This document summarizes the steps of a breadth-first search (BFS) algorithm on a graph. It begins by adding the starting vertex 0 to a queue. It then repeatedly removes the first vertex from the queue, checks its unvisited neighbors, adds them to the queue and marks them as visited, until the queue is empty. This process traces each vertex at distance 1, then 2, and so on from the starting point.

1. 10
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
Graph g:
myG.txt
6
8
0 5
2 4
2 3
1 2
0 1
3 4
3 5
0 2
V
E
Adjacency lists
adj[]
0
1
2
3
4
5
2
3
3
0
5
1
0
3
1
2
4
2
2
0
5
0
1
2
5
3 4
4
Challenge: build adjacency lists – Job done

2. 11
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
add 0 to queue:
myG.txt
6
8
0 5
2 4
2 3
1 2
0 1
3 4
3 5
0 2
V
E
Adjacency lists
adj[]
0
1
2
3
4
5
2
3
3
0
5
1
0
3
1
2
4
2
2
0
5
0
1
2
5
3 4
4

3. 12
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
add 0 to queue:
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 - -
2 - -
3 - -
4 - -
5 - -
queue
0

4. 13
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 0: check2, check 1 and check 5
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 - -
2 0 1
3 - -
4 - -
5 - -
queue
0
2 1 5adj[0]

5. 14
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 0: check2, check 1 and check 5
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 - -
2 0 1
3 - -
4 - -
5 - -
queue
2 1 5adj[0]

6. 15
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 0: check2, check 1 and check 5
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 - -
2 0 1
3 - -
4 - -
5 - -
queue
2
2 1 5adj[0]

7. 16
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 0: check2, check 1 and check 5
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 - -
2 0 1
3 - -
4 - -
5 - -
queue
2
2 1 5adj[0]

8. 17
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 0: check2, check 1 and check 5
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 - -
4 - -
5 - -
queue
1
2
2 1 5adj[0]

9. 18
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 0: check2, check 1 and check 5
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 - -
4 - -
5 - -
queue
1
2
2 1 5adj[0]

10. 19
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 0: check2, check 1 and check 5
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 - -
4 - -
5 0 1
queue
5
1
2
2 1 5adj[0]

11. 20
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
0 done
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 - -
4 - -
5 0 1
queue
5
1
2
2 1 5adj[0]

12. 21
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 2:
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 - -
4 - -
5 0 1
queue
5
1
2

13. 22
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 2: check 0, check 1, check 3 and check 4
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 - -
4 - -
5 0 1
queue
5
1
adj[2] 0 1 3 4

14. 23
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 2: check 0, check 1, check 3 and check 4
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 - -
4 - -
5 0 1
queue
5
1
adj[2] 0 1 3 4

15. 24
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 2: check 0, check 1, check 3 and check 4
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 - -
5 0 1
queue
3
5
1
adj[2] 0 1 3 4

16. 25
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 2: check 0, check 1, check 3 and check 4
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 - -
5 0 1
queue
3
5
1
adj[2] 0 1 3 4

17. 26
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 2: check 0, check 1, check 3 and check 4
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 - -
5 0 1
queue
4
3
5
1
adj[2] 0 1 3 4

18. 27
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
2 done
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
5
1
adj[2] 0 1 3 4

19. 28
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 1
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
5
1

20. 29
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 1
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
5

21. 30
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 1: check 0, and check 2
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
5
adj[1] 0 2

22. 31
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 1: check 0, and check 2
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
5
adj[1] 0 2

23. 32
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 1: check 0, and check 2
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
5
adj[1] 0 2

24. 33
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
1 done
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
5
adj[1] 0 2

25. 34
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 5: check 3 and check 0
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
5
adj[5] 3 0

26. 35
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
5 done
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
adj[5] 3 0

27. 36
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 3: Check 5, Check 4, and Check 2
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3
adj[3] 5 4 2

28. 37
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 3:
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
3

29. 38
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 3: Check 5, Check 4, and Check 2
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
adj[3] 5 4 2

30. 39
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
3 done
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4
adj[3] 5 4 2

31. 40
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 4
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
4

32. 41
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
dequeue 4: Check 3 and Check 2
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue
adj[4] 3 2

33. 42
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
4 done
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1
queue

34. 43
Breadth-first search demo
Repeat until queue is empty:
• Remove vertex v from queue.
• Add to queue all unmarked vertices adjacent to v and mark them.
done
0
1
2
5
3 4
v edgeTo[v] distTo[]
0 - 0
1 0 1
2 0 1
3 2 2
4 2 2
5 0 1