## graph-dfs

Depth-first search in a graph.

## Documentation

The graph-dfs library is an implementation of depth-first search on a graph object that follows the API of the digraph egg.

### Depth-first-search procedures

*[procedure]*

`foreach:: G FNODE FEDGE ROOTS -> UNDEFINED`

Depth-first search iterator; given a list of initial nodes, `ROOTS`, the successors of each initial node are visited in depth-first search order, and procedures `FNODE` and `FEDGE` are applied to each node or edge, respectively, as the graph is traversed. `FNODE` is of the form `LAMBDA N -> _` where `N` is node number; and `FEDGE` is of the form `LAMBDA EDGE` where `EDGE` is a list of the form `(I J INFO)`; `I` and `J` are the nodes defining the edge, and `INFO` is edge metadata.

*[procedure]*

`fold:: G FNODE FEDGE ROOTS NODE-INIT EDGE-INIT -> NODE-STATE EDGE-STATE`

Depth-first search iterator with state; given a list of initial nodes, `ROOTS`, and initial node state and edge state, `NODE-INIT` and `EDGE-INIT` the successors of each initial node are visited in depth-first search order, and procedures `FNODE` and `FEDGE` are applied to each node and the node state, or edge and the edge state, respectively, as the graph is traversed. `FNODE` is of the form `LAMBDA N NODE-STATE -> NODE-STATE` where `N` is node number, and NODE-STATE can be of arbitrary type and must of the same type as `NODE-INIT`. `FEDGE` is of the form `LAMBDA EDGE EDGE-STATE` where `EDGE` is a list of the form `(I J INFO)`; `I` and `J` are the nodes defining the edge, and `INFO` is edge metadata; `EDGE-STATE` must be of the same type as `EDGE-INIT`

*[procedure]*

`depth:: G ROOTS -> NODE-DEPTH TRAVERSAL-TIME`

Depth-first search depth; given a list of initial nodes, this procedure computes shortest DFS depth for each nodes traversed, and the number of nodes visited while traversing the successors of each node. `NODE-DEPTH` is an array that contains the corresponding DFS depth for each node; `TRAVERSAL-TIME` is also an array, where each value is the number of nodes visited in the sub-graph of that node.

*[procedure]*

`preorder:: G ROOT -> ((NODE NUM) ... )`

Computes the preorder traversal sequence number for each successor of the given initial node.

*[procedure]*

`postorder:: G ROOT -> ((NODE NUM) ... )`

Computes the postorder traversal sequence number for each successor of the given initial node.

## Examples

;; example adapted from graph example in the Boost library documentation (import srfi-1 digraph graph-dfs) (define g (make-digraph 'depgraph "dependency graph")) (define used-by (list (cons 'dax_h 'foo_cpp) (cons 'dax_h 'bar_cpp) (cons 'dax_h 'yow_h) (cons 'yow_h 'bar_cpp) (cons 'yow_h 'zag_cpp) (cons 'boz_h 'bar_cpp) (cons 'boz_h 'zig_cpp) (cons 'boz_h 'zag_cpp) (cons 'zow_h 'foo_cpp) (cons 'foo_cpp 'foo_o) (cons 'foo_o 'libfoobar_a) (cons 'bar_cpp 'bar_o) (cons 'bar_o 'libfoobar_a) (cons 'libfoobar_a 'libzigzag_a) (cons 'zig_cpp 'zig_o) (cons 'zig_o 'libzigzag_a) (cons 'zag_cpp 'zag_o) (cons 'zag_o 'libzigzag_a) (cons 'libzigzag_a 'killerapp))) (define node-list (delete-duplicates (concatenate (list (map car used-by) (map cdr used-by))))) (define node-ids (list-tabulate (length node-list) values)) (for-each (lambda (i n) (add-node! g i n)) node-ids node-list) (define node-map (zip node-list node-ids)) (for-each (lambda (e) (match e ((ni . nj) (let ((i (car (alist-ref ni node-map))) (j (car (alist-ref nj node-map)))) (add-edge! g (list i j (format "~A->~A" ni nj))))) (else (error "invalid edge " e)))) used-by) (define roots (map car (roots g))) (foreach g (lambda (n) (print (format "node ~A; " n))) (lambda (e) (print (format "edge ~A; " e))) roots) (fold g (lambda (n ax) (cons (list 'node n) ax)) (lambda (e ax) (cons (list 'edge e) ax)) roots (list) (list))

## About this egg

### Author

### Version history

- 2.0
- Ported to CHICKEN 5 and yasos-based graph interface
- 1.11
- Ensure test script returns proper exit code
- 1.9
- Documentation converted to wiki format
- 1.8
- Ported to Chicken 4
- 1.7
- Now using matchable extension
- 1.6
- Unit tests updated to use testbase
- 1.5
- Build script updated for better cross-platform compatibility
- 1.4
- eggdoc documentation fix
- 1.3
- License upgrade to GPL v3
- 1.2
- Added support for chicken-setup -test
- 1.1
- Fixed a syntactic error in graph-dfs-fold
- 1.0
- Initial release

### License

Copyright 2007-2018 Ivan Raikov This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. A full copy of the GPL license can be found at <http://www.gnu.org/licenses/>.