch color(v)
Daniel@0:     case white, % not visited v before (tree edge)
Daniel@0:      pred(v)=u;
Daniel@0:      dfs_visit(v, adj_mat, directed);
Daniel@0:    case gray, % back edge - v has been visited, but is still open
Daniel@0:     cycle = 1;
Daniel@0:     %fprintf('cycle: back edge from v=%d to u=%d\n', v, u);
Daniel@0:    case black, % v has been visited, but is closed
Daniel@0:     % no-op
Daniel@0:   end
Daniel@0: end
Daniel@0: color(u) = black;
Daniel@0: post = [post u];
Daniel@0: time_stamp = time_stamp + 1;
Daniel@0: f(u) = time_stamp;
Daniel@0: 
Daniel@0: