Breath First Searching & Depth First Searching

1. Breath First Searching & Depth First Searching C and Data Structures Baojian Hua bjhua@ustc.edu.cn

2. Searching • The systematic way to traverse all vertex in a graph • Two general methods: • breath first searching (BFS) • start from one vertex, first visit all the adjacency vertices • depth first searching (DFS) • eager method • These slides assume the adjacency list representation

3. Sample Graph 1 2 3 4 5 6

4. “graph” ADT in C: Interface // in file “graph.h” #ifndef GRAPH_H #define GRAPH_H typedef void (*tyVisitFn)(poly); typedef struct graph *graph; graph new (); void insertVertex (graph g, poly x); void insertEdge (graph g, poly from, poly to); void bfs (graph g, poly start, tyVisitFn visit); void dfs (graph g, poly start, tyVisitFn visit); // we’d see more later … #endif

5. Sample Graph BFS bfs (g, 1, natOutput); 1 2 3 4 5 6

6. Sample Graph BFS bfs (g, 1, natOutput); print 1; 1 2 3 4 5 6

7. Sample Graph BFS bfs (g, 1, natOutput); print 1; print 2; (choice) 1 2 3 4 5 6

8. Sample Graph BFS bfs (g, 1, natOutput); print 1; print 2; print 4; 1 2 3 4 5 6

9. Sample Graph BFS bfs (g, 1, natOutput); print 1; print 2; print 4; print 5; 1 2 3 4 5 6

10. Sample Graph BFS bfs (g, 1, natOutput); print 1; print 2; print 4; print 5; print 3; 1 2 3 4 5 6

11. Sample Graph BFS bfs (g, 1, natOutput); print 1; print 2; print 4; print 5; print 3; print 6; 1 2 3 4 5 6

12. Moral • BFS is very much like the level-order traversal on trees • Maintain internally a queue to control the visit order • Obtain a BFS forest when finished

13. Sample Graph DFS dfs (g, 1, natOutput); 1 2 3 4 5 6

14. Sample Graph DFS dfs (g, 1, natOutput); print 1; 1 2 3 4 5 6

15. Sample Graph DFS dfs (g, 1, natOutput); print 1; print 2; (choice) 1 2 3 4 5 6

16. Sample Graph DFS dfs (g, 1, natOutput); print 1; print 2; (choice) print 5; 1 2 3 4 5 6

17. Sample Graph DFS dfs (g, 1, natOutput); print 1; print 2; (choice) print 5; print 4; 1 2 3 4 5 6

18. Sample Graph DFS dfs (g, 1, natOutput); print 1; print 2; (choice) print 5; print 4; print 3; (choice) 1 2 3 4 5 6

19. Sample Graph DFS dfs (g, 1, natOutput); print 1; print 2; (choice) print 5; print 4; print 3; (choice) print 6; 1 2 3 4 5 6

20. Moral • DFS is very much like the pre-order traversal on trees • Maintain internally a stack to control the visit order • for recursion function, machine maintain the stack • Obtain a DFS forest when finished