// the depth first search
// parameters:
// GraphWin gw: the window as reference
// graph g: the graph as a reference
// node v: current node
// int round: a flag to find out if v is a element of set 1 or set 2
// node_array<int> level: the level-node-relation
// node_array<int> free: stores whether node is free
// edge<int> matching: stores whether edge is matched
// node parent: the parent of v
// int current_matching: the current matching
int dfs(GraphWin &gw, graph &g, node &v, int round, node_array<int> &level, node_array<int> &free, edge_array<int> &matching, node &parent, int ¤t_matching) {
int next_round = round + 1;
int invert; // stores whether we should invert the path or not (boolean)
// current node is blue
gw.set_color(v, blue);
control_wait(WAIT);
// check all edges of v
edge e;
forall_inout_edges(e, v) {
node opposite_node = g.opposite(v, e);
// dont check parent node
if (opposite_node == parent) {
p("dont check parent");
continue;
}
gw.set_color(e, green);
control_wait(WAIT);
if ((round % 2) == 0) { // node v is from vertex set 1
if (matching[e] == 0) { // unmatched
if (level[opposite_node] == level[v] + 1) { // level must be greater 1
gw.set_color(e, blue);
gw.set_color(opposite_node, blue);
control_wait(WAIT);
// check for augmented path
if (free[opposite_node] == 1) {
level[opposite_node] = -1;
gw.set_color(opposite_node, blue);
gw.set_user_label(opposite_node, string("%d", level[opposite_node]));
level[v] = -1;
gw.set_user_label(v, string("%d", level[v]));
// invert path
if (matching[e] == 0) {
gw.set_color(e, blue);
free[opposite_node] = 0;
gw.set_border_width(opposite_node, 1);
free[v] = 0;
gw.set_width(e, 10);
gw.set_border_width(v, 1);
matching[e] = 1;
current_matching++;
} else {
matching[e] = 0;
gw.set_width(e, 2);
current_matching--;
}
control_wait(WAIT);
return 1;
} else { // no augmented path yet
// call dfs for next node
invert = dfs(gw, g, opposite_node, next_round, level, free, matching, v, current_matching);
if (invert == 1) { // invert path
if (matching[e] == 0) {
free[opposite_node] = 0;
gw.set_border_width(opposite_node, 1);
gw.set_width(e, 10);
free[v] = 0;
gw.set_border_width(v, 1);
matching[e] = 1;
current_matching++;
} else {
gw.set_width(e, 1);
matching[e] = 0;
current_matching--;
}
level[v] = -1;
gw.set_user_label(v, string("%d", level[v]));
control_wait(WAIT);
return 1;
}
}
}
}
} else { // v is a element of vertex set 2
if (matching[e] == 1) { // matched
if (level[opposite_node] == level[v] + 1) { // level must be greater 1
gw.set_color(e, blue);
gw.set_color(opposite_node, blue);
control_wait(WAIT);
// call dfs for opposite_node
invert = dfs(gw, g, opposite_node, next_round, level, free, matching, v, current_matching); }
if (invert == 1) {
// invert path
if (matching[e] == 0) {
free[opposite_node] = 0;
gw.set_border_width(opposite_node, 5);
free[v] = 0;
gw.set_border_width(v, 10);
gw.set_width(e, 5);
matching[e] = 1;
current_matching++;
} else {
matching[e] = 0;
gw.set_width(e, 1);
current_matching--;
}
level[v] = -1;
gw.set_user_label(v, string("%d", level[v]));
control_wait(WAIT);
return 1;
}
}
}
}
// iterative function to conduct breadth-first-search (bfs);
// parameters:
// v: current node
// g: graph to be searched in (as reference)
// gw: Diplaying window of graph (as reference)
// height: Node array with all heights
// distance: distance from starting node
// flow: Edge array with all preflows
// capacity: Edge array with all capacities
void bfs(node v, graph &g, GraphWin &gw, node_array<int> &height, int &distance, edge_array<double> &flow, edge_array<double> &capacity) {
gw.message("start with a bfs to determine the height");
queue<node> fifo_queue; // queue for next bfs node
fifo_queue.push(v); // add the starting node
//gw.set_user_label(v, string("%d (%d)", distance, height[v])); // Display bfs number
//gw.set_color(v, red); // Color node in red
//gw.redraw(); // Update displayed graph
//control_wait(WAIT); // Wait for 0.5 sec
distance++;
// loop through all queue elements and add all childs to queue
// also add some graphical hints
do {
v = fifo_queue.pop(); // pop first element of search queue
//gw.set_color(v, green); // current node of queue, mark it green
//control_wait(WAIT); // Wait for 0.5sec
edge e;
forall_in_edges(e, v) { // all neighbour nodes of v
if (flow[e] != capacity[e]) {
node w = g.opposite(v, e); // neighbour node on the other side of edge e
if (height[w] < 0) { // if node w has not been visited yet
height[w] = height[v]+1; // assign to current node last assigned bfs number incremented by one
//gw.set_color(e, red); // color edge in red
//gw.set_color(w, red); // color node in red
//gw.set_width(e, 2);
//gw.set_user_label(w, string("%d (%d)", distance++, height[w])); // display order first, in brackets distance to starting node
fifo_queue.append(w); // add the child node to the queue
//control_wait(WAIT); // Wait for 0.5 sec
} else { // if node w has already been visited
if (height[w] < height[v]) { // Backward edge
//if (gw.get_color(e) == red){ // check, if edge is the connection between parent and child node
// gw.set_color(e, blue); // color edge in blue
//gw.set_width(e, 2);
//control_wait(WAIT); // wait for 0.5 sec
//} else {
// gw.set_color(e, green);
//}
} else { // edge to a node in queue
//gw.set_color(e, green); // color edge
//gw.set_width(e, 2);
//control_wait(WAIT); // wait for 0.5 sec
}
}
} else {
//gw.set_color(e, violet);
//control_wait(WAIT);
}
}
//gw.set_color(v, blue); // Color node in blue
//control_wait(WAIT); // wait for 0.5 sec
//gw.redraw();
// Update displayed graph (to ensure correct updation)
} while (!fifo_queue.empty()); // loop until queue is empty
}
