Depth-First Search D B A C E Depth-First Search Depth-First Search 2/19/2019 6:58 AM Depth-First Search D B A C E Depth-First Search

Depth-First Search Depth-first search (DFS) is a general technique for traversing a graph Similar to Pre-order traversal of a tree “children” -> neighbors level -> number of edges away from starting vertex Not to visit the same vertex more than once Depth-First Search

Depth-first Search Algorithm DFS(G, v) visit v setLabel(v, VISITED) neighbors  getAdjacentVertices(G, v) for each w  neighbors if getLabel(w) != VISITED // “children” DFS(G, w) Depth-First Search

Depth-first Search The book uses an iterative algorithm same as BFS Algorithm DFS(G, v) visit v setLabel(v, VISITED) neighbors  getAdjacentVertices(G, v) for each w  neighbors if getLabel(w) != VISITED // “children” DFS(G, w) The book uses an iterative algorithm same as BFS the DFS alg. uses a stack instead of a queue as the container C With recursion, we don’t need to manipulate a stack. Depth-First Search

Example unexplored vertex visited vertex unexplored edge B A C E A A visited vertex unexplored edge discovery edge back edge D B A C E D B A C E Depth-First Search

Example (cont.) D B A C E D B A C E D B A C E D B A C E Depth-First Search

Analysis of DFS Setting/getting a vertex/edge label takes O(1) time Each vertex is labeled twice once as UNEXPLORED once as VISITED O(n) getAdjacentVertices() is called once for each vertex Each edge in the graph is used as most twice Each edge has two vertices O(m) DFS runs in O(n + m) time provided the graph is represented by the adjacency list structure [less precisely, since m is O(n2), BFS is also O(n2)] Depth-First Search

Properties of DFS Property 1 Property 2 DFS(G, v) visits all the vertices and edges in the connected component of v Property 2 The discovery edges labeled by DFS(G, v) form a spanning tree of the connected component of v D B A C E Depth-First Search