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CS245-2009S-
BFS & DFS 1
16-0: Graph Traversals
- Visit every vertex, in an order defined by the topololgy of the graph.
- Two major traversals:
- Depth First Search
- Breadth First Search
16-1: Depth First Search
- Starting from a specific node (pseudo-code):
DFS(Edge G[], int vertex, boolean Visited[]) { Visited[vertex] = true; for each node w adajcent to vertex: if (!Visited[w]) DFS(G, w, Visited); }
16-2: Depth First Search
class Edge { public int neighbor; public int next; }
void DFS(Edge G[], int vertex, boolean Visited[]) { Edge tmp; Visited[vertex] = true; for (tmp = G[vertex]; tmp != null; tmp = tmp.next) { if (!Visited[tmp.neighbor]) DFS(G, tmp.neighbor, Visited); } }
16-3: Depth First Search
- Example
- Visited nodes cicrled in red
16-4: Depth First Search
CS245-2009S-
BFS & DFS 2
- Example
- Visited nodes cicrled in red
DFS(0)
16-5: Depth First Search
- Example
- Visited nodes cicrled in red
DFS(0)
DFS(1)
16-6: Depth First Search
- Example
- Visited nodes cicrled in red
DFS(0)
DFS(1)
DFS(3)
16-7: Depth First Search
CS245-2009S-
BFS & DFS 4
- Example
- Visited nodes cicrled in red
DFS(0)
DFS(1)
DFS(3)
DFS(4)
DFS(2)
DFS(5)
DFS(6)
16-11: Depth First Search
- To visit every node in the graph:
TraverseDFS(Edge G[]) { int i; boolean Visited = new Edge[G.length]; for (i=0; i<G.length; i++) Visited[i] = false; for (i=0; i<G.length; i++) if (!Visited[i]) DFS(G, i, Visited); }
16-12: Depth First Search
16-13: Depth First Search
CS245-2009S-
BFS & DFS 5
16-14: DFS & Stacks
- Keep track of what nodes we have left using a stack
- Recursive version implicitly uses the system stack
- Can write DFS non-recursively, using our own stack
16-15: DFS & Stacks
void DFS(Edge G[], int vertex, boolean Visited[]) { Edge tmp; Visited[vertex] = true; for (tmp = G[vertex]; tmp != null; tmp = tmp.next) { if (!Visited[tmp.neighbor]) DFS(G, tmp.neighbor, Visited); } }
16-16: DFS & Stacks
void DFS(Edge G[], int vertex, boolean Visited[]) { Edge tmp; int nextV; Stack S = new Stack(); S.push(new Integer(vertex)); while (!S.empty()) { nextV = ((Integer) S.pop()).intValue(); if (!Visited[nextV]) { Visited[nextV] = true; for (tmp = G[nextV]; tmp != null; tmp = tmp.next) { S.push(new Integer(tmp.neighbor)); }} } }
16-17: Breadth First Search
- DFS: Look as Deep as possible, before looking wide
- Examine all descendants of a node, before looking at siblings
- BFS: Look as Wide as possible, before looking deep
- Visit all nodes 1 away, then 2 away, then three away, and so on
CS245-2009S-
BFS & DFS 7
Queue: 0
16-22: Breadth First Search
Queue: 124
16-23: Breadth First Search
Queue: 24034
16-24: Breadth First Search
CS245-2009S-
BFS & DFS 8
Queue: 4034056
16-25: Breadth First Search
Queue: 034056013
16-26: Breadth First Search
Queue: 34056013
16-27: Breadth First Search
CS245-2009S-
BFS & DFS 10
Queue: 60131426
16-31: Breadth First Search
Queue: 013142625
16-32: Breadth First Search
- Alternate version of BFS
- Previous code marks nodes as VISITED as they are removed from the queue
- We could also mark nodes as VISITED when they are placed on the queue
16-33: Breadth First Search
- Coding BFS (Alternate version):
void BFS(Edge G[], int vertex, boolean Visited[]) { Edge tmp; int nextV; Queue Q = new Queue(); Viisited[vertex] = true; Q.enquque(new Integer(vertex)); while (!Q.empty()) { nextV = ((Integer) Q.dequeue()).intValue(); for (tmp = G[nextV]; tmp != null; tmp = tmp.next) { if (!Visited[tmp.neighbor]) { Visited[tmp.neighbor] = true; Q.enqueue(new Integer(tmp.neighbor)); } } } }
16-34: Breadth First Search
CS245-2009S-
BFS & DFS 11
- Alternate version of BFS
- Previous code marks nodes as VISITED as they are removed from the queue
- We could also mark nodes as VISITED when they are placed on the queue
- How does execution differ?
16-35: Breadth First Search
- Alternate version of BFS
- Previous code marks nodes as VISITED as they are removed from the queue
- We could also mark nodes as VISITED when they are placed on the queue
- How does execution differ?
- How does execution differ?
- Version I: A vertex is added to the queue for each edge in the graph (so the same vertex can be added to the queue more than once
- Version II: Each vertex is added to the queue at most once
16-36: Breadth First Search
16-37: Breadth First Search
Queue: 0
CS245-2009S-
BFS & DFS 13
Queue: 356
16-42: Breadth First Search
Queue: 56
16-43: Breadth First Search
Queue: 6
16-44: Breadth First Search
CS245-2009S-
BFS & DFS 14
Queue:
16-45: Search Trees
- Describes the order that nodes are examined in a traversal
- Directed Tree
- Directed edge from v 1 to v 2 if the edge (v 1 , v 2 ) was followed during the traversal
16-46: DFS Search Trees
- Starting from node 0, adjacency list sorted by vertex number:
16-47: DFS Search Trees
- Starting from node 0, adjacency list sorted by vertex number:
CS245-2009S-
BFS & DFS 16
16-51: DFS Search Trees
- Starting from node 2, adjacency list sorted by vertex number:
16-52: DFS Search Trees
- Starting from node 0, adjacency list sorted by vertex number:
16-53: DFS Search Trees
- Starting from node 0, adjacency list sorted by vertex number:
CS245-2009S-
BFS & DFS 17
16-54: DFS Search Trees
- Starting from node 2, adjacency list sorted by vertex number:
16-55: DFS Search Trees
- Starting from node 2, adjacency list sorted by vertex number:
16-56: BFS Search Trees
- Starting from node 0, adjacency list sorted by vertex number:
CS245-2009S-
BFS & DFS 19
16-60: DFS in Directed Graphs
- Starting from node 0, adjacency list sorted by vertex number:
16-61: DFS in Directed Graphs
- Starting from node 0, adjacency list sorted by vertex number:
