(load "Graph2.lisp")
(in-package :cl-graph)

(defun dfs (graph root visited)
  (if (null visited) (setq visited (cons 'dummy nil)))
  (push root (cdr visited))
  (iterate-neighbors root #'(lambda (x)
			      (unless (find x visited)
				(dfs graph x visited))))
  (reverse (cdr visited)))

(defun ford-fulkerson (source sink)
  (let* ((cur-flow 0)
	 (graph (generate-graph)) ;; maybe make that global variable, so that it can be changed from other functions
	 (augm-path (find-augmented-path (find-residual-graph graph) source sink)))
    (while augm-path
      (send-flow graph augm-path (weight (find-min-edge-in-path)))
      (incf cur-flow (weight (find-min-edge-in-path)))
      (setf augm-path (find-augmented-path (find-residual-graph graph) source sink)))))

(defun find-residual-graph (graph)
)

(defun find-augmented-path (graph source sink)
;;remember to return nil if i didn't find any augmented path, otherwise the algorithm will not work
)

(defun send-flow (graph path flow)
)

(defun find-min-edge-in-path (path)
  (let ((cur-weight (weight (car path)))
	(cur-edge (car path)))
    (dotimes (i (length path))
      (if (< (weight (elt path i)) cur-weight)
	  (setf cur-weight (weight (elt path i))
		cur-edge (elt path i)))) ;;probably don't need to keep cur-edge
    cur-weight))